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If the mean of the following frequency distribution is 7.2, find value of ‘k’.

x 2 4 6 8 10 12
f 4 7 10 16 k 3

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Σfi = 40 + k; 

Σfi xi = 260 + 10k

Given that \(\overline x\) = 7.2

But \(\overline x\) = \(\frac {\sum f_1x_i}{\sum f_i}\)

7.2 = \(\frac {260 + 10k}{40 + k}\)

288.0 + 7.2k = 260 + 10k

10k – 7.2k = 288 – 260 

2.8k = 28

k = 28/2.8 = 10

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