List of top Mathematics Questions on Variance and Standard Deviation asked in KEAM

Given the data: 5, 7, 9, 11, 13. The variance of the data, is

The variance for the data: $65, 70, 75$ is

The variance of 240, 260, 270, 280 is ________.

If the standard deviation of six numbers \(x_1,x_2,x_3,x_4,x_5,x_6\) is \(4\), then the variance of \(2x_1+3,2x_2+3,2x_3+3,2x_4+3,2x_5+3,2x_6+3\) is

The standard deviation of 1, 2, 3, ..., 100 is:

The standard deviation of the numbers \( -3, 0, 3, 8 \) is

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

The standard deviation of the data \( 6, 5, 9, 13, 12, 8, 10 \) is

The standard deviation of the data \( 6, 5, 9, 13, 12, 8, 10 \) is

The standard deviation of the data \( 6, 5, 9, 13, 12, 8, 10 \) is

Variance of first 20 natural numbers

The standard deviation of the data \( 6, 5, 9, 13, 12, 8, 10 \) is

Standard deviation of first \( n \) odd natural numbers is:

In an experiment with 15 observations on \( x \), the results \( \sum x^2 = 2830 \) and \( \sum x = 170 \) were available. One observation (20) was wrong and was replaced by 30. The corrected variance is:

If the mean of the numbers $a, b, 8, 5, 10$ is $6$ and their variance is $6.8$, then $ab$ is equal to:

The mean of five observations is 4 and their variance is $5.2$. If three of these observations are $2, 4$ and $6$, then the other two observations are

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