Statistics PYQs Set 2 (PDF)

Set 2 of 6 · Questions 31-60 of 171

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Statistics · Set 2 (Q31-60)
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31. $The mean of 5 observations is 4.4 and their variance is 8.24. If three of those observations are 1,2 and 6, then the other two observations are$ (1) $9,4$ (2) $9,5$ (3) $9,2$ (4) $9,13$ 32. $If both mean and variance of 50 observations x_{1}, x_{2}, \dots ., x_{50} are equal to 16 and 256 respectively, then mean of (x_{1} - 5)^{2}, (x_{2} - 5)^{2}, \dots .., (x_{50} - 5)^{2} is$ (1) $357$ (2) $367$ (3) $377$ (4) $387$ 33. $The frequency distribution of the age of students in a class of 40 students is given below. Age 151617181920 No of Students 58512 x y If the mean deviation about the median is 1.25 , then 4 x + 5 y is equal to :$ (1) $46$ (2) $43$ (3) $44$ (4) $47$ 34. $The variance of 50 observations is 7 . Suppose that each observation in this data is multiplied by 6 and then 5 is subtracted from it. Then the variance of that new data is$ (1) $37$ (2) $42$ (3) $247$ (4) $252$ 35. $The mean deviation about the mean for the following data is Class interval 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 Frequency 4616281664$ (1) $35$ (2) $10$ (3) $15$ (4) $12$ 36. $If the mean of the data p, 6, 6, 7, 8, 11, 15, 16, is 3 times p, then the mean deviation of the data from its mean is$ (1) $2.25$ (2) $3.75$ (3) $4.4$ (4) $2.5$ 37. $If the mean and variance of six observations 7,10,11,15,a,b are 10 and \frac{20}{3}, respectively, then the value of \|a-b\|is equal to :$ (1) $9$ (2) $11$ (3) $7$ (4) $1$ 38. $If x is the mean of n observations x_{1}, x_{2}, \dots x_{n} then the mean of the absolute deviations of these observations from x is$ (1) $the variance of the data$ (2) $the mean proportion of the data$ (3) $the standard deviation of the data$ (4) $the mean deviation of the data$ 39. $Let S be the set of all values of a_{1} for which the mean deviation about the mean of 100 consecutive positive integers a_{1}, a_{2}, a_{3}, \dots, a_{100} is 25. Then Sis$ (1) $\emptyset$ (2) $(99)$ (3) $N$ (4) $(9)$ 40. $Which of the following set of data has least standard deviation?$ (1) $10, 20, 30, 40$ (2) $2, 4, 6, 8$ (3) $3, 6, 9, 12$ (4) $1, 2, 3, 4$ 41. $If the mean of the discrete distribution 8, 9, 6, 5, x, 4, 6, 5 is 6 , then its standard deviation (nearest to two decimal places) is$ (1) $2.50$ (2) $1.58$ (3) $0.51$ (4) $1.41$ 42. $Let M denote the median of the following frequency distribution. Class 0 - 4 4 - 8 8 - 12 12 - 16 16 - 20 Frequency 391086 Then 20 M is equal to :$ (1) $416$ (2) $104$ (3) $52$ (4) $208$ 43. $For the frequency distribution: Variate (x) : x_{1} x_{2} x_{3} \dots x_{15} Frequency (f) : f_{1} f_{2} f_{3} \dots f_{15} where 0 < x_{1} < x_{2} < x_{3} < \dots x_{15} = 10 and \sum f_{i} > 0, the standard deviation cannot be :$ (1) $1$ (2) $6$ (3) $2$ (4) $4$ 44. $Let the mean and variance of the frequency distribution x : x_{1} = 2 x_{2} = 6 x_{3} = 8 x_{4} = 9 f : 4 4 α β be 6 and 6.8 respectively. If x_{3} is changed from 8to 7, then the mean for the new data will be:$ (1) $4$ (2) $5$ (3) $\frac{17}{3}$ (4) $\frac{16}{3}$ 45. $The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observations α in this data is replaced by β, then the mean and variance become 10.1 and 1.99, respectively. Then α + β equals$ (1) $15$ (2) $5$ (3) $10$ (4) $20$ 46. $Students of two sections A and B of a class show the following results in a test conducted for 100 marks. Section A Section B Number of students 5060 Average marks in the test 4545 Variance of distribution of marks 6481 Then$ (1) $variability of section B > variability of section A$ (2) $variability of section A > variability of section B$ (3) $variability of section A = variability of section B$ (4) $The data is not sufficient to compare the variability of the sections$ 47. $If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then a + b + ab is equal to:$ (1) $103$ (2) $106$ (3) $100$ (4) $105$ 48. $Assertion (A) : The variance of the first n odd natural numbers is \frac{n ^{2} - 1}{3} .Reason (R): The sum of the first n odd natural numbers is n^{2} and the sum of the squares of the first n odd natural numbers is \frac{n ( 4 n ^{2} - 1 )}{3} .Which of the following alternatives is correct?$ (1) $(A) and (R) are true. (R) is correct explanation of (A)$ (2) $(A) and (R) are true, but (R) is not a correct explanation of (A)$ (3) $(A) is true, but (R) is false$ (4) $(A) is false, but (R) is true$ 49. $If the variance of the data 2, 3, 5, 8, 12 is σ^{2} and the mean deviation from the median for this data is M, then σ^{2} - M =$ (1) $10.2$ (2) $5.8$ (3) $10.6$ (4) $8.2$ 50. $The number of values of a \in N such that the variance of 3, 7, 12, a, 43 - a is a natural number is:$ (1) $0$ (2) $2$ (3) $5$ (4) $infinite$ 51. $If the coeficient of variation and standard deviation are 60 and 21 respectively, the arithmetic mean of distribution is$ (1) $60$ (2) $30$ (3) $35$ (4) $21$ 52. $The mean and standard deviation of 20 observations are found to be 10 and 2 . respectively. On rechecking, it was found that an observation by mistake was taken 8 instead of 12 . The correct standard deviation is$ (1) $1.8$ (2) $1.94$ (3) $3.96$ (4) $3.86$ 53. $The variance of 20 observations is 5. If each one of the observations is multiplied by 2 , then the variance of the resulting observations is$ (1) $40$ (2) $80$ (3) $20$ (4) $10$ 54. $If the mean and variance of the frequency distribution x_{i} 2 4 6 8 10 12 14 16 f_{i} 4 4 α 15 8 β 4 5 are 9 and 15.08 respectively, then the value of α^{2} + β^{2} - α β is_____.$ 55. $Consider a set of 3 n numbers having variance 4 . In this set, the mean of first 2 n numbers is 6 and the mean ofthe remaining n numbers is 3 . A new set is constructed by adding 1 into each of first 2 n numbers, andsubtracting 1 from each of the remaining n numbers. If the variance of the new set is k, then 9 k is equal to____$ 56. $If the variance of the first n natural numbers is 10 and the variance of the first m even natural numbers is 16, then m + n is equal to \dots$ 57. $If the variance of 10 natural numbers 1, 1, 1, \dots, 1, k is less than 10, then the maximum possible value of k is$ 58. $Let X = (11, 12, 13, \dots, 40, 41) and Y = (61, 62, 63, \dots, 90, 91) be the two sets of observations. If x ˉ and y ˉ are their respective means and σ^{2} is the variance of all the observations in X \cup Y, then x ˉ + y ˉ - σ^{2} is equal to _________$ 59. $Let X_{1}, X_{2}, \dots \dots \dots . X_{18} be eighteen observation such that \sum (X_{i} - α) = 36 and \sum (X_{i} - β)^{2} = 90, where α and β are distinct real numbers. If the standard deviation of these observationsis 1, then the value of \| α - β \| is$ 60. $If the mean deviation about the mean of the numbers 1, 2, 3,....., n, where n is odd, is \frac{5 _{(} n + 1 _{)}}{n}, then n is equal to_____$