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For the data 0–10: 4, 10–20: f, 20–30: 9, 30–40: 7 the mean is 20. Which equation correctly determines f?

Class 10StatisticsStatistics and Probability
  • A
  • B
  • C
  • D

Step-by-Step Solution

Class marks are 5, 15, 25, 35, so Σfx = and Σ. The mean equation is , which gives . Dividing by 20 forgets that is part of the total, uses the lower limit instead of the class mark 15, and dividing by 4 divides by the number of classes.
Answer: A)

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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