Statistics PYQs Set 4 (PDF)

Set 4 of 6 · Questions 91-120 of 171

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Statistics · Set 4 (Q91-120)
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91. $The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the absolute difference of the remaining two observations is:$ (1) $2$ (2) $4$ (3) $3$ (4) $1$ 92. $Let α, β \in R . Let the mean and the variance of 6 observations - 3, 4, 7, - 6, α, β be 2 and 23 , respectively. The mean deviation about the mean of these 6 observations is :$ (1) $\frac{13}{3}$ (2) $\frac{16}{3}$ (3) $\frac{11}{3}$ (4) $\frac{14}{3}$ 93. $The mean deviation from the mean of the set of observation - 1, 0, 4 is$ (1) $3$ (2) $1$ (3) $-2$ (4) $2$ 94. $If coefficient of variation is 60 and standard deviation is 24 , then arithmetic mean is$ (1) $\frac{20}{7}$ (2) $\frac{7}{20}$ (3) $\frac{1}{40}$ (4) $40$ 95. $Consider three observations a, b and c such that b = a + c . If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?$ (1) $b^{2} = 3 (a^{2} + c^{2}) + 9 d^{2}$ (2) $b^{2} = a^{2} + c^{2} + 3 d^{2}$ (3) $b^{2} = 3 (a^{2} + c^{2} + d^{2})$ (4) $b^{2} = 3 (a^{2} + c^{2}) - 9 d^{2}$ 96. $If the mean of the following probability distribution of a random variable X : X 02468 P (X) a 2 a a + b 2 b 3 b is \frac{46}{9}, then the variance of the distribution is$ (1) $\frac{173}{27}$ (2) $\frac{566}{81}$ (3) $\frac{151}{27}$ (4) $\frac{581}{81}$ 97. $Two teams A and B have the same mean and their coefficients of variation are 4,2 , respectively. If σ_{A}, σ_{B} are the standard deviations of teams A, B respectively, then the relation between them is$ (1) $σ_{A} = σ_{B}$ (2) $σ_{B} = 2 σ_{A}$ (3) $σ_{A} = 2 σ_{B}$ (4) $σ_{B} = 4 σ_{A}$ 98. $The mean deviation about the median of the discrete data 12, 15, 7, 4, 4, 15, 23, 14 is$ (1) $5$ (2) $8$ (3) $13$ (4) $10$ 99. $The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance is:$ (1) $3.99$ (2) $3.98$ (3) $4.01$ (4) $4.02$ 100. $The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and σ^{2} respectively. If the variance of all the 30 numbers in the two sets is 13, then σ^{2} is equal to$ (1) $10$ (2) $11$ (3) $9$ (4) $12$ 101. $The mean deviation from the mean for the data 6, 7, 10, 12, 13, 4, 12, 16 is$ (1) $3.25$ (2) $3.52$ (3) $3.33$ (4) $2.35$ 102. $Then mean deviation about the median of the following distributions is x 6121824303642 f 4791815105$ (1) $7.5$ (2) $8.4$ (3) $9.2$ (4) $9.6$ 103. $The variance of the following frequency distribution is Class interval 0 - 4 4 - 8 8 - 12 12 - 16 16 - 20 Frequency 24631$ (1) $\frac{295}{16}$ (2) $\frac{304}{16}$ (3) $\frac{37}{4}$ (4) $\frac{97}{4}$ 104. $Let X = {x \in N : 1 \leq x \leq 19} and for some a, b \in R, Y = ax +b : x \in X . If the mean and variance of the elements of Y are 30 and 750, respectively, then the sum of all possible values of b is$ (1) $60$ (2) $100$ (3) $80$ (4) $20$ 105. $The mean of 5 observations is 4.4 and variance is 8.24. If three of the five observations are 1,2 and 6 , then the values of other two observations are$ (1) $4,9$ (2) $3,9$ (3) $4,8$ (4) $5,7$ 106. $What is the formula for finding coefficient of variation, given σ = standard deviation and x = mean \neq = 0 ?$ (1) $\frac{x}{σ} \times 100$ (2) $\frac{x}{σ}$ (3) $\frac{σ}{x}$ (4) $\frac{σ}{x} \times 100$ 107. $Mean and standard deviation of 100 items are 50 and 4 respectively. The sum of all squares of the items is$ (1) $251600$ (2) $266000$ (3) $256100$ (4) $261600$ 108. $The Standard Deviation of the numbers 31, 32, 33, \dots ., 46, 47 is$ (1) $\frac{17}{12}$ (2) $\frac{47 ^{2} - 1}{12}$ (3) $26$ (4) $43$ 109. $The mean of 5 observation is 15 and variance is 9 . If two observations having values -5 and 13 are combined with these observations, then what will be the new variance?$ (1) $\frac{6259}{7}$ (2) $\frac{6259}{49}$ (3) $\frac{2659}{7}$ (4) $\frac{2659}{49}$ 110. $The mean deviation about the mean for the following data: 5, 6, 7, 8, 6, 9, 13, 12, 15 is$ (1) $1.55$ (2) $2.88$ (3) $3.89$ (4) $5$ 111. $If each of the observations x_{1}, x_{2}, \dots, x_{n} is increased or decreased by k, where k is a positive number, then the variance of the data thus obtained$ (1) $increase by k$ (2) $do not change$ (3) $is equal to k^{2}$ (4) $is equal to 2 k$ 112. $The mean and the standard deviation (s, d) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then reduced by q where p \neq = 0 and q \neq = 0 . If the new mean and new s . d . become half of their original values, then q is equal to :$ (1) $- 10$ (2) $- 20$ (3) $- 5$ (4) $10$ 113. $Let the mean and the standard deviation of the observation 2, 3, 3, 4, 5, 7, a, b be 4 and 2 respectively. Then the mean deviation about the mode of these observations is:$ (1) $\frac{1}{2}$ (2) $\frac{3}{4}$ (3) $1$ (4) $2$ 114. $The mean deviation from the data 3, 10, 10, 4, 7, 10, 5 is$ (1) $2$ (2) $2.57$ (3) $3$ (4) $3.75$ 115. $The variance of the first 50 even natural numbers is$ (1) $\frac{833}{4}$ (2) $833$ (3) $437$ (4) $\frac{437}{4}$ 116. $The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12. If the new mean of the marks is 10.2. then their new variance is equal to$ (1) $4.04$ (2) $4.08$ (3) $3.96$ (4) $3.92$ 117. $The variance of the variates 112, 116, 120, 125 and 132 about their AM is$ (1) $58.8$ (2) $60$ (3) $48.8$ (4) $61.8$ 118. $Marks obtains by all the students of class 12 are presented in a freqency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is 18, then the total number of students is$ (1) $52$ (2) $48$ (3) $44$ (4) $40$ 119. $An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value of k when k consecutive heads are obtained for k = 3, 4, 5 otherwise X takes the value - 1 . Then the expected value of X, is :$ (1) $\frac{1}{8}$ (2) $- \frac{1}{8}$ (3) $\frac{3}{8}$ (4) $- \frac{3}{8}$ 120. $The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in place of 12 . If μ and σ^{2} denote the mean and variance of the correct observations respectively, then 15 (μ + μ^{2} + σ^{2}) is equal to$