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Question 12
Find the unknown entries a, b, c, d, e and f in the following distribution of heights of students in a class
Height(in cm)FrequencyCumulative frequency15015512a155160b2516016510c165170d43170175e481751802fTotal50

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Solution

Height(in cm)FrequencyCumulative frequency(given)Cumulative frequency15015512a12155160b2512+b16016510c22+b165170d4322+b+d170175e4822+b+d+e1751802f24+b+d+eTotal50
On comparing last two columns of the table, we get
a = 12 ------(1)
and 12 + b = 25
b = 25 - 12 = 13-----(2)
and 22 + b = c
c = 22 + 13 = 35-----(3)
and 22 + b + d = 43
22 + 13 + d = 43
d = 43 - 35 = 8-------(4)
and 22 + b + d + e = 48
e = 48 - 43 = 5------(5)
and 24 + b + d + e = f
24 + 13 + 8 + 5 = f
f = 50---------(6)

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