MTH201 MIDTERM SOLVED PAPERS
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“Grouping error” refers to the error that is introduced by the assumption that all the values falling in a class are equal to the mid-point of the class interval. In reality, it is highly improbable to have a class for which all the values lying in that class are equal to the mid-point of that class. This is why the mean that we calculate from a frequency distribution does not give exactly the same answer as what we would get by computing the mean of our raw data.
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As indicated earlier, a frequency distribution is used to calculate the approximate values of various descriptive measures. (The word ‘approximate’ is being used because of the grouping error that was just discussed.)
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This grouping error arises in the computation of many descriptive measures such as the geometric mean, harmonic mean, mean deviation, and standard deviation. But, experience has shown that in the calculation of the arithmetic mean, this error is usually small and never serious. Only a slight difference occurs between the true answer that we would get from the raw data and the answer that we get from the data that has been grouped in the form of a frequency distribution.