Central Tendency & DispersionPYQ Sep 24Question 2966 of 473
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The median of the following frequency distribution is: x | f(x) 0-10 | 8 10-20 | 30 20-30 | 40 30-40 | 12 40-50 | 10

Options

A22.5\displaystyle 22.5
B33\displaystyle 33
C23\displaystyle 23
D24\displaystyle 24
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Correct Answer

✅ Option c — 23\displaystyle 23

All Options:

  • A22.5\displaystyle 22.5
  • B33\displaystyle 33
  • C23\displaystyle 23
  • D24\displaystyle 24

Detailed Solution & Explanation

We are given the frequency distribution: - Class Interval: 0−10,10−20,20−30,30−40,40−50\displaystyle 0-10, 10-20, 20-30, 30-40, 40-50 - Frequency (f\displaystyle f): 8,30,40,12,10\displaystyle 8, 30, 40, 12, 10 1. Compute cumulative frequencies (cf\displaystyle cf): - 0−10\displaystyle 0-10: cf=8\displaystyle cf = 8 - 10−20\displaystyle 10-20: cf=8+30=38\displaystyle cf = 8 + 30 = 38 - 20−30\displaystyle 20-30: cf=38+40=78\displaystyle cf = 38 + 40 = 78 - 30−40\displaystyle 30-40: cf=78+12=90\displaystyle cf = 78 + 12 = 90 - 40−50\displaystyle 40-50: cf=90+10=100\displaystyle cf = 90 + 10 = 100 2. Total frequency N=100\displaystyle N = 100, so N2=50\displaystyle \frac{N}{2} = 50. 3. The cumulative frequency just greater than 50\displaystyle 50 is 78\displaystyle 78, which corresponds to the median class 20−30\displaystyle 20-30. Thus: - Lower limit of median class: L=20\displaystyle L = 20 - Cumulative frequency of preceding class: cf=38\displaystyle cf = 38 - Frequency of median class: f=40\displaystyle f = 40 - Class interval width: i=10\displaystyle i = 10 4. Applying the median formula: Median=L+N2−cff×i=20+50−3840×10=20+124=23\text{Median} = L + \frac{\frac{N}{2} - cf}{f} \times i = 20 + \frac{50 - 38}{40} \times 10 = 20 + \frac{12}{4} = 23 Hence, **Option C** is the correct answer.

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