Following is a pie chart showing the amount spent in rupees (in thousands) by a company on various modes of advertising for a product. Now answer the following questions. 1. Which type of media advertising is the greatest amount of the total? 2. Which type of media advertising is the least amount of the total? 3. What per cent of the total advertising amount is spent on direct mail campaigns? 4. What per cent of the advertising amount is spent on newspaper and magazine advertisements? 5. What media types do you think are included in miscellaneous? Why aren’t those media types given their own category? 1 Card Activity Have you ever seen a pack No didi. of cards? Then, take a pack of cards and try to It will complete the table be fun didi. given below. Face Cards Number Cards K Q J 10 9 8 7 6 5 4 3 2 A Total Spade Heart Diamond Club Total Yes Didi. Did you have But what do the a look at alphabets A, K, Q all the cards and J stand for? carefully? A stands for Ace, K stands for King, Q stands for Queen Ok J stands for Jack. Now, try to I will answer some try didi. questions. 1. How many colours can you observe? 2. How many cards are there in all? 3. How many cards of one type are there? 4. How many types of cards can you observe? Name them. 5. How many black cards are there in all? 6. How many red cards are there in all? 7. How many face cards of each type are there? 8. How many picture cards are there in all? Number of red cards What is the fraction is 26. of number of red Total cards are 52. cards to total So fraction becomes number of cards? Do you know Really didi. this fraction So now, I can is also the probability calculate the of getting a red probabilities also. card out of the pack of cards? Let us see if you can answer these questions? 9. From a pack of well-shuffled cards, what is the probability of getting (i) a black face card (ii) a red jack iii) a 4 of spade iv) a picture card (v) a red card of ace (vi) a black king (vii) an ordinary card (viii) a picture card of heart (ix) an ace of club (x) a king (xi) a card of diamond (xii) a black ordinary card 2 Playing with dice (a) Complete the table given below and answer the questions that follow: A B Out- Out- Dice 1 Dice 2 Sum Dice 1 Dice 2 Sum comes comes (1,1) 2 (1,2) 3 (1,3) 4 (1,4) 5 Pratibha’s desk has 8 drawers. When she receives a paper, she usually chooses a drawer at random to put it in. However, 2 out of 10 times she forgets to put the paper away, and it gets lost. The probability that a paper will get 2 1 lost is , or . 10 5 • What is the probability that a paper will be put into a drawer? • If all drawers are equally likely to be chosen, what is the probability that a paper will be put in drawer 3? When Pratibha needs a document, she looks first in drawer 1 and then checks each drawer in order until the paper is found or until she has looked in all the drawers. 1. If Pratibha checked drawer 1 and didn’t find the paper she was looking for, what is the probability that the paper will be found in one of the remaining 7 drawers? 2. If Pratibha checked drawers 1, 2 and 3, and didn’t find the paper she was looking for, what is the probability that the paper will be found in one of the remaining 5 drawers? 3. If Pratibha checked drawers 1–7 and didn’t find the paper she was looking for, what is the probability that the paper will be found in the last drawer? (b) Complete the table given below. Sum of dots Tally Number of Probability on both the dice marks outcomes Two dice are rolled together, using the above table find the probability of— (i) sum of digits to be more than 6. (ii) sum of digits to be less than 3. (iii) sum of digits to be either 5 or 6. (iv) sum of digits to be 12. (v) sum of digits to be less than 9 but more than 5. 3 DATA COLLECTION Read the paragraph given below and complete the tables given. All of us have some concept of statistics because magazines, newspapers, radio and TV advertisements are full of statistics or numerical data. Existence of the practice of collecting numerical data in ancient India is evident from the fact that during the reign of Chandragupta Maurya, there was a good system of collecting such data especially with regard to births and deaths. During Akbar’s reign, Raja Todarmal, the Land and Revenue Minister, maintained good records of land and agricultural statistics. In Ain- i-Akbari written by Abul Fazal, a detailed account of the administrative and statistical surveys conducted during that period can be found. From the paragraph given on the previous page prepare the frequency table of all the letters of the English alphabet and answer the questions that follow. 1. Frequency table for each letter of the alphabet. Letter Tally marks Frequency - - - (a) Which is the least frequently occuring letter? (b) Which vowel is most commonly used? (c) Which consonant is most commonly used? (d) Find the ratio of vowels to that of consonants. 2. Frequecy table for words with two or more letters. Number of words with Tally marks Frequency 2 letters 3 letters 4 letters 5 letters 6 letters more than 6 letters (a) How many two letter words are used in the paragraph? (b) How many words are used in all? (c) How many words have five letters or more? (d) What is the ratio of three letter words and five letter words? 4 Fun Activity Take a packet which has different colours of toffees/candies in it. Count the number of toffees of each colour and fill the data in the table given below. Also draw a pie chart to depict the data. Colour of candies Number Fraction Fraction of 360° Green 5 Conducting Survey Conduct a class survey to know the favourite T.V. channels and note the responses in the following table. Channels Number Fraction of Estimated per cent Caculated per cent of Votes Total Votes of Total Votes of Total Votes News Movies History and Nature Cartoon Sports How accurate is your estimation? Now, take a strip of thick chart paper, 1 cm wide and divide it into equal-sized rectangles – one for each student of your class. The entire strip represents your whole class, or 100% of the votes. On your strip, colour groups of rectangles according to the number of votes each choice received. Use a different colour for each choice. For example, if 5 students voted for movie, colour the first 5 rectangles blue. If 7 choose cartoon, colour the next 7 rectangle green. When you are finished, all the rectangles should be coloured. movie cartoon Now create a circle graph as shown below. – Tape the ends of your strip together, Movie with no overlap, to form a loop with the coloured rectangles inside. – Tape four copies of the quarter-circle template together to form a circle. – Place your above loop around the Movie circle. On the edge of the circle, mark rto where each colour begins and ends. – Remove the loop, and use a ruler to connect each mark you made to the centre of the circle. – Colour the sections of your graph. Label each section with the channels name and the fraction of votes that channel received. For example, your circle graph known as pie chart might look like this. Circle graphs in books, magazines, and newspapers are often labeled with per cents. Add per cent labels to your pie chart. 6 Marble Game Pramod is babysitting his little sister Monika and her two friends, Puja and Jyoti. Monika is wearing red, Puja is wearing blue and Jyoti is wearing green coloured clothes. Pramod fills a bucket with 12 red (R) marbles, 8 blue (B) marbles and 4 green (G) marbles. He tells the girls that they will play a game. He will reach into the bucket and pull out a marble at random. The girl whose clothes match the colour of the marble scores 1 point.
- a.What is the probability of each girl scoring 1 point on the first draw? Monika : Puja : Jyoti :
- b.What is the probability of not drawing a green marble on the first draw?
- c.If two marbles of each colour are added to the bucket, do the probabilities in part (a) change? Explain your answer.
- d.If the number of each colour is doubled, do the probabilities in part (a) change? Explain why or why not. 7 Crossword Puzzle Solve the crossword (given on the next page) and then fill up the given boxes. Clues are given below for across as well as downward filling. Also, for across and down clues, due number is written at the corner of the boxes. Answer of clues have to be filled in their respective boxes. Across 1. Another name for a circle graph is ____________. 5. Class width of the interval 10-15 is ____________. 7. Difference of highest and lowest observations in a given data is called ____________. 8. Each outcome or a collection of outcomes in an experiment is known as ____________. 9. Pie chart represents the comparison of parts to a ____________. 10. Probability of sun rising in the east is ____________. 12. Probability of getting a head or a tail on tossing a coin once is ____________. Down 2. Representation of grouped data graphically is called ____________. 3. Unorganised and ungrouped data are called ____________. 4. Difference between upper and lower class limit is known as ____________. 6. The number of times a particular observation occurs in the given data is called ____________. 11. If today is Saturday, then the probability of two days after tomorrow being a Monday is ____________. MATHEMATICS Rough Work UNIT-2 Rough Work DATA HANDLING 71 MATHEMATICS Rough Work
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a. What is the probability of each girl scoring 1 point on the first draw? Monika : Puja : Jyoti :
b. What is the probability of not drawing a green marble on the first draw?
c. If two marbles of each colour are added to the bucket, do the probabilities in part (a) change? Explain your answer.
d. If the number of each colour is doubled, do the probabilities in part (a) change? Explain why or why not. 7 Crossword Puzzle Solve the crossword (given on the next page) and then fill up the given boxes. Clues are given below for across as well as downward filling. Also, for across and down clues, due number is written at the corner of the boxes. Answer of clues have to be filled in their respective boxes. Across 1. Another name for a circle graph is ____________. 5. Class width of the interval 10-15 is ____________. 7. Difference of highest and lowest observations in a given data is called ____________. 8. Each outcome or a collection of outcomes in an experiment is known as ____________. 9. Pie chart represents the comparison of parts to a ____________. 10. Probability of sun rising in the east is ____________. 12. Probability of getting a head or a tail on tossing a coin once is ____________. Down 2. Representation of grouped data graphically is called ____________. 3. Unorganised and ungrouped data are called ____________. 4. Difference between upper and lower class limit is known as ____________. 6. The number of times a particular observation occurs in the given data is called ____________. 11. If today is Saturday, then the probability of two days after tomorrow being a Monday is ____________. MATHEMATICS Rough Work UNIT-2 Rough Work DATA HANDLING 71 MATHEMATICS Rough Work