Mean of a Grouped Distribution

Mean of a Grouped Distribution

 

The mean of a distribution, where x represents the midpoints, f the frequencies, and n = ∑f , is

\overline{x} = \frac{\sum xf}{n}.

 

Example

Listed below is the grouped frequency distribution for the 30 business executives

Find the mean from the grouped frequency distribution.

 

Interval Midpoint, x Frequency, f Product, xf
0-4 2 3 6
5-9 7 4 28
10-14 12 6 72
15-19 17 8 136
20-24 22 5 110
25-29 27 3 81
30-34 32 1 32
    Total 30 Total 465

 

\overline{x} = \frac{465}{30} = 15.5.

 

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