# Why are Measures of Dispersion Important?

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While quantities such as the mean, median, and the mode give us some idea about the central tendency of the data they give us no understanding of the spread of the data values. This information is given to us by the measures of dispersion. In this article, we explain the importance of measures of dispersion and why they are needed in statistics.

### Need/Importance of Measures of Dispersion:

#### 1. Test the reliability of an average:

Measures of variation are used to test to what extent an average represents the characteristic of a data set. If the variation is small, that is, the extent of dispersion or scatter is less on each side of an average, then it indicates a high uniformity of values in the distribution and the average represents an individual value in the data set. On
the other hand, if the variation is large, then it indicates a lower degree of uniformity in values in the data set, and the average may be unreliable. No variation indicates perfect uniformity and, therefore, values in the data set are identical.

#### 2. Control the variability:

Measuring variation helps to identify the nature and causes of variation. Such information is useful in controlling the variations. In matters of health, variations in body temperature, pulse beat, and blood pressure are the basic guides to diagnosis. The prescribed treatment is designed to control their variation. In industrial production, the efficient operation requires control of quality variation, the causes of which are found through inspection and quality control programs. In social science, the measurement of ‘inequality’ in the distribution of income and wealth requires the measurement of variability.

#### 3. Compare two or more data sets

Measures of variation help in the comparison of the spread in two or more sets of data with respect to their uniformity or consistency. For example, the measurement of variation in share prices and their comparison with respect to different companies over a period of time requires the measurement of variation. The measurement of variation in the length of stay of patients in a hospital every month may be used to set staffing levels, number of beds, number of doctors, and other trained staff, patient admission rates, and so on.

#### 4. Facilitate the use of other statistical techniques

Measures of variation facilitate the use of other statistical techniques such as correlation and regression analysis, hypothesis testing, forecasting, quality control, and so on.

References:

Fundamentals of Business Statistics – JK Sharma