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The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the monthly mean consumption from the data.
begin{tabular}{|c|c|}
hline Monthly Consumption (in units) & Number of Consumers
hline 50-100 & 4
hline 100-150 & 5
hline 150-200 & 13
hline 200-250 & 20
hline 250-300 & 14
hline 300-350 & 8
hline 350-400 & 4
hline
end{tabular}
begin{tabular}{|c|c|}
hline Monthly Consumption (in units) & Number of Consumers
hline 50-100 & 4
hline 100-150 & 5
hline 150-200 & 13
hline 200-250 & 20
hline 250-300 & 14
hline 300-350 & 8
hline 350-400 & 4
hline
end{tabular}
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begin{tabular}{|c|c|c|c|c|}
hline CI & $x_i$ & $f_i$ & $u_i$ & $f_i u_i$
hline 50-100 & 75 & 4 & -3 & -12
hline 100-150 & 125 & 5 & -2 & -10
hline 150-200 & 175 & 13 & -1 & -13
hline 200-250 & 225 = a & 20 & 0 & 0
hline 250-300 & 275 & 14 & 1 & 14
hline 300-350 & 325 & 8 & 2 & 16
hline 350-400 & 375 & 4 & 3 & 12
hline Total & & 68 & & 7
hline
end{tabular}
Mean $= 225 + \frac{7}{68} \times 50$
Mean $= 230.15$
Thus, the monthly mean consumption from the data is 230.15
hline CI & $x_i$ & $f_i$ & $u_i$ & $f_i u_i$
hline 50-100 & 75 & 4 & -3 & -12
hline 100-150 & 125 & 5 & -2 & -10
hline 150-200 & 175 & 13 & -1 & -13
hline 200-250 & 225 = a & 20 & 0 & 0
hline 250-300 & 275 & 14 & 1 & 14
hline 300-350 & 325 & 8 & 2 & 16
hline 350-400 & 375 & 4 & 3 & 12
hline Total & & 68 & & 7
hline
end{tabular}
Mean $= 225 + \frac{7}{68} \times 50$
Mean $= 230.15$
Thus, the monthly mean consumption from the data is 230.15