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Question 1

The number of values of a $\in$ N such that the variance of 3, 7, 12, a, 43 $-$ a is a natural number is :

Question 2

1.

Consider the statistics of two sets of observations as follows :

	Size	Mean	Variance
Observation I	10	2	2
Observation II	n	3	1

If the variance of the combined set of these two observations is $${{17} \over 9}$$, then the value of n is equal to ___________.

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Question 3

1.

Let the mean and the variance of 20 observations $x_{1}, x_{2}, \ldots, x_{20}$ be 15 and 9 , respectively. For $\alpha \in \mathbf{R}$ , if the mean of $\left(x_{1}+\alpha\right)^{2},\left(x_{2}+\alpha\right)^{2}, \ldots,\left(x_{20}+\alpha\right)^{2}$ is 178 , then the square of the maximum value of $\alpha$ is equal to ________.

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Question 4

Let in a series of 2n observations, half of them are equal to a and remaining half are equal to $-$ a. Also by adding 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 a² + b² is equal to :

Question 5

Let the mean and the variance of 6 observations $a, b, 68,44,48,60$ be $55$ and $194$ , respectively. If $a>b$ , then $a+3 b$ is

Question 6

1.

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 $\frac{31}{40}$ and $a_{3}+a_{4}+a_{5}=14$ , then $m+n$ is equal to ___________.

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Question 7

If mean and standard deviation of 5 observations x₁, x₂, x₃, x₄, x₅ are 10 and 3, respectively, then the variance of 6 observations x₁, x₂, ….., x₅ and –50 is equal to

Question 8

The mean and the standard deviation(s.d.) of five observations are9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :

Question 9

The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is -

Question 10

If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is :

Statistics

Statistics