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Mathematics

The mean of the following distribution is 50. Find the unknown frequency.

Class IntervalFrequency
0 - 206
20 - 40f
40 - 608
60 - 8012
80 - 1008

Measures of Central Tendency

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Answer

Class IntervalClass mark (xi)Frequency (fi)fixi
0 - 2010660
20 - 4030f30f
40 - 60508400
60 - 807012840
80 - 100908720
TotalΣfi = 34 + fΣfixi = 2020 + 30f

By formula,

Mean = fixifi\dfrac{∑fixi}{∑f_i}

Substituting values we get :

50=2020+30f34+f50(34+f)=2020+30f1700+50f=2020+30f50f30f=2020170020f=320f=32020f=16.\Rightarrow 50 = \dfrac{2020 + 30f}{34 + f}\\[1em] \Rightarrow 50(34 + f) = 2020 + 30f\\[1em] \Rightarrow 1700 + 50f = 2020 + 30f\\[1em] \Rightarrow 50f - 30f = 2020 - 1700\\[1em] \Rightarrow 20f = 320\\[1em] \Rightarrow f = \dfrac{320}{20}\\[1em] \Rightarrow f = 16.

Hence, the value of f = 16.

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