General Limitations of Average

1.    Since an average is a single value representing a group of values, it must be properly interpreted, otherwise, there is every possibility of jumping to wrong conclusions. This is illustrated with the help of the story. A person had to cross the river from one bank to another. He was not aware of the depth of the river, so he enquired of another man who told him that the average depth of water is 5’4”. The man was 5’6” and he thought that he can every easily cross the river because at all times he would be above the lever of water.

So, he started. In the beginning the level of water was very low but as he reached the middle, water was 15 ft. deep and he lost his life. The man was drowned because he had a misconception that average depth means uniform depth throughout. But it is not so. An average represents a group of values and lies somewhere in between the two extremes, i.e., the largest and the smallest items of the series.

2.    An average may give us a value that does not exist in the data. For example, the arithmetic mean of 100, 300, 250, 50, 100 is 800/5 = 160, a value that does not exist in the data.

3.    At times the average may give a very absurd result. For example, if we are calculating average size of a family we may get a value 4.8. But this is impossible as persons cannot be in fractions. However, we should remember that it is an average value representing the entire group.

4.    Measures of central value fail to give any idea about the formation of the series. Two or more series may have the same central value but may differ widely in compositions.

5.    We must remember that an average is a measure of central tendency. Hence, unless the data shows a clear single concentration of observations, an average may not be meaningful at all. This evidently precludes the use of any average to typify a bimodal, a U-shaped or a J-shaped distribution.

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