104
Find 'mean' and 'mode' of the following data :
begin{tabular}{|l|c|c|c|c|c|c|}
hline Class & 10-25 & 25-40 & 40-55 & 55-70 & 70-85 & 85-100
hline Number of Students & 12 & 10 & 15 & 13 & 8 & 12
hline
end{tabular}
begin{tabular}{|l|c|c|c|c|c|c|}
hline Class & 10-25 & 25-40 & 40-55 & 55-70 & 70-85 & 85-100
hline Number of Students & 12 & 10 & 15 & 13 & 8 & 12
hline
end{tabular}
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Solution: (a)
begin{tabular}{|c|c|c|c|c|}
hline CI & $x_i$ & $f_i$ & $u_i = \frac{x_i - 47.5}{15}$ & $f_iu_i$
hline 10-25 & 17.5 & 12 & -2 & -24
hline 25-40 & 32.5 & 10 & -1 & -10
hline 40-55 & 47.5 & 15 & 0 & 0
hline 55-70 & 62.5 & 13 & 1 & 13
hline 70-85 & 77.5 & 8 & 2 & 16
hline 85-100 & 92.5 & 12 & 3 & 36
hline & & 70 & & 31
hline
end{tabular}
Mean = $47.5 + 15 \times \frac{31}{70} = 54.14$
Modal class is 40 - 55
Mode = $40 + 15 \times \frac{15 - 10}{30 - 10 - 13} = 50.71$
begin{tabular}{|c|c|c|c|c|}
hline CI & $x_i$ & $f_i$ & $u_i = \frac{x_i - 47.5}{15}$ & $f_iu_i$
hline 10-25 & 17.5 & 12 & -2 & -24
hline 25-40 & 32.5 & 10 & -1 & -10
hline 40-55 & 47.5 & 15 & 0 & 0
hline 55-70 & 62.5 & 13 & 1 & 13
hline 70-85 & 77.5 & 8 & 2 & 16
hline 85-100 & 92.5 & 12 & 3 & 36
hline & & 70 & & 31
hline
end{tabular}
Mean = $47.5 + 15 \times \frac{31}{70} = 54.14$
Modal class is 40 - 55
Mode = $40 + 15 \times \frac{15 - 10}{30 - 10 - 13} = 50.71$