Q39Multiple choice
(M.C.Q.). 24. The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from the mean is
- (A)2
- (B)2.57
- (C)3
- (D)3.75 25. Mean deviation for n observations x1, x2, ..., xn from their mean x is given by 1 n (A) ∑ ( xi − x ) (B) ∑ xi − x n i =1 i =1 2 1 n 2 (C) ∑ ( xi − x ) (D) ∑ ( xi − x ) i =1 n i =1 26. When tested, the lives (in hours) of 5 bulbs were noted as follows: 1357, 1090, 1666, 1494, 1623 The mean deviations (in hours) from their mean is (A) 178 (B) 179 (C) 220 (D) 356 27. Following are the marks obtained by 9 students in a mathematics test: 50, 69, 20, 33, 53, 39, 40, 65, 59 The mean deviation from the median is: (A) 9 (B) 10.5 (C) 12.67 (D) 14.76 28. The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is 52 52 (A) (B) (C) 6 (D) 6 7 7 29. Let x1, x2, ..., xn be n observations and x be their arithmetic mean. The formula for the standard deviation is given by 2 ∑ ( xi − x )2 (A) ∑ ( xi − x ) (B) (C) ∑( xi − x ) (D) ∑ xi2 + x 2 n n 30. The mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is (A) 50000 (B) 250000 (C) 252500 (D) 255000 31. Let a, b, c, d, e be the observations with mean m and standard deviation s. The standard deviation of the observations a + k, b + k, c + k, d + k, e + k is (A) s (B) ks (C) s+k (D) 32. Let x1, x2, x3, x4, x5 be the observations with mean m and standard deviation s. The standard deviation of the observations kx1, kx2, kx3, kx4, kx5 is (A) k + s (B) (C) ks (D) s 33. Let x1, x2, ... xn be n observations. Let wi = lxi + k for i = 1, 2, ...n, where l and k are constants. If the mean of xi’s is 48 and their standard deviation is 12, the mean of wi’s is 55 and standard deviation of wi’s is 15, the values of l and k should be (A) l = 1.25, k = – 5 (B) l = – 1.25, k = 5 (C) l = 2.5, k = – 5 (D) l = 2.5, k = 5 34. Standard deviations for first 10 natural numbers is (A) 5.5 (B) 3.87 (C) 2.97 (D) 2.87 35. Consider the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. If 1 is added to each number, the variance of the numbers so obtained is STATISTICS 283 (A) 6.5 (B) 2.87 (C) 3.87 (D) 8.25 36. Consider the first 10 positive integers. If we multiply each number by –1 and then add 1 to each number, the variance of the numbers so obtained is (A) 8.25 (B) 6.5 (C) 3.87 (D) 2.87 37. The following information relates to a sample of size 60: ∑ x 2 = 18000, ∑ x = 960 The variance is (A) 6.63 (B) 16 (C) 22 (D) 44 38. Coefficient of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25 respectively. Difference of their standard deviation is (A) 0 (B) 1 (C) 1.5 (D) 2.5 39. The standard deviation of some temperature data in °C is 5. If the data were converted into ºF, the variance would be (A) 81 (B) 57 (C) 36 (D) 25 Fill in the blanks in Exercises from 40 to 46. ...