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Maths > Statistics > Range and Mean Deviation

Range and Mean Deviation

The field of statistics has practical applications in almost all fields of life. In finance and investing and manufacturing and various other fields. Whether you want to launch a rocket or calculate a students performance we take the help of statistics. Now let us learn the concepts of range and mean deviation.

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Range and Mean Deviation

For a given series of data, statistics aims at analysis and drawing conclusions. The various measures of central tendency – mean, median and mode represent the values in a series. However, we can further implement this analytical claim of statistics, by measuring the scattering and dispersion of data around these measures of central tendency.

For example, the range, in a series of men distributed by their ages, gives us an idea of how much the ages can vary from the central value. So without further ado, let us jump right into the concepts of range and mean deviation.

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The range can be simply understood as the value that tells us about the scattering of data. This gives us an idea of how much the data can vary. Consequently, it is related to the maximum and minimum values in a distribution. The range is the difference between the maximum and the minimum value in a distribution. Notably, it only gives us the idea of the spread of data. It does not tell us about the dispersion of values from a measure of central tendency.

Range = Maximum value – Minimum value

Mean Deviation

Range and Mean Deviation

To understand the dispersion of data from a measure of central tendency, we can use mean deviation. It comes as an improvement over the range. It basically measures the deviations from a value. This value is generally mean or median. Hence although mean deviation about mode can be calculated, mean deviation about mean and median are frequently used.

Note that the deviation of an observation from a value a is d= x-a. To find out mean deviation we need to take the mean of these deviations. However, when this value of a is taken as mean, the deviations are both negative and positive since it is the central value.

This further means that when we sum up these deviations to find out their average, the sum essentially vanishes. Thus to resolve this problem we use absolute values or the magnitude of deviation. The basic formula for finding out mean deviation is :

Mean deviation= Sum of absolute values of deviations from ‘a’ ÷ The number of observations

Solved Example for You

Q: The sum of squares of deviation of variates from their A.M. is always

  1. Zero
  2. Minimum
  3. Maximum
  4. Cannot be said

Sol: The correct option is “B”. It is a fundamental concept that the sum of squares of deviation of any variate from their arithmetic mean is always minimum.

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