Question

Symbols Identify the symbols used for each of the following: (a) sample standard deviation;(b) population standard deviation;(c) sample variance;(d) population variance.

Short answer

The following symbols are used:

(a) Sample standard deviation:$s$

(b) Population standard deviation:$\sigma$

(c) Sample variance:$s^2$

(d) Population variance:${\sigma }^2$

Step-by-step solution

Parameter and statistics

The various mathematical measures computed for the population are called theparameters, and those computed for the sample are called thestatistics.

The mean and variance of a population are categorized as parameters.

The mean and variance of a sample are categorized as statistics.

Symbols for parameter and statistics

Different symbols are used to denote parameters and statistics. Some of the commonly used symbols are as follows:

(a)

The notation s is used for the standard deviation of the sample.

(b)

The notation$\sigma$is used for the standard deviation of the population.

(c)

The notation$s^2$is used for the sample variance.

(d)

The notation${\sigma }^2$is used for the population variance.