Statistics PYQs Set 3 (PDF)

Set 3 of 6 · Questions 61-90 of 171

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Statistics · Set 3 (Q61-90)
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61. $A player tosses 2 fair coins. He wins ₹ 5 if 2 heads appear, ₹ 2 if 1 head appears and ₹ 1 if no heads appear, then the variance of his winning amount is$ (1) $\frac{9}{4}$ (2) $\frac{17}{2}$ (3) $6$ (4) $\frac{5}{2}$ 62. $If the median of the data 6, 7, x - 2, x, 18 and 21 written in ascending order is 16 , then the variance of that data is$ (1) $30 \frac{1}{5}$ (2) $31 \frac{1}{3}$ (3) $32 \frac{1}{2}$ (4) $33 \frac{1}{3}$ 63. $The mean and the standard deviation of a data of 8 items are 25 and 5 respectively. If two items 15 and 25 are added to this data, then the variance of the new data is$ (1) $29$ (2) $24$ (3) $26$ (4) $31$ 64. $Let the six numbers a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}, be in A.P and a_{1} + a_{3} = 10 . If the mean of these six numbers is \frac{19}{2} and their variance is σ^{2}, then 8 σ^{2} is equal to$ (1) $200$ (2) $210$ (3) $195$ (4) $105$ 65. $Which of the following data has minimum variance?$ (1) $1, 2, 3, 4, 5$ (2) $1, 1, 2, 3, 6$ (3) $1, 1, 2, 3, 5$ (4) $1, 1, 2, 2, 5$ 66. $If x_{1}, x_{2}, \dots x_{n} are ' n' observations and x is their mean. If \sum_{i = 1}^{n} (x_{1} - x)^{2} is almost zero, then a true statement among the following is$ (1) $It indicates a higher degree of dispersion of the observations from the mean x$ (2) $It indicates that there is no dispersion$ (3) $\sumi=1m x_{i} -x2 is the arithmetic mean of the data$ (4) $It indicates that each observation x_{i} is very close to the mean x and hence degree of dispersion is low.$ 67. $For a data consisting of 15 observations x_{i}, i = 1, 2, 3, \dots, 15 the following results are obtained: \sum_{i = 1}^{15} x_{i} = 170; \sum_{i = 1}^{15} x_{i}^{2} = 2830 . If one of the observation namely 20 was found wrong and was replaced by its correct value 30 , then the corrected variance is$ (1) $80$ (2) $78$ (3) $76$ (4) $75$ 68. $Let the mean and variance of 8 numbers - 10, - 7, - 1, x, y, 9, 2, 16 be \frac{7}{2} and \frac{293}{4}, respectively. Then the mean of 4 numbers x, y, x + y + 1, \| x - y \| is:$ (1) $11$ (2) $12$ (3) $10$ (4) $9$ 69. $The mean and standard deviation of a distribution of weight: of a group of 20 boys are 40 kg and 5 kg respectively. If two boys of weights 43 kg and 37 kg are exclude from this group, then the variance of the distribution of weights of the remaining group of boys is$ (1) $26.18$ (2) $5.27$ (3) $26.78$ (4) $5.17$ 70. $If the mean deviation about the median of the numbers k, 2 k, 3 k, \dots, 1000 k is 500 , then k^{2} is equal to :$ (1) $9$ (2) $1$ (3) $4$ (4) $16$ 71. $The mean of 100 observations is 50 and their standard deviation is 5 . Then the sum of squares of all observations is$ (1) $250000$ (2) $50000$ (3) $255000$ (4) $252500$ 72. $The standard deviation of the data 6, 7, 8, 9, 10 is$ (1) $10$ (2) $2$ (3) $10$ (4) $2$ 73. $The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2, 3, 5, 10, 11, 13, 15, 21, then the mean deviation about the median of all the 10 observations is$ (1) $4$ (2) $7$ (3) $5$ (4) $6$ 74. $Let 9 = x_{1} < x_{2} < \dots . < x_{7} be in an A.P with common difference d. If the standard deviation of x_{1}, x_{2}, \dots . x_{7} is 4 and the mean is x, then x + x_{6} is equal to$ (1) $18 (1 + \frac{1}{3})$ (2) $34$ (3) $2 (9 + \frac{8}{7})$ (4) $25$ 75. $If \sum (x_{i} - a) = n and \sum (x_{i} - a)^{2} = na, (n, a > 1) then the standard deviation of n observations x_{1}, x_{2}, \dots, x_{n} is:$ (1) $a - 1$ (2) $n a - 1$ (3) $n (a - 1)$ (4) $a - 1$ 76. $The mean deviation about the median for the following data 6, 3, 4, 9, 2, 7 and 11 is$ (1) $1.89$ (2) $2.57$ (3) $3.14$ (4) $6.23$ 77. $Consider 10 observation x_{1}, x_{2}, \dots, x_{10} . such that \sum_{i = 1}^{10} (x_{i} - α) = 2 and \sum_{i = 1}^{10} (x_{i} - β)^{2} = 40, where α, β are positive integers. Let the mean and the variance of the observations be \frac{6}{5} and \frac{84}{25} respectively. The \frac{β}{α} is equal to :$ (1) $2$ (2) $\frac{3}{2}$ (3) $\frac{5}{2}$ (4) $1$ 78. $If A and B are variances of the 1^{st} ‘n’ even numbers and 1^{st} ‘n’ odd numbers respectively then$ (1) $A = B$ (2) $A > B$ (3) $A < B$ (4) $A = B - 1$ 79. $The coefficient of variation for the following data is: x_{i} 57911 f_{i} 3212$ (1) $9 \frac{23}{2}$ (2) $20 \frac{23}{3}$ (3) $15 \frac{23}{4}$ (4) $7 \frac{23}{6}$ 80. $The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is:$ (1) $9$ (2) $3$ (3) $7$ (4) $5$ 81. $The mean and standard deviation of 100 observations were calculated as 40 and 5.1 respectively. Later on it was found that one of the observations was taken as 50 in the place of 40. If the wrong entry is replaced by the correct one, then the sum of the squares of all the observations is$ (1) $162701$ (2) $163501$ (3) $162601$ (4) $161701$ 82. $The variance of the following frequency distribution is Classes 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Frequency 112918453$ (1) $165.3$ (2) $161.1$ (3) $282.1$ (4) $152.5$ 83. $Let X = {x \in N : 1 \leq x \leq 17} and Y = {a x + b : x \in X and a, b \in R, a > 0} . If mean and variance of elements of Y are 17 and 216 respectively then a + b is equal to:$ (1) $7$ (2) $- 27$ (3) $9$ (4) $- 7$ 84. $If M and σ^{2} represent respectively the mean deviation from the mean and the variance for the data 1, 3, 5, 7, 11, 13, 17, 19, 23 then 3 (σ^{2} - M) =$ (1) $232$ (2) $112$ (3) $224$ (4) $136$ 85. $Let in a series of 2 n observations, half of them are equal to a and remaining half are equal to - a . Also byadding a constant b in each of these observations, the mean and standard deviation of new set become 5 and 20, respectively. Then the value of a^{2} + b^{2} is equal to:$ (1) $425$ (2) $650$ (3) $250$ (4) $925$ 86. $If the total number of observations is 20, \sum x_{i} = 1000 and \sum x_{i}^{2} = 84000, then the variance of the distribution is$ (1) $1500$ (2) $1600$ (3) $1700$ (4) $1800$ 87. $Let x_{i} (1 \leq i \leq 10) be ten observations of a random variable x . If \sum (x_{i} - p) = 3 and \sum (x_{i} - p)^{2} = 9 where 0 \neq = 0 p \in R, then the standard deviation of these observations is$ (1) $\frac{7}{10}$ (2) $\frac{9}{10}$ (3) $\frac{3}{5}$ (4) $\frac{4}{5}$ 88. $If the variance of terms in an increasing A.P. b_{1}, b_{2}, b_{3} \dots, b_{11} s 90, then the common difference of this A.P. is ..$ 89. $If the mean and variance of the data 65, 68, 58, 44, 48, 45, 60, α, β, 60 where α > β are 56 and 66.2 respectively, then α^{2} + β^{2} is equal to$ 90. $The variance σ^{2} of the data x_{i} 0156101217 f_{i} 3232633 Is________$