## Short Questions and Answers about Measure of Dispersion

This page contains short questions and answers about Measure of Dispersion which includes introduction to measure of Dispersion or variation, different types of dispersion such as range, standard deviation, variance, interquartile deviation, mean deviation etc.

**Variability **is the **spread** or **dispersion** in a data set. Variability/ dispersion means the extent to which the data/values are spread out from the average value. Consider the following sets of data.

- 9, 9, 9, 9, 9, 9, 9, 9, 9, 9
- 10, 6, 2, 8, 4, 14, 16, 12
- 13 10, 7, 6, 21, 3, 7, 5

Finding of deviation is important in real life because it helps in data analysis and compiling it easily.

Average (Arithmetic mean) of absolute deviations of values from suitable average is called mean or **average deviation**. For a given data set of numbers, having its mean, we can find the difference between each of the numbers and the mean. If we take the mean of these differences, the result is called the mean deviation of the numbers. Absolute deviations means all the deviations (differences) are taken as positive i.e. absolute values are taken.

**Dispersion ** is used to studied to observe the degree to which the data tend to spread about its average in data. There are many situations in which two different data having the same average but different variation spread or dispersion. e.g.

*Data 1:* 5, 5, 5, 5, 5 having mean=5 i.e. $\overline{x}=5$

*Data 2:* 1, 5, 6, 6, 7 having mean=5 i.e. $\overline{x}=5$

Hence in such a situation we, need another measure which tell us how dispersed the different data set are. The measure used for this purpose is called Measure of Dispersion. There are two types of measures of dispersion used for this purpose:

- Absolute Measures of Dispersion
- Relative Measures of Dispersion

Quantities that measure the dispersion in the same units as the units of data are called absolute measures of dispersion. Absolute measures of dispersions cannot be used to compare the variation of two or more data set measured in different units. Following are examples of Absolute measures of dispersions.

Quantities that measure the dispersion in the form of ratio, percentage or coefficient are called **relative measures of dispersion**. These quantities have no unit of measurement and dimension and are used to compare the dispersion in two or more data sets measured in different units. Commonly used measure of relative dispersions are:

- Coefficient of Range
- Coefficient of Quartile Deviation
- Coefficient of Mean Deviation
- Coefficient of Variation
- Coefficient of standard deviation

**Mean deviation from median ** is defined as the average deviations of the values from their median. In mean deviation the deviations are taken without considering algebraic signs i.e absolute deviation is taken. The median deviation of a set of *n* values $X_1, X_2, \cdots,X_n$, denoted by **M.D.**, is given by $M.D = \frac{\sum| X – median |}{n}$, where $| X – median |$ indicate the absolute deviations of the observations from the median of a sample and *n* is number of observation in data set.