Statistics PYQs Set 6 (PDF)

Set 6 of 6 · Questions 151-171 of 171

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Statistics · Set 6 (Q151-171)
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151. $The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation 13.44, then the standard deviation of the second sample is :$ (1) $8$ (2) $6$ (3) $4$ (4) $5$ 152. $Let x_{1}, x_{2}, \dots, x_{10} be ten observations such that \sum_{i = 1}^{10} (x_{i} - 2) = 30, \sum_{i = 1}^{10} (x_{i} - β)^{2} = 98, β > 2, and their variance is \frac{4}{5} . If μ and σ^{2} are respectively the mean and the variance of 2 (x_{1} - 1) + 4 β, 2 (x_{2} - 1) + 4 β, \dots, 2 (x_{10} - 1) + 4 β, then \frac{β μ}{σ ^{2}} is equal to:$ (1) $100$ (2) $120$ (3) $110$ (4) $90$ 153. $The means of two groups of observations A and B are x, y respectively and their standard deviations are respectively 2 and 3. In order that the group A is to be more consistent than the group B, \frac{x}{y} >$ (1) $\frac{3}{2}$ (2) $\frac{5}{1}$ (3) $\frac{2}{3}$ (4) $\frac{6}{5}$ 154. $The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5 then the sum of cubes of the remaining two observations is$ (1) $1072$ (2) $1792$ (3) $1216$ (4) $1456$ 155. $Statement (I) : The range of the ungrouped data does not change even if certain intermediate observations are removed. Statement (II) : The value of the mean deviation of an ungrouped data about the median is always less than or equal to the value of the mean deviation computed about any other measure of central tendency. Statement (III) : For a grouped data, range is approximated as the difference between the lower limit of the largest class and the upper limit of the smallest class.$ (1) $Statements I and II are true but statement III is false$ (2) $Statements II and III are true but statement I is false$ (3) $Statements III and I are true but statement II is false$ (4) $Statements I, II and III are true$ 156. $Which one of the following is false?$ (1) $Mean deviation from the mean and the Mean deviation from the Median must always be equal.$ (2) $The measure of variability which is a number independent of units, is called the coefficient of variation$ (3) $The coefficient of variation is a relative measure of variation$ (4) $Among two given data, the one having greater coefficient of variation is said to have more variability than the other.$ 157. $Let O be the mean deviation of the first five odd natural numbers about their mean and P be the mean deviation of the first five prime numbers about their mean. Then P - O is equal to$ (1) $0.3$ (2) $0.32$ (3) $0.23$ (4) $0.2$ 158. $If α, β, γ are the mean deviations about the mean, median and mode of the data 1, 2, 2, 3, 3, 3, 4, 6 respectively, then$ (1) $α < β < γ$ (2) $α = β = γ$ (3) $α \neq = β = γ$ (4) $β < α < γ$ 159. $Let an angle of a triangle is 60^{\circ} . If the variance of the angles of the triangle is 1014^{\circ}, then the other two angles are$ (1) $23^{\circ} and 97^{\circ}$ (2) $22^{\circ} and 98^{\circ}$ (3) $21^{\circ} and 99^{\circ}$ (4) $20^{\circ} and 100^{\circ}$ 160. $The standard deviation of a, a + d, a + 2 d, \dots, a + 2 n d is$ (1) $n d$ (2) $n^{2} d$ (3) $\frac{n ( n + 1 )}{3} d$ (4) $\frac{n ( n + 3 )}{3} d$ 161. $The mean deviation from the median of the data 16, 22, 3, 14, 5, 10, 8, 6, 11, 4 is$ (1) $5$ (2) $5.7$ (3) $4.7$ (4) $4$ 162. $The variance of the following data is x_{i} 6101418242830 f_{i} 24712843$ (1) $33.4$ (2) $34.3$ (3) $43.4$ (4) $44.3$ 163. $If the mean of 10 observations is 50 and the sum of the squares of the deviations of the observations from the mean is 250, then the coefficient of variation of those observations is$ (1) $25$ (2) $50$ (3) $10$ (4) $5$ 164. $The mean deviation about the mean for the following data Marks obtained 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Number of Boys 681042 is$ (1) $9.33$ (2) $5.6$ (3) $8.33$ (4) $9.6$ 165. $p, x_{1}, x_{2} \dots, x_{n} and q, y_{1}, y_{2}, \dots, y_{n} are two arithmetic progressions with common differences a and b respectively. If α and β are the arithmetic means of x_{1}, x_{2}, \dots . x_{n}, and y_{1}, y_{2}, \dots, y_{n} respectively. Then the locus of P (α, β) is$ (1) $a (x - p) = b (y - q)$ (2) $b (x - p) = a (y - q)$ (3) $α (x - p) = β (y - q)$ (4) $p (x - α) = q (y - β)$ 166. $The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14 is omitted and a and b are respectively mean and variance of remaining 6 observations, then a + 3 b - 5 is equal to$ 167. $If the variance of the frequency distribution x_{i} : 2, 3, 4, 5, 6, 7, 8 Frequency f_{i} : 3, 6, 16, α, 9, 5, 6 is 3, then α is equal to ______$ 168. $Consider the data on x taking the values 0, 2, 4, 8, \dots, 2^{n} with frequencies^{n} C_{0},^{n} C_{1},^{n} C_{2}, \dots,^{n} C_{n} respectively. If the mean of this data is \frac{728}{2 ^{n}} then n is equal to:$ 169. $Let the mean and variance of four numbers 3, 7, x andy(x > y) be 5 and 10 respectively. Then the mean of four numbers 3 + 2x, 7 + 2y, x + y and x - y is.$ 170. $The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 were wrongly read as 45 and 50 respectively. Then the correct variance is$ 171. $Let the positive numbers a_{1}, a_{2} a_{3}, a_{4} and a_{5} be in a G.P. Let their mean and variance be \frac{31}{10} and \frac{m}{n} respectively, where m and n are co-prime. If the mean of their reciprocals is \frac{31}{10} and a_{3} + a_{4} + a_{5} = 14, then m + n is equal to____________.$