# Standard Error

In statistics, the standard error is the term used in the case of standard deviation. The sample mean of a data is generally varied from the actual population mean. It is represented as SE. It is used to measure the amount of accuracy by which the given sample represents its population. Statistics is a vast topic in which we learn about data, sample and population, mean, median, mode, dependent and independent variables, standard deviation, variance, etc.

## Standard Error Formula

The accuracy of a sample that describes a population is identified through SE formula. The sample mean which deviates from the given population and that deviation is given as;

Where S is the standard deviation and n is the number of observation.

## Standard Error of the Mean (SEM)

The standard error of the mean is represented as the standard deviation of the measure of sample mean of the mean of population. It is abbreviated as SEM. For example, normally, the estimator of population mean is the sample mean. But, if we draw another sample from the same population, it may provide distinct value.

Thus, there would be a population of the sampled means having its distinct variance and mean. It may be defined as the standard deviation of such sample means of all the possible samples taken from the same given population. SEM defines an estimate of standard deviation which has been computed from the sample. It is calculated as the ratio of the standard deviation to the root of sample size, such as:

.

Where s is the standard deviation and n is the number of observation.

### Standard Error of Estimate (SEE)

The deviation of some estimate from intended values is given by standard error of estimate formula. It is denoted as SEE.

Where, xi stands for data values, x bar is the mean value and n is the sample size.

### Example

Calculate the standard error of the given data:

y: 5, 10, 12, 15, 20

Solution: First we have to find the mean of the given data;

Mean = (5+10+12+15+20)/5 = 62/5 = 10.5

Now, the standard deviation can be calculated as;

S = Summation of difference between each value of given data and the mean value/Number of values.

Hence,

After solving the above equation, we get;

S = 5.35

Therefore, SE can be estimated with the formula;

SE = S/√n

SE = 5.35/√5 = 2.39. Ans.