  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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