example-1Multiple choice
The range of the data 14, 6, 12, 17, 21, 10, 4, 3 is
- (a)21
- (b)17
- (c)18
- (d)11
Show solution
Solution: Correct answer is (c)
Chapter 3
Class 7 Mathematics · 90 questions · 83 with answers
Solved examples
example-2Multiple choice
The mode of the data 23, 26, 22, 29, 23, 29, 26, 29, 22, 23 is
- (a)23 and 29
- (b)23 only
- (c)29 only
- (d)26 only
Show solution
Solution: Correct answer is (a)
example-3Multiple choice
The median of the data 40, 50, 99, 68, 98, 60, 94 is
- (a)40
- (b)60
- (c)68
- (d)99
Show solution
Solution: Correct answer is (c) In Examples 4 and 5, fill in the blanks to make the statements true.
example-4Fill in the blanks
The mean of first five prime numbers is __________.
Show solution
Solution: 5.6 [Hint : First five prime numbers are 2, 3, 5, 7 and 11]
example-5Fill in the blanks
The probability of getting a number greater than 2 on throwing a die once is _________.
Show solution
Solution: 15-04-2018 In Examples 6, 7 and 8, state whether the statements are True or False .
example-6Short answer
The mode of the observations 23, 26, 15, 12, 28, 38, 19, 23, 26, 23 is 28.
Show solution
Solution: False.
example-7Multiple choice
Size of Sweater Number of Sweaters Sold 40 15 42 17 44 13 46 14 48 11 Total 70 In the above table
- (a)The most popular size is 17.
- (b)17 is the median for above data.
Show solution
Solution: (a) False (The numbers of sweater 17 tells us that 42 is the most common size. Thus, 17 is not mode rather 42 is mode.) (b) False
example-8Short answer
Median of the data: 4, 5, 9, 2, 6, 8, 7 is 2
Show solution
Solution: False
example-9Short answer
Find the median of the data: 3, 11, 7, 2, 5, 9, 9, 2, 10, 15, 7
Show solution
Solution: Arranging in ascending order. 2, 2, 3, 5, 7, 7, 9, 9, 10, 11, 15 Since number of observations is odd, the middle most value is the median. The middle most value is 7, so median is 7. 15-04-2018 Example10: Find the median of the data : 21, 15, 6, 25, 18, 13, 20, 9, 8, 12 Solution: Arranging in ascending order : 6, 8, 9, 12, 13, 15, 18, 20, 21, 25 Since number of observations is even, the median is given by finding the average or mean of the two middle most observations: 13 +15 28 So, median = = = 14 2 2 Note : In this data, there are two middle most terms 13 and 15. So, median is the average of these observations.
example-11Multiple choice
The cards bearing letters of the word “MATHEMATICS” are placed in a bag. A card is taken out from the bag without looking into the bag (at random). (a) How many outcomes are possible when a letter is taken out of the bag at random? (b) What is the probability of getting
- (i)M?
- (ii)Any vowel?
- (iii)Any consonant?
- (iv)X?
Show solution
Solution: (a) There are 11 outcomes namely M, M, A, A, T, T, H, E, I, C, S. (b) (i) Probability of getting ‘M’ = (ii) Probability of getting a vowel = (iii) Probability of getting a consonant = (iv) Probability of getting X = 0 = 15-04-2018
example-12Short answer
If the mean of 26, 28, 25, x, 24 is 27, find the value of x. Sum of all observations
Show solution
Solution: Mean = Number of observations 26 + 28 + 25 + x + 24 or, 27= 103 + x or, 27 = or, 135 = 103 + x or, x = 135 – 103 So, x = 32
example-13Short answer
The mean of 10 observations was calculated as 40. It was detected on rechecking that the value of 45 was wrongly copied as 15. Find the correct mean. Sum of all observations
Show solution
Solution: Mean = Number of observations Sum of all observations or, 40 = So, sum of all observations = 400 But this is incorrect sum, since one observation was copied wrongly. So, correct sum = Incorrect sum – Incorrect observation + correct observation = 400 – 15 + 45 = 430 Correct Sum 430 Correct Mean = = = 43 Number of observations 10
example-14Short answer
The median of observations 11, 12, 14, 18, x + 2, 20, 22, 25, 61 arranged in ascending order is 21. Find the value of x.
Show solution
Solution: Median from data = x + 2 or, 21 = x + 2 or, x = 21 – 2 or, x = 19 15-04-2018
example-15Multiple choice
Study the double bar graph given below and answer the questions that follow: Fig. 3.1
- (a)What information does the above double graph depict?
- (b)Name the fruits for which cost of 1 kg is greater in City I as compared to City II.
- (c)What is the difference of rates for apples in both the cities?
- (d)Find the ratio of the cost of mangoes per kg in City I to the cost of mangoes per kg in City II.
Show solution
Solution: (a) The double bar graph compares the cost of different fruits per kg in Cities I and II. (b) Apple, Banana, Mango and Cherry. (c) Since 82 – 75 = 7 therefore, in both the cities the difference of rates of apples is 7/kg. (d) 75 : 60 = 5 : 4 15-04-2018
example-16Multiple choice
The following double bar graph represents test matches results summary for Cricket Team of country X against different countries: Fig. 3.2 Use the bar graph to answer the following questions:
- (a)Which country has managed maximum wins against country X?
- (b)The difference between the number of matches won and lost is highest for which country against country X?
- (c)Number of wins of country E is the same as number of losses of which country against country X?
Show solution
Solution: (a) Country B (b) Country G (c) Country F 15-04-2018
example-17Short answer
The double bar graph given below compares the class-averages in half yearly and annual examinations of 5 sections of Class VII. Observe the graph carefully and tell which section showed the most improvement and by how much?
Show solution
Solution: Understand and Explore the Problem • What information is given in the question? The average result of half yearly and annual examinations of 5 different sections of Class VII are compared. • What are you trying to find? The section of Class VII that has showed the most improvement and the per cent of improvement shown. Plan a Strategy • Observe the graph and find out the sections in which the annual examination result is more than the half yearly result. Improvement is in these sections only. 15-04-2018 • Then only for these sections, compare the results graphically and locate the section for which the difference of results is the maximum. • For this section, find the difference of the results. Solve • The sections in which the results of annual examination is more than half yearly examination are sections A, B and D. • Observing the graph of these sections we locate that section A has the maximum difference between the results. The difference of results of section A = 75 – 62 = 13 Hence, section A has shown the maximum improvement and it is 13 per cent. Revise • Find the difference of the annual examination results and the half yearly examination results for each section. Difference in results of section A = 75 – 62 = 13 Difference in results of section B = 66 – 58 = 8 Difference in results of section C = 56 – 70 = –14 Difference in results of section D = 82 – 74 = 8 Difference in results of section E = 65 – 69 = – 4 We see that the difference is maximum for Section A and the difference is 13, which is same as our answer.
Questions
Q1Short answer
Can you compare the ratio of difference of results of Sections B and D?
Show answer
(a) (b) (c) 1 1
Q2Multiple choice
From the graph, can you observe the sections where there was no improvement? 15-04-2018 In Questions 1 to 16, there are four options, out of which only one is correct. Write the correct answer. 1. Let x, y, z be three observations. The mean of these observations is x ×y×z x +y +z x −y −z x ×y + z
- (a)
- (b)
- (c)
- (d)
Show answer
(a)
(b)
(c)
Q3Multiple choice
3 3 3 2. The number of trees in different parks of a city are 33, 38, 48, 33, 34, 34, 33 and 24. The mode of this data is
- (a)24
- (b)34
- (c)33
- (d)48 3. Which measures of central tendency get affected if the extreme observations on both the ends of a data arranged in descending order are removed? (a) Mean and mode (b) Mean and Median (c) Mode and Median (d) Mean, Median and Mode
Q4Multiple choice
The range of the data : 21, 6, 17, 18, 12, 8, 4, 13 is
- (a)17
- (b)12
- (c)8
- (d)15
Show answer
Sleep→8hrs, Study→3hrs, Meals→2hrs, School→7hrs and Personal time 4 hrs.
Q5Multiple choice
The median of the data : 3, 4, 5, 6, 7, 3, 4 is
- (a)5
- (b)3
- (c)4
- (d)6
Show answer
(a) 5
(b) 3
(c) 4
(d) 6
Q6Multiple choice
Out of 5 brands of chocolates in a shop, a boy has to purchase the brand which is most liked by children. What measure of central tendency would be most appropriate if the data is provided to him?
- (a)Mean
- (b)Mode
- (c)Median
- (d)Any of the three
Q7Multiple choice
There are 2 aces in each of the given set of cards placed face down. From which set are you certain to pick the two aces in the first go?
- (a)
- (b)
- (c)
- (d)15-04-2018
Q8Short answer
In the previous question, what is the probability of picking up an ace from set (d)? 1 2 3 4 (a) (b) (c) (d) 6 6 6 6
Show answer
Box 1 Box 2 Box 3 0.096 0.376 1.808 0.001 0.4200 0.987 0.066 0.62 11.00 0.0864 0.578 0.888
Q9Multiple choice
The difference between the highest and the lowest observations in a data is its
- (a)frequency
- (b)width
- (c)range
- (d)mode
Show answer
OSKNRKPNOV
Q10Multiple choice
In a school, only 2 out of 5 students can participate in a quiz. What is the chance that a student picked at random makes it to the competition?
- (a)20%
- (b)40%
- (c)50%
- (d)30%
Show answer
1. 20 cm 2. cm 3. Length of bottom of vertical support = 9 cm Length of upper of vertical support = 3 cm
Q11Multiple choice
Some integers are marked on a board. What is the range of these integers?
- (a)31
- (b)37
- (c)20
- (d)3
Q12Multiple choice
On tossing a coin, the outcome is
This question refers to a figure in the original PDF.
- (a)only head
- (b)only tail Fig. 3.3
- (c)neither head nor tail
- (d)either head or tail
Show answer
Across : 1. Proper 2. Denominator 3. Equivalent 4. Greator 5. Improper 6. One Down : 1. Product 2. Decimal 8. Reciprocal 9. Fraction
Q13Multiple choice
The mean of three numbers is 40. All the three numbers are different natural numbers. If lowest is 19, what could be highest possible number of remaining two numbers?
- (a)81
- (b)40
- (c)100
- (d)71
Show answer
(a) 81
(b) 40
(c) 100
(d) 71
Q14Multiple choice
Khilona earned scores of 97, 73 and 88 respectively in her first three examinations. If she scored 80 in the fourth examination, then her average score will be
- (a)increased by 1
- (b)increased by 1.5
- (c)decreased by 1
- (d)decreased by 1.5
Show answer
(d) decreased by 1.5
Q15Multiple choice
Which measure of central tendency best represents the data of the most popular politician after a debate?
- (a)Mean
- (b)Median
- (c)Mode
- (d)Any of the above 15-04-2018
Show answer
(c) Mode
Q16Multiple choice
Which of the following has the same mean, median and mode?
- (a)6, 2, 5, 4, 3, 4, 1
- (b)4, 2, 2, 1, 3, 2, 3
- (c)2, 3, 7, 3, 8, 3, 2
- (d)4, 3, 4, 3, 4, 6, 4 In Questions 17 to 31, fill in the blanks to make the statements true.
Show answer
(d) 4, 3, 4, 3, 4, 6, 4 In Questions 17 to 31, fill in the blanks to make the statements true.
Q17Fill in the blanks
The difference between the highest and the lowest observations of a data is called _________.
Show answer
Range Sum of all observations
Q18Fill in the blanks
The mean of a data is defined as _________.
Q19Fill in the blanks
In a set of observations, the observation that occurs the most often is called _________.
Show answer
Mode
Q20Fill in the blanks
In a given data, arranged in ascending or descending order, the middle most observation is called _________.
Show answer
Median Number of observations
Q21Fill in the blanks
Mean, Median, Mode are the measures of _________.
Show answer
Central tendency
Q22Fill in the blanks
The probability of an event which is certain to happen is _________.
Show answer
1
Q23Fill in the blanks
The probability of an event which is impossible to happen is _________.
Show answer
0
Q24Fill in the blanks
When a die is thrown, the probability of getting a number less than 7 is _________.
Show answer
1
Q25Fill in the blanks
In Throwing a die the number of possible outcomes is _________.
Show answer
6
Q26Fill in the blanks
_________ can be used to compare two collections of data.
Show answer
A double bar graph
Q27Fill in the blanks
The representation of data with bars of uniform width is called _________.
Show answer
Bar graph
Q28Fill in the blanks
If the arithmetic mean of 8, 4, x, 6, 2, 7 is 5, then the value of x is _________.
Show answer
3
Q29Fill in the blanks
The median of any data lies between the _________ and _________ observations.
Show answer
Minimum, Maximum
Q30Fill in the blanks
Median is one of the observations in the data if number of observations is _________. What is the difference between a bar graph and a histogram. 15-04-2018
Show answer
Odd
Q31Fill in the blanks
Rohit collected the data regarding weights of students of his class and prepared the following table: Weight (in kg) 44 – 47 48 – 51 52 – 55 56 – 60 Number of Students 3 5 25 7 A student is to be selected randomly from his class for some competition. The probability of selection of the student is highest whose weight is in the interval _________. In Questions 32 to 49, state whether the statements are True or False.
Show answer
52–55
Q32Short answer
If a die is thrown, the probability of getting a number greater than 6 is 1.
Show answer
False
Q33Short answer
When a coin is tossed, there are 2 possible outcomes.
Show answer
True
Q34Short answer
If the extreme observations on both the ends of a data arranged in ascending order are removed, the median gets affected.
Show answer
False
Q35Short answer
The measures of central tendency may not lie between the maximum and minimum values of data.
Show answer
False
Q36Short answer
It is impossible to get a sum of 14 of the numbers on both dice when a pair of dice is thrown together.
Show answer
True
Q37Short answer
The probability of the spinning arrow stopping in the shaded region (Fig. 3.4) is .
This question refers to a figure in the original PDF.
Show answer
True
Q38Short answer
A coin is tossed 15 times and the outcomes are recorded as follows : Fig. 3.4 H T T H T H H H T T H T H T T. The chance of occurence of a head is 50 per cent.
This question refers to a figure in the original PDF.
Show answer
False
Q39Short answer
Mean, Median and Mode may be the same for some data.
Show answer
True
Q40Short answer
The probability of getting an ace out of a deck of cards is greater than 1.
Show answer
False
Q41Short answer
Mean of the data is always from the given data.
Show answer
False
Q42Short answer
Median of the data may or may not be from the given data.
Show answer
True
Q43Short answer
Mode of the data is always from the given data.
Show answer
True
Q44Short answer
Mean of the observations can be lesser than each of the observations.
Show answer
False
Q45Short answer
Mean can never be a fraction. 15-04-2018
Show answer
False
Q46Short answer
Range of the data is always from the data.
Show answer
False
Q47Short answer
The data 12, 13, 14, 15, 16 has every observation as mode.
Show answer
True
Q48Short answer
The range of the data 2, –5, 4, 3, 7, 6 would change if 2 was subtracted from each value in the data.
Show answer
False
Q49Short answer
The range of the data 3, 7, 1, –2, 2, 6, –3, –5 would change if 8 was added to each value in the data.
Show answer
False
Q50Short answer
Calculate the Mean, Median and Mode of the following data: 5, 10, 10, 12, 13. Are these three equal ?
Show answer
10, 10, 10, Yes
Q51Short answer
Find the mean of the first ten even natural numbers.
Show answer
11
Q52Short answer
A data constitutes of heights (in cm) of 50 children. What do you understand by mode for the data?
Show answer
(Mode is the observation that occurs most frequently in a set of observation).
Q53Multiple choice
A car seller collects the following data of cars sold in his shop. Colour of Car Number of Cars Sold Red 15 Black 20 White 17 Silver 12 Others 9
- (a)Which colour of the car is most liked?
- (b)Which measure of central tendency was used in (a)?
Show answer
(a) Which colour of the car is most liked?
(b) Which measure of central tendency was used in (a)?
Q54Multiple choice
The marks in a subject for 12 students are as follows: 31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29 For the given data, find the
- (a)Range
- (b)Mean
- (c)Median
- (d)Mode
Show answer
(a) Range
(b) Mean
(c) Median
Q55Multiple choice
The following are weights (in kg) of 12 people. 70, 62, 54, 57, 62, 84, 75, 59, 62, 65, 78, 60
- (a)Find the mean of the weights of the people. 15-04-2018
- (b)How many people weigh above the mean weight?
- (c)Find the range of the given data.
Show answer
(a) Find the mean of the weights of the people. 15-04-2018
(b) How many people weigh above the mean weight?
(c) Find the range of the given data.
Q56Multiple choice
Following cards are put facing down: A E I O U What is the chance of drawing out
- (a)a vowel
- (b)A or I
- (c)a card marked U
- (d)a consonant
Show answer
(a) a vowel
(b) A or I
(c) a card marked U
(d) a consonant
Q57Short answer
For the given data given below, calculate the mean of its median and mode. 6, 2, 5, 4, 3, 4, 4, 2, 3
Show answer
4
Q58Short answer
Find the median of the given data if the mean is 4.5. 5, 7, 7, 8, x, 5, 4, 3, 1, 2
Show answer
4.5
Q59Short answer
What is the probability of the sun setting tomorrow?
Show answer
One 5 5 4 1
Q60Short answer
When a spinner with three colours (Fig. 3.5) is rotated, which colour has more chance to show up with arrow Fig. 3.5 than the others?
This question refers to a figure in the original PDF.
Show answer
Blue
Q61Short answer
What is the probability that a student chosen at random out of 3 girls and 4 boys is a boy?
Q62Short answer
The letters written on paper slips of the word MEDIAN are put in a bag. If one slip is drawn randomly, what is the probability that it bears the letter D?
Show answer
7 6
Q63Multiple choice
Classify the following events as certain to happen, impossible to happen, may or may not happen:
- (a)Getting a number less than 1 on throwing a die.
- (b)Getting head when a coin is tossed.
- (c)A team winning the match.
- (d)Christmas will be on 25 December. (e) Today moon will not revolve around the earth. (f) A ball thrown up in the air will fall down after some time.
Show answer
(a) Getting a number less than 1 on throwing a die.
(b) Getting head when a coin is tossed.
(c) A team winning the match.
(d) Christmas will be on 25 December. (e) Today moon will not revolve around the earth. (f) A ball thrown up in the air will fall down after some time.
Q64Short answer
A die was thrown 15 times and the outcomes recorded were 5, 3, 4, 1, 2, 6, 4, 2, 2, 3, 1, 5, 6, 1, 2 Find the mean, median and mode of the data.
Show answer
Mean = 3.13, Median = 3, Mode = 2
Q65Short answer
Find the mean of first six multiples of 4.
Show answer
14
Q66Short answer
Find the median of first nine even natural numbers. 15-04-2018
Show answer
10
Q67Short answer
The mean of three numbers is 10. The mean of other four numbers is 12. Find the mean of all the numbers.
Show answer
11.14
Q68Short answer
Find the mode of the given data: 10, 8, 4, 7, 8, 11, 15, 8, 4, 2, 3, 6, 8
Show answer
8
Q69Multiple choice
Given below are heights of 15 boys of a class measured in cm: 128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154. Find
- (a)The height of the tallest boy.
- (b)The height of the shortest boy.
- (c)The range of the given data.
- (d)The median height of the boys.
Show answer
(a) The height of the tallest boy.
(b) The height of the shortest boy.
(c) The range of the given data.
(d) The median height of the boys.
Q70Multiple choice
Observe the data and answer the questions that follow: 16, 15, 16, 16, 8, 15, 17
- (a)Which data value can be put in the data so that the mode remains the same?
- (b)At least how many and which value(s) must be put in to change the mode to 15?
- (c)What is the least number of data values that must be put in to change the mode to 17? Name them.
Show answer
(a) Which data value can be put in the data so that the mode remains the same?
(b) At least how many and which value(s) must be put in to change the mode to 15?
(c) What is the least number of data values that must be put in to change the mode to 17? Name them.
Q71Multiple choice
Age (in years) of 6 children of two groups are recorded as below: Age (in Years) Group A Group B 7 7 7 9 9 11 8 12 10 12 10 12
- (a)Find the mode and range for each group.
- (b)Find the range and mode if the two groups are combined together. 15-04-2018 Measures of central tendency are used to describe the middle of a data set. Mean, median, and mode are measures of central tendency. Description Mean To find the mean (average), add the values in the data set. Then divide by the number of values in the set. Median The middle value or the mean of the two middle values, in an ordered (ascending or descending) set of data. Mode The value(s) that occur most frequently. Range The difference between the least and the greatest values in a data set.
Show answer
(a) Find the mode and range for each group.
(b) Find the range and mode if the two groups are combined together. 15-04-2018 Measures of central tendency are used to describe the middle of a data set. Mean, median, and mode are measures of central tendency. Description Mean To find the mean (average), add the values in the data set. Then divide by the number of values in the set. Median The middle value or the mean of the two middle values, in an ordered (ascending or descending) set of data. Mode The value(s) that occur most frequently. Range The difference between the least and the greatest values in a data set.
Q72Multiple choice
Observe the given bar graph carefully and answer the questions that follow. Fig. 3.6
This question refers to a figure in the original PDF.
- (a)What information does the bar graph depict?
- (b)How many motor bikes were produced in the first three months?
- (c)Calculate the increase in production in May over the production in January. 15-04-2018
- (d)In which month the production was minimum and what was it? (e) Calculate the average (mean) production of bikes in 6 months.
Show answer
(a) What information does the bar graph depict?
(b) How many motor bikes were produced in the first three months?
(c) Calculate the increase in production in May over the production in January. 15-04-2018
(d) In which month the production was minimum and what was it? (e) Calculate the average (mean) production of bikes in 6 months.
Q73Multiple choice
The bar graph given below shows the marks of students of a class in a particular subject: Fig. 3.7 Study the bar graph and answer the following questions:
This question refers to a figure in the original PDF.
- (a)If 40 is the pass mark, then how many students have failed?
- (b)How many students got marks from 50 to 69?
- (c)How many students scored 90 marks and above?
- (d)If students who scored marks above 80 are given merits then how many merit holders are there? (e) What is the strength of the class? 15-04-2018
Show answer
(a) If 40 is the pass mark, then how many students have failed?
(b) How many students got marks from 50 to 69?
(c) How many students scored 90 marks and above?
(d) If students who scored marks above 80 are given merits then how many merit holders are there? (e) What is the strength of the class? 15-04-2018
Q74Multiple choice
Study the bar graph given below and answer the questions that follow. Fig. 3.8
This question refers to a figure in the original PDF.
- (a)What information does the above bar graph represent?
- (b)In which year was production the least?
- (c)After which year was the maximum rise in the production?
- (d)Find the average production of rice during the 5 years. (e) Find difference of rice production between years 2006 and 2008. 15-04-2018 To become familiar with some of the vocabulary terms in the chapter, fill up the following: • Population 1. The population of an area is the total • Median number of people living in that area. • Sample What might mean in the process of gathering data? 2. The word median is derived from the Latin word medius, meaning “middle,” What might the value in a set of data be? 3. When you sample a food, you taste a small portion. What might a be in data collection?
Show answer
(a) What information does the above bar graph represent?
(b) In which year was production the least?
(c) After which year was the maximum rise in the production?
(d) Find the average production of rice during the 5 years. (e) Find difference of rice production between years 2006 and 2008. 15-04-2018 To become familiar with some of the vocabulary terms in the chapter, fill up the following: • Population 1. The population of an area is the total • Median number of people living in that area. • Sample What might mean in the process of gathering data? 2. The word median is derived from the Latin word medius, meaning “middle,” What might the value in a set of data be? 3. When you sample a food, you taste a small portion. What might a be in data collection?
Q75Multiple choice
Study the bar graph given below and answer the questions that follow : Fig. 3.9 15-04-2018
This question refers to a figure in the original PDF.
- (a)What information is depicted from the bar graph?
- (b)In which subject is the student very good?
- (c)Calculate the average marks of the student.
- (d)If 75 and above marks denote a distinction, then name the subjects in which the student got distinction. (e) Calculate the percentage of marks the student got out of 500.
Show answer
(a) What information is depicted from the bar graph?
(b) In which subject is the student very good?
(c) Calculate the average marks of the student.
(d) If 75 and above marks denote a distinction, then name the subjects in which the student got distinction. (e) Calculate the percentage of marks the student got out of 500.
Q76Multiple choice
The bar graph given below represents the circulation of newspapers (dailies) in a town in six languages (the figures are approximated to hundreds). Fig. 3.10 Study the bar graph and answer the following questions:
This question refers to a figure in the original PDF.
- (a)Find the total number of newspapers read in Hindi, Punjabi, Urdu, Marathi and Tamil.
- (b)Find the excess number of newspapers read in Hindi than those in English.
- (c)Name the language in which the least number of newspapers are read.
- (d)Write the total circulation of newspapers in the town. 15-04-2018
Show answer
(a) Find the total number of newspapers read in Hindi, Punjabi, Urdu, Marathi and Tamil.
(b) Find the excess number of newspapers read in Hindi than those in English.
(c) Name the language in which the least number of newspapers are read.
(d) Write the total circulation of newspapers in the town. 15-04-2018
Q77Multiple choice
Study the double bar graphs given below and answer the following questions: Fig. 3.11
This question refers to a figure in the original PDF.
- (a)Which sport is liked the most by Class VIII students?
- (b)How many students of Class VII like Hockey and Tennis in all?
- (c)How many students are there in Class VII?
- (d)For which sport is the number of students of Class VII less than that of Class VIII? (e) For how many sports students of Class VIII are less than Class VII? (f) Find the ratio of students who like Badminton in Class VII to students who like Tennis in Class VIII. 15-04-2018
Show answer
(a) Which sport is liked the most by Class VIII students?
(b) How many students of Class VII like Hockey and Tennis in all?
(c) How many students are there in Class VII?
(d) For which sport is the number of students of Class VII less than that of Class VIII? (e) For how many sports students of Class VIII are less than Class VII? (f) Find the ratio of students who like Badminton in Class VII to students who like Tennis in Class VIII. 15-04-2018
Q78Multiple choice
Study the double bar graph shown below and answer the questions that follow: Fig. 3.12
This question refers to a figure in the original PDF.
- (a)What information is represented by the above double bar graph?
- (b)In which month sales of Brand A decreased as compared to the previous month?
- (c)What is the difference in sales of both the Brands for the month of June?
- (d)Find the average sales of Brand B for the six months. (e) List all months for which the sales of Brand B was less than that of Brand A. (f) Find the ratio of sales of Brand A as compared to Brand B for the month of January. 15-04-2018
Show answer
(a) What information is represented by the above double bar graph?
(b) In which month sales of Brand A decreased as compared to the previous month?
(c) What is the difference in sales of both the Brands for the month of June?
(d) Find the average sales of Brand B for the six months. (e) List all months for which the sales of Brand B was less than that of Brand A. (f) Find the ratio of sales of Brand A as compared to Brand B for the month of January. 15-04-2018
Q79Multiple choice
Study the double bar graph given below and answer the questions that follow: Fig. 3.13
This question refers to a figure in the original PDF.
- (a)What information is compared in the above given double bar graph?
- (b)Calculate the ratio of minimum temperatures in the year 2008 to the year 2009 for the month of November.
- (c)For how many months was the minimum temperature in the year 2008 greater than that of year 2009? Name those months.
- (d)Find the average minimum temperature for the year 2008 for the four months. (e) In which month is the variation in the two temperatures maximum?
Show answer
(a) What information is compared in the above given double bar graph?
(b) Calculate the ratio of minimum temperatures in the year 2008 to the year 2009 for the month of November.
(c) For how many months was the minimum temperature in the year 2008 greater than that of year 2009? Name those months.
(d) Find the average minimum temperature for the year 2008 for the four months. (e) In which month is the variation in the two temperatures maximum?
Q80Long answer
The following table shows the average intake of nutrients in calories by rural and urban groups in a particular year. Using a suitable scale for the given data, draw a double bar graph to compare the data. 15-04-2018 Foodstuff Rural Urban Pulses 35 49 Leafy vegetables 14 21 Other vegetables 51 89 Fruits 35 66 Milk 70 250 Fish and flesh foods 10 22 Fats and Oils 9 35 Sugar/Jaggery 19 31
Show answer
Give the double bar graph here
Q81Multiple choice
Study the double bar graph and answer the quesions that follow: Fig. 3.14
This question refers to a figure in the original PDF.
- (a)What information does the double bar graph represent?
- (b)Find the total number of boys in all sections of Class VII.
- (c)In which sections, the number of girls is greater than the number of boys?
- (d)In which section, the number of boys is the maximum? (e) In which section, the number of girls is the least? 15-04-2018
Show answer
(a) What information does the double bar graph represent?
(b) Find the total number of boys in all sections of Class VII.
(c) In which sections, the number of girls is greater than the number of boys?
(d) In which section, the number of boys is the maximum? (e) In which section, the number of girls is the least? 15-04-2018
Q82Multiple choice
In a public library, the following observations were recorded by the librarian in a particular week: Days Mon Tues Wed Thurs Fri Sat Newspaper 400 600 350 550 500 350 Readers Magazine 150 100 200 300 250 200 Readers
- (a)Draw a double bar graph choosing an appropriate scale.
- (b)On which day, the number of readers in the library was maximum?
- (c)What is the mean number of magazine readers?
Show answer
(a) Draw a double bar graph choosing an appropriate scale.
(b) On which day, the number of readers in the library was maximum?
(c) What is the mean number of magazine readers?
Q83Multiple choice
Observe the following data: Government School, Chandpur Daily Attendance Date : 15.4.2009 Class Total Students Number of Students Present on that Day VI 90 81 VII 82 76 VIII 95 91 IX 70 65 X 63 62
- (a)Draw a double bar graph choosing an appropriate scale. What do you infer from the bar graph?
- (b)Which class has the maximum number of students?
- (c)In which class, the difference of total students and number of students present is minimum?
- (d)Find the ratio of number of students present to the total number of students of Class IX. (e) What per cent of Class VI students were absent? 15-04-2018 Plan a Strategy • Identify too much/too little Information. When you read a problem, you must decide if the problem has too much or too little information. If the problem has too much information, you must decide what information to use to solve the problem. If the problem has too little information, then you should determine what additional information you need to solve the problem. • Read the problems below and decide if there is too much or too little information in each problem. If there is too much information, tell what information you would use to solve the problem. If there is too little information, tell what additional information you would need to solve the problem. • On Monday, 20 students took • Aayesha is practising for a an examination. There were marathon. She ran for 50 10 students who scored above minutes on Monday, 70 minutes
Show answer
(a) Draw a double bar graph choosing an appropriate scale. What do you infer from the bar graph?
(b) Which class has the maximum number of students?
(c) In which class, the difference of total students and number of students present is minimum?
(d) Find the ratio of number of students present to the total number of students of Class IX. (e) What per cent of Class VI students were absent? 15-04-2018 Plan a Strategy • Identify too much/too little Information. When you read a problem, you must decide if the problem has too much or too little information. If the problem has too much information, you must decide what information to use to solve the problem. If the problem has too little information, then you should determine what additional information you need to solve the problem. • Read the problems below and decide if there is too much or too little information in each problem. If there is too much information, tell what information you would use to solve the problem. If there is too little information, tell what additional information you would need to solve the problem. • On Monday, 20 students took • Aayesha is practising for a an examination. There were marathon. She ran for 50 10 students who scored above minutes on Monday, 70 minutes
Q85Multiple choice
and 10 students who on Wednesday, and 45 minutes scored below 85. What was on Friday. On Tuesday and the average score? Thursday, she lifted weights at the gym for 45 minutes each day. She swam for 45 minutes over the weekend. What was the average amount of time per day Aayesha spent running last week? 84. Observe the given data: Days of Mon Tues Wed Thurs Fri Sat the Week Number of 50 45 30 55 27 60 Mobile Phone Sets Sold
- (a)Draw a bar graph to represent the above given information.
- (b)On which day of the week was the sales maximum?
- (c)Find the total sales during the week.
- (d)Find the ratio of the minimum sale to the maximum sale. (e) Calculate the average sale during the week. (f) On how many days of the week was the sale above the average sales? 15-04-2018 85. Below is a list of 10 tallest buildings in India. This list ranks buildings in India that stand at least 150m (492 ft.) tall, based on standard height measurement. This includes spires and architectural details but does not include antenna marks. Following data is given as per the available information till 2009. Since new buildings are always under construction, go on-line to check new taller buildings. Use the information given in the table about sky scrapers to answer the following questions: Name City Height Floors Year Planet Mumbai 181m 51 2009 UB Tower Bengaluru 184 m 20 2006 Ashok Towers Mumbai 193 m 49 2009 The Imperial I Mumbai 249 m 60 2009 The Imperial II Mumbai 249 m 60 2009 RNA Mirage Mumbai 180 m 40 2009 Oberoi Woods Tower I Mumbai 170 m 40 2009 Oberoi Woods Tower II Mumbai 170 m 40 2009 Oberoi Woods Tower III Mumbai 170 m 40 2009 MVRDC Mumbai 156 m 35 2002 (a) Find the height of each storey of the three tallest buildings and write them in the following table: Building Height Number of Height of Storeys Each Storey (b) The average height of one storey for the buildings given in (a) is ______________. (c) Which city in this list has the largest percentage of skyscrappers? What is the percentage? (d) What is the range of data? (e) Find the median of the data. (f) Draw a bar graph for given data. 15-04-2018
Show answer
(a) Draw a bar graph to represent the above given information.
Q86Multiple choice
The marks out of 100 obtained by Kunal and Soni in the Half Yearly Examination are given below: Subjects English Hindi Maths Science S. Science Sanskrit Kunal 72 81 92 96 64 85 Soni 86 89 90 82 75 82
- (a)Draw a double bar graph by choosing appropriate scale.
- (b)Calculate the total percentage of marks obtained by Soni.
- (c)Calculate the total percentage of marks obtained by Kunal.
- (d)Compare the percentages of marks obtained by Kunal and Soni. (e) In how many subjects did Soni get more marks than Kunal? Which are those subjects? (f) Who got more marks in S. Science and what was the difference of marks? (g) In which subject the difference of marks was maximum and by how much?
Show answer
(a) Draw a double bar graph by choosing appropriate scale.
(b) Calculate the total percentage of marks obtained by Soni.
(c) Calculate the total percentage of marks obtained by Kunal.
(d) Compare the percentages of marks obtained by Kunal and Soni. (e) In how many subjects did Soni get more marks than Kunal? Which are those subjects? (f) Who got more marks in S. Science and what was the difference of marks? (g) In which subject the difference of marks was maximum and by how much?
Q87Multiple choice
The students of Class VII have to choose one club from Music, Dance, Yoga, Dramatics, Fine arts and Electronics clubs. The data given below shows the choices made by girls and boys of the class. Study the table and answer the questions that follow: Clubs Music Dance Yoga Dramatics Fine Arts Electronics Girls 15 24 10 19 27 21 Boys 12 16 8 17 11 30
- (a)Draw a double bar graph using appropriate scale to depict the above data.
- (b)How many students are there in Class VII?
- (c)Which is the most preferred club by boys?
- (d)Which is the least preferred club by girls? (e) For which club the difference between boys and girls is the least? (f) For which club is the difference between boys and girls the maximum? 15-04-2018
Show answer
(a) Draw a double bar graph using appropriate scale to depict the above data.
(b) How many students are there in Class VII?
(c) Which is the most preferred club by boys?
(d) Which is the least preferred club by girls? (e) For which club the difference between boys and girls is the least? (f) For which club is the difference between boys and girls the maximum? 15-04-2018
Q88Multiple choice
The data given below shows the production of motor bikes in a factory for some months of two consecutive years. Months Feb May August October December 2008 2700 3200 6000 5000 4200 2007 2800 4500 4800 4800 5200 Study the table given above and answer the following questions:
- (a)Draw a double bar graph using appropriate scale to depict the above information and compare them.
- (b)In which year was the total output the maximum?
- (c)Find the mean production for the year 2007.
- (d)For which month was the difference between the production for the two years the maximum? (e) In which month for the year 2008, the production was the maximum? (f) In which month for the year 2007, the production was the least?
Show answer
(a) Draw a double bar graph using appropriate scale to depict the above information and compare them.
(b) In which year was the total output the maximum?
(c) Find the mean production for the year 2007.
(d) For which month was the difference between the production for the two years the maximum? (e) In which month for the year 2008, the production was the maximum? (f) In which month for the year 2007, the production was the least?
Q89Multiple choice
The table below compares the population (in hundreds) of 4 towns over two years: Towns A B C D 2007 2900 6400 8300 4600 2009 3200 7500 9200 6300 Study the table and answer the following questions:
- (a)Draw a double bar graph using appropriate scale to depict the above information.
- (b)In which town was the population growth maximum?
- (c)In which town was the population growth least?
Q90Multiple choice
The table below gives the data of tourists visiting 5 hill stations over two consecutive years. Study the table and answer the questions that follow: Hill stations Nainital Shimla Manali Mussoorie Kullu 2008 4000 5200 3700 5800 3500 2009 4800 4500 4200 6200 4600
- (a)Draw a double bar graph to depict the above information using appropriate scale. 15-04-2018
- (b)Which hill station was visited by the maximum number of tourists in 2008?
- (c)Which hill station was visited by the least number of tourists in 2009?
- (d)In which hill stations was there increase in number of tourists in the year 2009?
Show answer
(a) Draw a double bar graph to depict the above information using appropriate scale. 15-04-2018
(b) Which hill station was visited by the maximum number of tourists in 2008?
(c) Which hill station was visited by the least number of tourists in 2009?
(d) In which hill stations was there increase in number of tourists in the year 2009?
Q91Multiple choice
The table below gives the flavours of ice cream liked by children (boys and girls) of a society. Flavours Vanilla Chocolate Strawberry Mango Butterscotch Boys 4 9 3 8 13 Girls 8 12 7 9 10 Study the table and answer the following questions:
- (a)Draw a double bar graph using appropriate scale to represent the above information.
- (b)Which flavour is liked the most by the boys?
- (c)How many girls are there in all?
- (d)How many children like chocolate flavour of ice cream? (e) Find the ratio of children who like strawberry flavour to vanilla flavour of ice cream. Application 1: Create a table like the one shown Object Estimate Measure (in cm) (in cm) Length of a pen Length of an eraser Length of your palm Length of your geometry box Length of your math notebook Draw a double bar graph for the above. How accurate are your estimations? 15-04-2018 Application 2: The Body Mass Index (BMI) is a statistical measurement which compares an individual’s weight and height. It is a very useful tool to estimate a healthy body weight based on how tall an individual is. Indeed, it is the most widely used tool to identify the weight problem. BMI is very easy to measure and evaluate. With the help of BMI, one can come to know whether one is underweight, normal weight, over weight or in the category of obesity. Its value is measured in kg/m2. BMI of any individual is calculated with the help of the following formula : Body Weight Body Mass Index (BMI) = Height × Height Here the weight of the individual is measured in kilograms and the height of that individual is taken in metres. The categories in BMI are given in the following table : Category BMI Under weight <18.5 Normal weight 18.5 – 24.9 Over weight 25.0 – 29.9 Obesity Class I 30.0 – 34.9 Obesity Class II 35.0 – 39.9 Obesity Class III ≥ 40 After having a glance at the table given above, one can come to know the category in which any individual falls. Now fill the table given below using the data for the children of your class : Sl. No. Name of Body Weight Height Value Cateogry Student (in kg) (in mtrs) (BMI) Also draw a bar graph for the data received. 15-04-2018 Game 3: Collect the data from students of your class about their favourite programmes on television and prepare a table as shown below: Sl.No. Programmes Number Number of Girls of Boys 1. Cartoons 2. Serials 3. Reality shows 4. Songs 5. Movies 6. News 7. Others (a) Represent the above information on a double bar graph using appropriate scale. (b) Study the graph and find out the favourite programme of the most of students. (c) Which programme is liked by most of the boys? (d) Name the programme for which difference between likings of the number of boys and girls is the maximum. (e) Calculate the percentage of boys who like to watch News. (f) Calculate the percentage of girls who like to watch Cartoons. Game 4: Throw a die 20 times and record the outcomes in the following table: No. on Die 1 2 3 4 5 6 No. of Times (Frequency) Calculate the probability of getting the following numbers using your recorded data: (i) 6 (ii) greater than 6 (iii) 3 or 4 15-04-2018 Write about your observation about the certainty of getting any particular number by throwing a die. Cross Word Puzzle 5 Solve the given crossword and then fill up the given blanks and then boxes. Clues are given below for across as well as downward filling. Also for across and down clues. Clue number is written at the corner of boxes. Answers of clues have to fill up their respective boxes. Clues Across Down 1. Arranging the collected 6. The most common data in tabular form is representative value of a called _______ of data. group of data is the _______. 2. Mean is defined as sum of 7. Tossing a coin gives all observations divided by outcomes. ________ number of 8. The observation that occurs observations. most often is called the _____. 3. Mean, median and mode 9. The difference between the are collectively known as highest and lowest measures of ________. observations gives the ______. 4. Throwing a die gives 10. gives the middle ________ possible observation of a given data. outcomes. 11. A _______ bar graph helps in 5. A ________ is the comparing two collections of representation of data data at a glance. using bars of uniform width and varying 12. The number of times each heights. observation occurs can be represented by ________. 15-04-2018 UNIT 3 DATA HANDLING 97 15-04-2018
Show answer
(a) Draw a double bar graph using appropriate scale to represent the above information.
(b) Which flavour is liked the most by the boys?
(c) How many girls are there in all?
(d) How many children like chocolate flavour of ice cream? (e) Find the ratio of children who like strawberry flavour to vanilla flavour of ice cream. Application 1: Create a table like the one shown Object Estimate Measure (in cm) (in cm) Length of a pen Length of an eraser Length of your palm Length of your geometry box Length of your math notebook Draw a double bar graph for the above. How accurate are your estimations? 15-04-2018 Application 2: The Body Mass Index (BMI) is a statistical measurement which compares an individual’s weight and height. It is a very useful tool to estimate a healthy body weight based on how tall an individual is. Indeed, it is the most widely used tool to identify the weight problem. BMI is very easy to measure and evaluate. With the help of BMI, one can come to know whether one is underweight, normal weight, over weight or in the category of obesity. Its value is measured in kg/m2. BMI of any individual is calculated with the help of the following formula : Body Weight Body Mass Index (BMI) = Height × Height Here the weight of the individual is measured in kilograms and the height of that individual is taken in metres. The categories in BMI are given in the following table : Category BMI Under weight <18.5 Normal weight 18.5 – 24.9 Over weight 25.0 – 29.9 Obesity Class I 30.0 – 34.9 Obesity Class II 35.0 – 39.9 Obesity Class III ≥ 40 After having a glance at the table given above, one can come to know the category in which any individual falls. Now fill the table given below using the data for the children of your class : Sl. No. Name of Body Weight Height Value Cateogry Student (in kg) (in mtrs) (BMI) Also draw a bar graph for the data received. 15-04-2018 Game 3: Collect the data from students of your class about their favourite programmes on television and prepare a table as shown below: Sl.No. Programmes Number Number of Girls of Boys 1. Cartoons 2. Serials 3. Reality shows 4. Songs 5. Movies 6. News 7. Others (a) Represent the above information on a double bar graph using appropriate scale. (b) Study the graph and find out the favourite programme of the most of students. (c) Which programme is liked by most of the boys? (d) Name the programme for which difference between likings of the number of boys and girls is the maximum. (e) Calculate the percentage of boys who like to watch News. (f) Calculate the percentage of girls who like to watch Cartoons. Game 4: Throw a die 20 times and record the outcomes in the following table: No. on Die 1 2 3 4 5 6 No. of Times (Frequency) Calculate the probability of getting the following numbers using your recorded data: (i) 6 (ii) greater than 6 (iii) 3 or 4 15-04-2018 Write about your observation about the certainty of getting any particular number by throwing a die. Cross Word Puzzle 5 Solve the given crossword and then fill up the given blanks and then boxes. Clues are given below for across as well as downward filling. Also for across and down clues. Clue number is written at the corner of boxes. Answers of clues have to fill up their respective boxes. Clues Across Down 1. Arranging the collected 6. The most common data in tabular form is representative value of a called _______ of data. group of data is the _______. 2. Mean is defined as sum of 7. Tossing a coin gives all observations divided by outcomes. ________ number of 8. The observation that occurs observations. most often is called the _____. 3. Mean, median and mode 9. The difference between the are collectively known as highest and lowest measures of ________. observations gives the ______. 4. Throwing a die gives 10. gives the middle ________ possible observation of a given data. outcomes. 11. A _______ bar graph helps in 5. A ________ is the comparing two collections of representation of data data at a glance. using bars of uniform width and varying 12. The number of times each heights. observation occurs can be represented by ________. 15-04-2018 UNIT 3 DATA HANDLING 97 15-04-2018