Difference Between Standard Deviation and Standard Error with Proper Definition and Brief Explanation

Standard deviation It is defined as an absolute measure of dispersion of a series. Clarify the standard amount of variation on each side of the mean. It is often misinterpreted with the standard error as it is based on the standard deviation and the sample size.

Standard error Used to measure the statistical precision of an estimate. It is mainly used in the process of hypothesis testing and estimation interval.

These are two important concepts in statistics, which are widely used in the field of 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.

Content: Standard Deviation Vs Standard Error

  1. Comparative graph
  2. Definition
  3. Key differences
  4. conclusion

Comparative graph

Basis for comparison Standard deviation Standard error
Sense The standard deviation implies a measure of dispersion of the set of values ​​of its mean. Standard error connotes the measure of statistical accuracy of an estimate.
Statistics Descriptive Inferential
Measures How many observations vary from each other? How accurate is the sample relative to the true population?
Distribution Distribution of the observation on the normal curve. Distribution of an estimate relative to the normal curve.
Formula Square root of variance Standard deviation divided by the square root of the sample size.
Increased sample size. Give a more specific measure of standard deviation. Decrease the standard error.

Definition of standard deviation

The standard deviation is a measure of the extension of a series or the distance from the norm. In 1893, Karl Pearson coined the notion of standard deviation, which is undoubtedly the most widely used measure, in research studies.

It is the square root of the mean of squares of deviations from its mean. In other words, for a given data set, the standard deviation is the mean square deviation of the arithmetic mean. For the entire population, it is indicated by the Greek letter ‘sigma (σ)’, and for a sample, it is represented by the Latin letter ‘s’.

The 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 spread out over a wider range of values ​​and vice versa.

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

Definition of standard error

You may have observed that different samples, of identical size, drawn from the same population, will give different statistical values ​​under consideration, that is, sample mean. The standard error (SE) provides the standard deviation at different values ​​of the sample mean. It is used to make a comparison between sample means in the populations.

In short, the standard error of a statistic is nothing more than the standard deviation of its sampling distribution. It has a great role to play statistical hypothesis testing and interval estimation. 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 the sample mean = σ / √n
    Where, σ is the standard deviation of the population

Key differences between standard deviation and standard error

The points listed below are substantial when it comes to the difference between the standard deviation:

  1. The standard deviation is the measure that evaluates the amount of variation in the set of observations. The standard error measures the precision of an estimate, that is, it is the measure of the variability of the theoretical distribution of a statistic.
  2. The standard deviation is a descriptive statistic, while the standard error is an inferential statistic.
  3. The standard deviation measures how far the individual values ​​are from the mean value. Rather, how close is the sample mean to the population mean?
  4. The standard deviation is the distribution of observations with reference to the normal curve. In contrast to this, the standard error is the distribution of an estimate with reference to the normal curve.
  5. The standard deviation is defined as the square root of the variance. Conversely, the standard error is described as the standard deviation divided by the square root of the sample size.
  6. As the sample size increases, it provides a more particular measure of the standard deviation. Unlike the standard error, when the sample size increases, the standard error tends to decrease.


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

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