Standard Deviation as a measure of dispersion

Standard deviation is a statistical measure of dispersion or variability that indicates how much the individual data points deviate from the mean or average value. It is a widely used measure of dispersion in statistical analysis and has some desirable mathematical properties, which are discussed below:

Properties of Standard Deviation:

1. It considers all data points: Standard deviation takes into account all the data points in a distribution and gives equal importance to each of them.

2. It is sensitive to outliers: Standard deviation is sensitive to outliers, which are extreme values that lie far away from the other data points. It reflects the variability of the data more accurately than measures of central tendency such as mean or median.

3. It is the most commonly used measure of dispersion: Standard deviation is the most widely used measure of dispersion because of its desirable mathematical properties.

4. It is based on squared deviations: Standard deviation is based on the squared deviations of each data point from the mean. Squaring the deviations ensures that all deviations are positive and eliminates the problem of negative deviations cancelling out positive deviations.

5. It is easy to use in statistical analysis: Standard deviation is easy to calculate and interpret, making it a popular measure of dispersion in statistical analysis.

Conclusion:

Therefore, Standard deviation is the best measure of dispersion because of its desirable mathematical properties, which make it easy to use and interpret in statistical analysis.

Standard deviation (SD) is the most commonly used measure of dispersion. It is a measure of spread of data about the mean. SD is the square root of sum of squared deviation from the mean divided by the number of observations.It is based on all values and thus, provides information about the complete series. Because of this reason, a change in even one value affects the value of standard deviation and it is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.