Statistics PYQs Set 5 (PDF)

Set 5 of 6 · Questions 121-150 of 171

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Statistics · Set 5 (Q121-150)
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121. $For a statistical data x_{1}, x_{2}, \dots, x_{10} of 10 values, a student obtained the mean as 5.5 and \sum_{i = 1}^{10} x_{i}^{2} = 371 . He later found that he had noted two values in the data incorrectly as 4 and 5, instead of the correct values 6 and 8, respectively. The variance of the corrected data is$ (1) $9$ (2) $5$ (3) $7$ (4) $4$ 122. $Let the mean and variance of 7 observations 2, 4, 10, x, 12, 14, y, x > y, be 8 and 16 respectively. Two numbers are chosen from 1, 2, 3, x-4, y, 5 one after another without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4 , is :$ (1) $\frac{3}{5}$ (2) $\frac{1}{3}$ (3) $\frac{2}{5}$ (4) $\frac{4}{5}$ 123. $Let the median and the mean deviation about the median of 7 observation 170, 125, 230, 190, 210, a, b be 170 and \frac{205}{7} respectively. Then the mean deviation about the mean of these 7 observations is :$ (1) $31$ (2) $28$ (3) $30$ (4) $32$ 124. $If the sum of squares of the deviations from the mean of the data x_{i}, (i = 1, 2, \dots, n) is n x^{2}, where x is the mean of x_{1}'s, then the sum of squares of x_{i}'s is$ (1) $4 n x^{- 2}$ (2) $3 n x^{- 2}$ (3) $12 n x^{- 2}$ (4) $2 n x^{2}$ 125. $If the mean and the variance of the data Class Frequency 4 - 8 3 8 - 12 λ 12 - 16 4 16 - 20 7 are μ and 19 respectively, then the value of λ + μ is$ (1) $21$ (2) $19$ (3) $20$ (4) $18$ 126. $The variance of 20 observations is 5 . If each observation is multiplied by 2 , then variance of resulting observations is$ (1) $5$ (2) $10$ (3) $4$ (4) $20$ 127. $If the mean and variance of five observations are \frac{24}{5} and \frac{194}{25} respectively and the mean of first four observations is \frac{7}{2}, then the variance of the first four observations in equal to$ (1) $\frac{4}{5}$ (2) $\frac{77}{12}$ (3) $\frac{5}{4}$ (4) $\frac{105}{4}$ 128. $For observations x_{i} given \sum (x_{i} - 5) = 10 and \sum (x_{i} - 5)^{2} = 40 . If mean and variance of observations (x_{1} - 3), (x_{2} - 3) \dots (x_{10} - 3) is λ & μ respectively then ordered pair (λ, μ) is$ (1) $(3, 3)$ (2) $(1, 3)$ (3) $(3, 1)$ (4) $(1, 1)$ 129. $Let the mean of 6 observations 1,2,4,5, x and y be 5 and their variance be 10. Then their mean deviation about the mean is equal to$ (1) $\frac{7}{3}$ (2) $3$ (3) $\frac{8}{3}$ (4) $\frac{10}{3}$ 130. $Let μ be the mean and a be the standard deviation of the distribution X_{i} 012345 f_{i} k+2 2k k^{2} -1 k^{2} -1 k^{2} +1 k-3 where \sum_{i}^{f} = 62. If [x] denotes the greatest integer \leq x, then [μ^{2} + σ^{2}] is equal to$ (1) $9$ (2) $8$ (3) $7$ (4) $6$ 131. $The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of the remaining 5 observations is :$ (1) $\frac{92}{5}$ (2) $\frac{134}{5}$ (3) $\frac{536}{25}$ (4) $\frac{112}{5}$ 132. $Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of A and adding 2 to each element of B. Then the sum of the mean and variance of the elements of C is$ (1) $40$ (2) $32$ (3) $38$ (4) $36$ 133. $The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observations are:$ (1) $10,11$ (2) $3,18$ (3) $8,13$ (4) $1,20$ 134. $Let the mean and variance of 12 observations be \frac{9}{2} and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is \frac{m}{n}, where m and n are coprime, then m + n are coprime, then m + n is equal to$ (1) $315$ (2) $316$ (3) $314$ (4) $317$ 135. $If the mean and variance of the following data: 6,10,7,13,a,12,b,12 are 9 and \frac{37}{4} respectively, then (a - b)^{2} is equal to:$ (1) $24$ (2) $12$ (3) $32$ (4) $16$ 136. $Let the mean and the variance of 5 observations x_{1}, x_{2}, x_{3}, x_{4}, x_{5} be \frac{24}{5} and \frac{194}{25} respectively. If the mean and variance of the first 4 observation are \frac{7}{2} and a respectively, then (4a + x_{5}) is equal to:$ (1) $13$ (2) $15$ (3) $17$ (4) $18$ 137. $The mean and variance of the data4, 5, 6, 6, 7, 8, x, y where x < y are 6, and \frac{9}{4} respectively. Then x^{4} + y^{2} is equal to$ (1) $162$ (2) $320$ (3) $674$ (4) $420$ 138. $The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded as 50 instead of 40. Then the correct variance is$ (1) $11$ (2) $13$ (3) $12$ (4) $14$ 139. $The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M is equal to:$ (1) $60$ (2) $55$ (3) $50$ (4) $45$ 140. $If the variance of the following frequency distribution: Class : 10:20 20:30 30:40 Frequency : 2 x 2 is 50, then x is equal to:$ 141. $Let a, b, c \in N and a < b < c . Let the mean, the mean deviation about the mean and the variance of the 5 observations 9, 25, a, b, c be 18,4 and \frac{136}{5}, respectively. Then 2 a + b - c is equal to_______$ 142. $The mean of 10 numbers 7 \times 8, 10 \times 10, 13 \times 12, 16 \times 14,\dots.is .$ 143. $If the mean of the frequency distribution Class: 0-10 10-20 20-30 30-40 40-50 Frequency: 2 3 x 5 4 is 28, then its variance is _____$ 144. $The maximum value of z in the following equation z = 6 xy + y^{2}, where 3 x + 4 y \leq 100 and 4 x + 3 y \leq 75 for x \geq 0 and y \geq 0 is____ (Round off to the Nearest Integer)$ 145. $An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of marks obtained by 30 girls is also 2. The average marks of all 50 candidates is 15. If μ is the average marks of girls and σ^{2} is the variance of marks of 50 candidates, then μ + σ^{2} is equal to .$ 146. $Let the mean and variance of 8 numbers x, y, 10, 12, 6,12, 4, 8 be 9 and 9. 25 respectively. If x > y, then 3x-2y is equal to________$ 147. $The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is __________.$ 148. $Consider the statistics of two sets ofobservations as follows: Size Mean Variance Observation I 1022 Observation II n 31 If the variance of the combined set of these twoobservations is \frac{17}{9 ¯}, then the value of n is equal to____$ 149. $Consider the following frequency distribution class 10-20 20-30 30-40 40-50 50-60 Frequency α 1105430 β If the sum of all frequencies is 584 and median is 45, then ∣ α - β ∣ is equal to$ 150. $Let the mean of the data x 13579 Frequency (f) 42428 α 8 be 5. If m and α^{2} are respectively the mean deviation about the mean and the variance of the data, then \frac{3 α}{m + σ ^{2}} is equal to________.$