Question

The variance of a sample of 121 observations equals 441. The standard deviation of the sample equals

A. 11

B. 21.

C. 31

D. 45

Answer 1

Concepts and reason

The variance is always in squared units. Therefore, it is always recommended to find the square root of the variance which is known as standard deviation. The standard deviation is a standard measure to define the variability in the data.

Compute the squared difference of individual observations from mean, multiply them by the probability density function and integrate them over the range to find ${s^2}$ .

Fundamentals

The sample variance is the second central moment about mean. The formula for sample variance of a continuous variable is:

${s^2} = \int_{ - \infty }^\infty {{{\left( {x - \mu } \right)}^2}f\left( x \right)dx}$

The sample standard deviation is:

$s = \sqrt {{s^2}}$

The variance of a population is a term which shows variability in the sample data. The units of variance are in terms of squared units of the variable. To fix this scalability issue, the square root of the variance is taken and standard deviation is listed.

The standard deviation is calculated as:

$\begin{array}{c}\\s = \sqrt {441} \\\\ = 21\\\end{array}$

Ans:

The sample standard deviation is $21$ .