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Which set of values for one distribution fits the empirical relation Mode = 3 Median − 2 Mean?

Class 10StatisticsStatistics and Probability
  • AMean = 20, Median = 22, Mode = 24
  • BMean = 20, Median = 22, Mode = 26
  • CMean = 25, Median = 25, Mode = 20
  • DMean = 30, Median = 28, Mode = 30

Step-by-Step Solution

Test each set. 3(22) − 2(20) = 26, which matches only the second set. For the others 26 ≠ 24; 3(25) − 2(25) = 25 ≠ 20 (when mean and median agree all three measures agree); and 3(28) − 2(30) = 24 ≠ 30.
Answer: B) Mean = 20, Median = 22, Mode = 26

Key idea: Median for grouped data

**Step 1**: build cumulative frequency (cf) column.
**Step 2**: find n/2 (half the total frequency).
**Step 3**: locate the **median class** — the FIRST class whose cumulative frequency ≥ n/2.
**Step 4**: Apply formula.

**Median formula**:
**Median = l + h × (n/2 − cf) / f**

Where:
- l = lower limit of median class
- h = class width
- n = total frequency
- cf = cumulative frequency of class BEFORE median class
- f = frequency of median class

The formula uses linear interpolation within the median class to find where the n/2-th item falls.

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