Multiple choice

The mode and the mean of a grouped data are 20 and 26 respectively. Find the median.

  1. 24

  2. 46

  3. 72

  4. 8
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A Correct answer
Explanation

The empirical relationship between mean, median, and mode is: Mode = 3*Median - 2*Mean. Substituting the given values: 20 = 3*Median - 2*26. 20 = 3*Median - 52, so 72 = 3*Median, which gives Median = 24.

AI explanation

We use the empirical relationship between the mean, median, and mode for a moderately skewed distribution, which states that Mode equals 3 times Median minus 2 times Mean. Substituting the given values, we get 20 = 3(Median) - 2(26). Solving this, 3(Median) equals 72, giving a median of 24.

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