Question

Calculate the arithmetic mean, median, mode and standard deviation for the following data.

Age in Years 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

Number of people 8 7 15 18 22 14 10 5

Answer 1

MEDIAN

To find Median Class
= value of (n/2)th observation

= value of (99/2)th observation

= value of 49th observation

From the column of cumulative frequency cf, we find that the 49th observation lies in the class 40-50.

∴ The median class is 40-50.

Now,
∴L=lower boundary point of median class =40

∴n=Total frequency =99

∴cf=Cumulative frequency of the class preceding the median class =48

∴f=Frequency of the median class =22

∴c=class length of median class =10

Median

MODE

To find Mode Class
Here, the maximum frequency is 22.

∴ The mode class is 40-50.

∴L=lower boundary point of mode class =40

∴f1= frequency of the mode class =22

∴f0= frequency of the preceding class =18

∴f2= frequency of the succeeding class =14

∴c= class length of mode class =10

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