Multiple choice

The mean and mode of a frequency distribution are respectively $25.55$ and $18.30$. Find the median of the distribution.

  1. $23.13$
  2. $21.4$
  3. $20.45$
  4. $22.7$
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A Correct answer
Explanation

The empirical relationship between mean, median, and mode is: Mode = 3(Median) - 2(Mean). Substituting the values: 18.30 = 3(Median) - 2(25.55). 18.30 = 3(Median) - 51.10. 3(Median) = 69.40. Median = 69.40 / 3 = 23.133.

AI explanation

Use the empirical relationship formula: Mode equals 3 multiplied by Median minus 2 multiplied by Mean. Substitute the known values into the rearranged formula: Median equals Mode plus 2 multiplied by Mean, all divided by 3. Calculate (18.30 plus 2 times 25.55) divided by 3 to get (18.30 plus 51.10) divided by 3. This equals 69.40 divided by 3, resulting in 23.13. The median is 23.13.

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