 # Sampling Error Formula

The sampling error formula, as the name suggests, is used to calculate the overall sampling error in statistical analysis. To recall, statistical error arising out of nature of sampling is known as sampling error. The error in statistical analysis arises because of the unrepresentativeness of the observation in the samples taken.

For example, the weight of two thousand citizens from a country of two million is taken and the average weight is taken out from that, then it’s not the same as the average weight of the two million people in the country.

Since to determine the characteristics of a whole population the sampling is done, the difference between the sample values and population is called sampling error. We should note that the exact value of sampling cannot be done since the population value if not known although often sampling error can be found out by probabilistic modelling of a sample.

Thus, the sampling error formula is given by:

$\large Sampling\;Error=\pm \sqrt{\frac{2500}{Sample\;Size}}\times 1.96$

### Solved Examples

Question: What is the sampling error if the average weight of 60 men is 58 kg?

Solution: Sampling error can be found out using the formula: $=\pm \sqrt{\frac{2500}{Sample\;Size}}\times 1.96$

= $\pm \sqrt{\frac{2500}{60}}\times 1.96$

= $\pm 12.65$