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For the moderately skewed distribution of marks in the picture, the mean and the median are marked. Use the empirical relation to find the mode.

Class 10StatisticsStatistics and Probability
  • A20
  • B28
  • C30
  • D25

Step-by-Step Solution

, so and Mode . (Swapping mean and median gives )
Answer: C) 30

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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