**The standard deviation**defined as an absolute measure of the dispersion of a series. Clarifies the standard amount of variation on both sides of the mean. It is often misunderstood with the standard error, since it is based on the standard deviation and the sample size.

**The standard error** it is used to measure the statistical accuracy of an estimate. It is mainly used in the hypothesis testing and interval estimation process.

These are two important statistics concepts, which are widely used in research. The difference between the standard deviation and the standard error is based on the difference between the description of the data and its inference.

### Comparative chart

Basis for comparison Standard deviation Standard errorSense | The standard deviation implies a measure of the dispersion of the set of values from their average. | The standard error connotes the measurement of the statistical accuracy of an estimate. |

statistical | Descriptive | inductive |

Measures | How many observations vary from each other. | How precise the meaning of the sample is for the average of the real population. |

Distribution | Distribution of the observation relative to the normal curve. | Distribution of an estimate relating to the normal curve. |

Formula | Square root of variance | Standard deviation divided by square root of the sample size. |

Increase in sample size | Provides a more specific measure of the standard deviation. | Reduces the standard error. |

### Definition of standard deviation

Standard deviation, a measure of the spread of a series or the distance from the standard. In 1893, Karl Pearson conceived the notion of standard deviation, which is undoubtedly the most widely used measure, in research studies.

the square root of the mean of the squares of the deviations from their mean. In other words, for a given data set, the standard deviation is the deviation from the quadratic mean, from the arithmetic mean. For the whole population, indicated by the Greek letter "sigma ()", and for a sample, represented by the Latin letter "s".

Standard deviation is a measure that quantifies the degree of dispersion of the set of observations. The further the data points are from the mean value, the greater the deviation within the data set, which represents that the data points are scattered over a wider range of values and vice versa.

**For unclassified data:****For the grouped frequency distribution:**

### Standard error definition

You may have observed that different samples, with identical dimensions, obtained from the same population, will give different statistical values taken into consideration, ie sample mean. Standard Error (SE) provides, the standard deviation in different values of the sample mean. used to compare sample means across populations.

In short, the standard error of a statistic is nothing more than the standard deviation of its sample distribution. It has a great role in testing the statistical hypothesis and estimating the interval. It gives an idea of the accuracy and reliability of the estimate. The smaller the standard error, the greater the uniformity of the theoretical distribution and vice versa.

**Formula**standard error for sample mean =**/ n**Where, the population standard deviation

## Key differences between standard deviation and standard error

The following points are substantial as regards the difference between the standard deviation:

- Standard deviation is the measure that evaluates the amount of variation in the set of observations. The standard error measures the accuracy of an estimate, that is, the measure of the variability of the theoretical distribution of a statistic.
- Standard deviation is a descriptive statistic, while standard error is an inferential statistic.
- The standard deviation measures how far the individual values are from the mean value. On the contrary, as much as the sample mean close to the population average.
- The standard deviation is the distribution of the observations with reference to the normal curve. On the contrary, the standard error is the distribution of an estimate with reference to the normal curve.
- The standard deviation defined as the square root of the variance. In contrast, the standard error described as the standard deviation divided by square root of the sample size.
- When the sample size is increased, it provides a more particular measure of the standard deviation. Unlike the standard error when the sample size is increased, the standard error tends to decrease.

### Conclusion

In general, the standard deviation considered one of the best dispersion measures, which measures the dispersion of values from the central value. On the other hand, the standard error is mainly used to verify the reliability and accuracy of the estimate and therefore, the smaller the error, the greater the reliability and accuracy.