Find the mean and the median for the following frequency distribution : Class 11-13 13-15 15-17 17-19 19-21 21-23…
CBSE Class 10 Maths PYQ · Statistics · Find Mean, median, mode · 2 Marks · July 2023 · Standard
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292 Marks · July 2023 · Standard
Find the mean and the median for the following frequency distribution : Class $11-13$ $13-15$ $15-17$ $17-19$ $19-21$ $21-23$ $23-25$ Frequency $7$ $6$ $9$ $13$ $20$ $5$ $4$
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Calculation of Mean: $\sum f_i = 64$ $\sum f_i x_i = 1152$ Mean $= \frac{\sum f_i x_i}{\sum f_i} = \frac{1152}{64} = 18$. Calculation of Median: $N = 64 \Rightarrow \frac{N}{2} = 32$. The median class is $17-19$ (since cumulative frequency $22 < 32 < 35$). Lower limit of median class $l = 17$. Cumulative frequency of class preceding median class $cf = 22$. Frequency of median class $f = 13$. Class size $h = 2$. Median $= l + (\frac{\frac{N}{2} - cf}{f}) \times h$ Median $= 17 + (\frac{32 - 22}{13}) \times 2$ Median $= 17 + (\frac{10}{13}) \times 2 = 17 + \frac{20}{13}$ Median $= 17 + 1.538 \approx 18.54$.
