Question

calculate the arithmetic mean ​

Answer 1

Question :-

calculate the arithmetic mean.

Solution :-

Given Data :

$\small\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c} \bf Wages \: in \: Rs & \bf Number \: of \: workers\\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 10 - 20 & \sf 5 \\ \\ \sf 20 - 30 & \sf 10 \\ \\ \sf 30 - 40 & \sf 30 \\ \\\sf 40 - 50& \sf20 \\ \\ \sf 50 - 60 & \sf 15 \\ \\\sf 60 - 70 & \sf 10 \end{array}} \\ \end{gathered}\end{gathered}$

Frequency Table :-

$\tiny\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf C. I. & \bf frequency (f_i) & \bf Classmark (x_i) & \bf f_{i} x_{i} \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 10 - 20 & \sf 5 & \sf \frac{10 + 20}{2} = 15 & \sf5 \times 15 = 75\\ \\ \sf 20 - 30 & \sf 10& \sf \frac{20 + 30}{2} = 25 & \sf10 \times 25 = 250\\ \\ \sf 30 - 40 & \sf 30& \sf \frac{30 + 40}{2} = 35 & \sf30 \times 35 = 1050\\ \\ \sf40 - 50 & \sf20 & \sf \frac{40 + 50}{2} = 45 & \sf20 \times 45 = 900\\ \\ \sf50 - 60& \sf15 & \sf \frac{50 + 60}{2} = 55 & \sf15 \times 55 = 825\\ \\ \sf60 - 70& \sf10 & \sf \frac{60 + 70}{2} = 65 & \sf10 \times 65 = 650\\ & \frac{\qquad \qquad}{} & & \frac{\qquad \qquad}{} \\ & \sf \sum f_i = 90 & & \sf \sum f_i x_i = 3750\end{array}} \\ \end{gathered}\end{gathered}$

$\sf:\longmapsto{mean = \frac{\sum f_i x_i }{\sum f_i} } \: \: \: \\ \\ \sf:\longmapsto{mean = \frac{3750}{90}} \: \: \: \: \: \\ \\ \bf:\longmapsto \red{41.67(approx)}$

Mean = 41.67.

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