95
Find the mode and the mean of the following frequency distribution :
begin{tabular}{|l|c|c|c|c|c|}
hline Class & $0-8$ & $8-16$ & $16-24$ & $24-32$ & $32-40$
hline Frequency & $6$ & $7$ & $10$ & $8$ & $9$
hline
end{tabular}
begin{tabular}{|l|c|c|c|c|c|}
hline Class & $0-8$ & $8-16$ & $16-24$ & $24-32$ & $32-40$
hline Frequency & $6$ & $7$ & $10$ & $8$ & $9$
hline
end{tabular}
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begin{tabular}{|l|l|l|l|}
hline C.I & Frequency & $x_i$ & $f_i x_i$
hline $0-8$ & $6$ & $4$ & $24$
hline $8-16$ & $7$ & $12$ & $84$
hline $16-24$ & $10$ & $20$ & $200$
hline $24-32$ & $8$ & $28$ & $224$
hline $32-40$ & $9$ & $36$ & $324$
hline Total & $40$ & & $856$
hline
end{tabular}
Mean $= \frac{856}{40} = 21.4$
Modal class : $16 - 24$
Mode $= 16 + \frac{10-7}{2(10)-7-8} \times 8 = 20.8$
hline C.I & Frequency & $x_i$ & $f_i x_i$
hline $0-8$ & $6$ & $4$ & $24$
hline $8-16$ & $7$ & $12$ & $84$
hline $16-24$ & $10$ & $20$ & $200$
hline $24-32$ & $8$ & $28$ & $224$
hline $32-40$ & $9$ & $36$ & $324$
hline Total & $40$ & & $856$
hline
end{tabular}
Mean $= \frac{856}{40} = 21.4$
Modal class : $16 - 24$
Mode $= 16 + \frac{10-7}{2(10)-7-8} \times 8 = 20.8$