Question

What is the meaning of sampling distribution?

Answer 1

Hint: A sample distribution is similar to a probability distribution of a statistic that we choose from random samples of a given population. It is also known as a finite sample distribution, it represents the distribution of frequencies for how to spread apart various outcomes for a specific population.

Complete step-by-step solution:
A sampling distribution is a probability distribution of a statistic obtained from a larger number of samples drawn from a specific population. The sampling distribution of a given population is the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population.
The sample mean refers to the average value found in a sample. A sample is just a small part of a whole data. The sample mean is useful when we have to estimate what the whole population is doing.
Finding the mean of the sampling distribution is easy, since it is equal to the population.
Formula of sample mean is $\overline X = \dfrac{{\sum {{x_i}} }}{n}$
Where $\overline X $ just stands for the “sample mean”.
$\sum {} $ is summation notation.
${x_i}$ all of the x-values.
$n$ is the number of items in the sample mean.
e.g., For samples of any size drawn from a normally distributed population, the sample mean is normally distributed, with mean \[\mu X = \mu \] and standard deviation $\sigma X = \dfrac{\sigma }{{\sqrt n }}$, where $n$ is the sample size.

Note: The sampling distribution depends on multiple factors such as statistics, sample size, sampling process and the overall population. It is used to help calculate statistics such as means , ranges, variances and standard deviations for the given sample.