Statistics PYQs - Last 5 Years

Let the six numbers \(\mathrm{a_1,a_2,a_3,a_4,a_5,a_6}\), be in A.P. and \(\mathrm{a_1+a_3=10}\). If the mean of these six numbers is \(\frac{19}{2}\) and their variance is \(\sigma^2\), then 8\(\sigma^2\) is equal to :

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 :

Let \(9=x_{1} < x_{2} < \ldots < x_{7}\) be in an A.P. with common difference d. If the standard deviation of \(x_{1}, x_{2}..., x_{7}\) is 4 and the mean is \(\bar{x}\), then \(\bar{x}+x_{6}\) is equal to :

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 :

Let the mean of the data

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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 _________

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 $$...

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 fr...

Let the mean of 6 observations \(1,2,4,5, \mathrm{x}\) and \(\mathrm{y}\) be 5 and their variance be 10 .

Then their mean deviation about the mean is equal to :

If the mean of the frequency distribution

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Let \(\mu\) be the mean and \(\sigma\) be the standard deviation of the distribution

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Let the mean and the variance of 5 observations x1, x2, x3, x4, x5 be \({24 \over 5}\) and \({194 \over 25}\) respectively. If the mean and variance of the first 4 observation are \({7 \over 2}\) and a respectively, then (4a + x5) is equal ...

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

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}+\...

The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to _____________.

Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their variance is 20. A student fails in the examination if he/she gets less than 50 marks, then in worst case, the number of stud...

Let \(x_{1}, x_{2}, x_{3}, \ldots, x_{20}\) be in geometric progression with \(x_{1}=3\) and the common ratio \(\frac{1}{2}\). A new data is constructed replacing each \(x_{i}\) by \(\left(x_{i}-i\right)^{2}\). If \(\bar{x}\) is the mean of...

The mean and variance of the data 4, 5, 6, 6, 7, 8, x, y, where x < y, are 6 and \({9 \over 4}\) respectively. Then \({x^4} + {y^2}\) is equal to :

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 _____________.

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 :

The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct v...

The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If \(\sigma\) is the standard deviation of the data after omitting the two wrong ob...

If the mean deviation about the mean of the numbers 1, 2, 3, .........., n, where n is odd, is \({{5(n + 1)} \over n}\), then n is equal to ______________.

If the mean deviation about median for the numbers 3, 5, 7, 2k, 12, 16, 21, 24, arranged in the ascending order, is 6 then the median is :