Standard Error of The Mean – Definition, Explanation and Solved Examples

# Standard Error of The Mean – Definition, Explanation and Solved Examples

## Standard Error of the Mean Definition

The standard error of the mean (SEM) is a measure of the variability of the sample mean. It is calculated as the standard deviation of the sample mean divided by the square root of the sample size. The SEM is a measure of the precision of the sample mean.

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## Standard Error of Mean

The standard error of the mean (SEM) is a statistic that measures the variability of the sample mean around the population mean. It is calculated as the standard deviation of the sample mean divided by the square root of the sample size. The SEM is a measure of the precision of the sample mean.

The SEM is used to calculate confidence intervals for the population mean. A 95% confidence interval is calculated as the population mean ± 1.96 SEM. This means that there is a 95% probability that the population mean lies within 1.96 SEM of the sample mean.

The SEM can also be used to calculate the probability of obtaining a sample mean that is different from the population mean. This is known as the p-value. The p-value is the probability of obtaining a sample mean that is more extreme than the sample mean. The smaller the p-value, the more likely it is that the sample mean is different from the population mean.

## How to Calculate Standard Error of Mean

The standard error of the mean (SEM) is a measure of the variability of the sample mean around the population mean. It is calculated as the standard deviation of the sample mean divided by the square root of the sample size.

The SEM is important because it is used to calculate confidence intervals around the population mean. A 95% confidence interval means that there is a 95% probability that the population mean lies within the confidence interval.

## 1. Calculate the Standard Error of the Mean for the Given Data: 5,10,15,20,25.

The Standard Error of the Mean is 2.5.

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