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For \( 10 \) observations \( x_{1},x_{2},\ldots,x_{10} \), if and then their standard deviation is:

A set of four observations has mean \( 1 \) and variance \( 13 \). Another set of six observations has mean \( 2 \) and variance \( 1 \). Then, the variance of all these \( 10 \) observations is equal to:

If the mean deviation about the median of the numbers \( k, 2k, 3k, \ldots, 1000k \) is \( 500 \), then \( k^{2} \) is equal to:

Let \( X = \{ x \in N : 1 \le x \le 19 \} \) 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:

A data consists of \( 20 \) observations \( x_{1}, x_{2}, \ldots, x_{20} \). If \( \sum_{i=1}^{20} (x_{i}+5)^{2} = 2500 \) and \( \sum_{i=1}^{20} (x_{i}-5)^{2} = 100 \), then the ratio of mean to standard deviation of this data is:

The mean and variance of a data of \( 10 \) observations are \( 10 \) and \( 2 \), respectively. If an observations \( \alpha \) in this data is replaced by \( \beta \), then the mean and variance become \( 10.1 \) and \( 1.99 \), respectively. Then \( \alpha + \beta \) equals.

The mean deviation about the mean for the data

\( x_i \)	\( 5 \)	\( 7 \)	\( 9 \)	\( 10 \)	\( 12 \)	\( 15 \)
\( f_i \)	\( 8 \)	\( 6 \)	\( 2 \)	\( 2 \)	\( 2 \)	\( 6 \)

is equal to:

Let the mean and variance of \( 8 \) numbers \( -10, -7, -1, x, y, 9, 2, 16 \) be \( \frac{7}{2} \) and \( \frac{293}{4} \), respectively. Then the mean of \( 4 \) numbers \( x, y, x + y + 1, |x - y| \) is:

If the mean of the data

Class	\( 5\text{-}10 \)	\( 10\text{-}15 \)	\( 15\text{-}20 \)	\( 20\text{-}25 \)	\( 25\text{-}30 \)	\( 30\text{-}35 \)
Frequency	\( 2 \)	\( k \)	\( 28 \)	\( 54 \)	\( k+1 \)	\( 5 \)

is \( 21 \), then \( 1 \) is one of the roots of the equation:

10.

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:

11.

The mean and variance of \( n \) observations are \( 8 \) and \( 16 \), respectively. If the sum of the first \( (n-1) \) observations is \( 48 \) and the sum of squares of the first \( (n-1) \) observations is \( 496 \), then the value of \( n \) is:

12.

Let the mean and the variance of seven observations \( 2,\, 4,\, \alpha,\, 8,\, \beta,\, 12,\, 14 \), \( \alpha < \beta \), be \( 8 \) and \( 16 \) respectively. Then the quadratic equation whose roots are \( 3\alpha + 2 \) and \( 2\beta + 1 \) is:

13.

The mean and variance of \( 10 \) observations are \( 9 \) and \( 34.2 \), respectively. If \( 8 \) of these observations are \( 2, 3, 5, 10, 11, 13, 15, 21 \), then the mean deviation about the median of all the \( 10 \) observations is:

14.

Suppose that the mean and median of the non-negative numbers \( 21, 8, 17, a, 51, 103, b, 13, 67 \), \( (a > b) \), are \( 40 \) and \( 21 \), respectively. If the mean deviation about the median is \( 26 \), then \( 2a \) is equal to:

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JEE Main 2026 22nd Jan Evening Shift

If the mean deviation about the median of the numbers \( k, 2k, 3k, \ldots, 1000k \) is \( 500 \), then \( k^{2} \) is equal to:

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