Multiple choice

If the sum of the mode and mean of the certain frequency distribution in $129$ and the median of the observations is $63$, mode and mean are respectively

  1. $69$ and $60$
  2. $65$ and $64$
  3. $68$ and $61$

  4. none of these
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A Correct answer
Explanation

Empirical formula: Mode = 3*Median - 2*Mean. Given Mode + Mean = 129 and Median = 63. Mode = 3(63) - 2*Mean = 189 - 2*Mean. Substitute into Mode + Mean = 129: (189 - 2*Mean) + Mean = 129 => 189 - Mean = 129 => Mean = 60. Mode = 129 - 60 = 69.

AI explanation

Using the empirical relationship in statistics, Mode equals 3 times Median minus 2 times Mean. Substituting the given median of 63 and the combined sum of mode and mean of 129 into the formulas, we set M + m = 129 and M = 189 minus 2m. Solving this system of equations, we add the two equations to get 2M = 318, resulting in a mode of 69. Subtracting the mode from the total of 129 gives a mean of 60.

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