Central Tendency & DispersionPYQ June 19Question 2952 of 473
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For the distribution, The value of median is x: 1, 2, 3, 4, 5, 6; f: 6, 9, 10, 14, 12, 8

Options

A3.5
B3
C4
D5
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Correct Answer

✅ Option c — 4

All Options:

  • A3.5
  • B3
  • C4
  • D5

Detailed Solution & Explanation

We are given the following frequency distribution: - x\displaystyle x: 1,2,3,4,5,6\displaystyle 1, 2, 3, 4, 5, 6 - f\displaystyle f: 6,9,10,14,12,8\displaystyle 6, 9, 10, 14, 12, 8 1. Compute the cumulative frequencies (cf\displaystyle cf): - For x=1\displaystyle x = 1: cf=6\displaystyle cf = 6 - For x=2\displaystyle x = 2: cf=6+9=15\displaystyle cf = 6 + 9 = 15 - For x=3\displaystyle x = 3: cf=15+10=25\displaystyle cf = 15 + 10 = 25 - For x=4\displaystyle x = 4: cf=25+14=39\displaystyle cf = 25 + 14 = 39 - For x=5\displaystyle x = 5: cf=39+12=51\displaystyle cf = 39 + 12 = 51 - For x=6\displaystyle x = 6: cf=51+8=59\displaystyle cf = 51 + 8 = 59 2. Total number of observations: N=∑fi=59\displaystyle N = \sum f_i = 59. 3. The median position is N2=592=29.5\displaystyle \frac{N}{2} = \frac{59}{2} = 29.5. 4. The cumulative frequency just greater than 29.5\displaystyle 29.5 is 39\displaystyle 39, which corresponds to the class x=4\displaystyle x = 4. Thus, the median value is 4\displaystyle 4. Although the textbook key lists Option D, the mathematically correct choice is Option C. Hence, **Option C** is the correct answer.

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