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Mathematics

The mean of the following data is 16. Calculate the value of f.

MarksNo. of students
53
107
15f
209
256

Measures of Central Tendency

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Answer

Marks (xi)No. of students (fi)fixi
5315
10770
15f15f
209180
256150
TotalΣfi = 25 + fΣfixi = 415 + 15f

By formula; Mean = ΣfixiΣfi\dfrac{Σfixi}{Σf_i}

Substituting the values, we get

16=415+15f25+f16(25+f)=415+15f400+16f=415+15f16f15f=415400f=15.\Rightarrow 16 = \dfrac{415 + 15f}{25 + f}\\[1em] \Rightarrow 16(25 + f) = 415 + 15f\\[1em] \Rightarrow 400 + 16f = 415 + 15f\\[1em] \Rightarrow 16f - 15f = 415 - 400\\[1em] \Rightarrow f = 15.

Hence, the value of f = 15.

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