Sampling Fraction

Sample

Any part of a population is called a sample. A study of a sample enables us to make some decisions about the properties of the population. The number of units included in the sample is called the size of the sample and is denoted by $n$. A good sample is one which exemplifies the qualities of the population. A sample study leads us to make some inferences about the population measures. This process is called sampling.

Parameter and Statistic

Any measure of the population is called a parameter and the word statistic is used for any value calculated from the sample. The population mean $\mu$ is a parameter and the sample mean $\overline X$ is a statistic. The sample mean $\overline X$ is used to estimate the population mean $\mu$. Similarly, the population variance ${\sigma ^2}$ is a parameter and the sample variance ${S^2}$ is a statistic. In general, the symbol $\theta$ is used for a parameter and the symbol $\widehat \theta$ is used for a statistic. The value of the parameter is mostly unknown and the sample statistic is used to make some inferences about the unknown parameter.

Sampling Fraction

If the size of the population is $N$ and the size of the sample is $n$, the ratio $\frac{n}{N}$ is called the sampling fraction. If $N = 100,{\text{ }}n = 10$, the ratio $\frac{n}{N} = \frac{{10}}{{100}} = \frac{1}{{10}}$. This means that on average, $10$ units of the population will be represented by one unit in the sample. If the sampling fraction $\frac{n}{N}$ is multiplied by $100$, we get the sampling fraction in percentage form. Thus, $\frac{n}{N} \times 100 = \frac{{10}}{{100}} \times 100 = 10\%$. This means $10\%$ of the population is included in the sample.