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Statistics question

2005 · Shift 0 · Q66
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Statistics question

2005 · Shift 0 · Q66

JEE MainMathematicsStatisticsMCQ+4 / −1
If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately :
  1. A
    20.5
  2. B
    22.0
  3. C
    24.0
  4. D
    25.5
View written solutionFree

Correct answer: C

  1. We use the empirical relation between mean, median, and mode for a moderately skewed distribution:

Mode=3 Median−2 Mean\text{Mode} = 3\,\text{Median} - 2\,\text{Mean}Mode=3Median−2Mean

  1. Substitute the given values:
  • Mean =21= 21=21
  • Median =22= 22=22

So,

Mode=3(22)−2(21)\text{Mode} = 3(22) - 2(21)Mode=3(22)−2(21)

  1. Calculate:

Mode=66−42=24\text{Mode} = 66 - 42 = 24Mode=66−42=24

  1. Therefore, the approximate mode is:

24.0\boxed{24.0}24.0​

  1. Comparing with the options:
  • A: 20.520.520.5
  • B: 22.022.022.0
  • C: 24.024.024.0
  • D: 25.525.525.5

Hence, the correct option is C.

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