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Question

Calculate the Mean and Standard Deviation from the following distribution.
Age (years) 15−19 20−24 25−29 30−34 35−39 40−44
No. of Persons 4 20 38 24 10 4

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Solution

In order to calculate the mean and standard deviation, we first need to convert the inclusive series into exclusive series as given below:
Age
(X)
Frequency
(f)
Mid-Values
(m)
fm m2 fm2
14.5−19.5 4 17 68 289 1156
19.5−24.5 20 22 440 484 9680
24.5−29.5 38 27 1026 729 27702
29.5−34.5 24 32 768 1024 24576
34.5−39.5 10 37 370 1369 13690
39.5−44.5 4 42 168 1764 7056
Σf=100 Σfm=2840 Σfm2=83860


Mean, X¯=ΣfmΣf=2840100=28.4 yearsStandard deviation, σ=Σfm2Σf-X¯2or, σ=83860100-28.42or, σ=838.6-806.56or, σ=32.04σ=5.66 years

Hence, mean age of the persons is 28.4 years and standard deviation is 5.66 years.

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