Find the median of the following data. (Rounded off to 2 decimal places.) Class interval 0-5 5-10 10-15 15-20 20-25 25-30 30-35 Frequency 3 5 4 2 7 6 5
21.43
Total frequency \(N = 3+5+4+2+7+6+5 = 32\), so \(N/2 = 16\).
Cumulative frequencies: 3, 8, 12, 14, 21, 27, 32.
The 16th value first appears in the class whose cumulative frequency just exceeds 16, i.e. cf = 21. Hence the median class is 20-25.
Here \(l = 20\), cf (of class before) \(= 14\), \(f = 7\), \(h = 5\).
\(\text{Median} = l + \dfrac{(N/2 - cf)}{f} \times h = 20 + \dfrac{(16 - 14)}{7} \times 5\)
\(= 20 + \dfrac{10}{7} \approx 20 + 1.43 = 21.43\)
Hence the median is 21.43.
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