Question

What term refers to the standard deviation of the sampling distribution?

Answer 1

Hint: The Standard Deviation in descriptive statistics is the degree of dispersion / scatter of data points relative to the mean. It is a measure of the deviation from the mean of the data points and describes how the values are distributed across the data sample. The square root of the variance is the standard deviation of the following: (sample, statistical population, random variable, data collection, or probability distribution).

Formula Used:
Standard deviation $\sigma = \sqrt {Variance} $
Standard error –
$S{E_s} = \dfrac{s}{{\sqrt n }}$, $s$ is the standard deviation and $n$ is the number of terms in the data set.

Complete step by step Solution:
The term which refers to the standard deviation of the sampling data is Standard error. Despite the fact that the mean of a given sampling distribution is known to be equal to the mean of the population, the standard error is known to be dependent on the population size, standard deviation, and sample size.
Let, the data set be $10,12,16,21,25$ and its standard deviation is $s = 6.22$
Then, using standard error formula, $S{E_s} = \dfrac{s}{{\sqrt n }}$
Here, $n$ is the number of terms in the given data
$ = \dfrac{{6.22}}{{\sqrt 5 }}$
$ = 2.82$
Therefore, the standard error of the data $10,12,16,21,25$ is $2.82$.

Note:The standard error is very similar to the standard deviation in that both measures how much data is spread out. The greater the number, the more widely distributed the data. Although the standard deviation and standard error are similar, there is one significant difference. The standard error is calculated using sample data, whereas the standard deviation is calculated using population data.