Question

# The age distribution of 100 life-insurance policy holders is as follows: Age (on nearest birth day) 17-19.5 20-25.5 26-35.5 36-40.5 41-50.5 51-55.5 56-60.5 61-70.5 No. of persons 5 16 12 26 14 12 6 5 Calculate the mean deviation from the median age.

Solution

## To make this function continuous, we need to subtract 0.25 from the lower limit and add 0.25 to the upper limit of the class.   Age  Number of People ${f}_{i}$ Cumulative Frequency   Midpoints ${x}_{i}$ $\left|{d}_{i}\right|=\left|{x}_{i}-38.63\right|$ 16.75−19.75   5 5 18.25 20.38 101.9 19.75−25.75 16 21 22.75 15.88 254.08   25.75−35.75 12 33 30.75 7.88 94.56   35.75−40.75 26 59 38.25 0.38 9.38   40.75−50.75 14 73 45.75 7.12 99.68   50.75−55.75 12 85 53.25 14.62 175.44   55.75−60.75 6 91 58.25 19.62 117.72   60.75−70.75 5 96 65.75 27.12 135.6           $\sum _{i=1}^{8}{f}_{i}\left|{d}_{i}\right|=988.36$                                                                                                                                                                                     MathematicsRD Sharma XI (2015)Standard XI

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