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To find the mean of 5–15: 6, 15–25: 9, 25–35: 5 a student multiplied each frequency by the LOWER LIMIT of its class and obtained 14.5. What is the correct mean?

Class 10StatisticsStatistics and Probability
  • A14.5
  • B20.0
  • C19.5
  • D24.5

Step-by-Step Solution

The mean of grouped data uses class marks, not lower limits. The marks are 10, 20, 30, so Σfx = 60 + 180 + 150 = 390 and Σf = 20, giving mean = 390/20 = 19.5. The student’s value is short by exactly half a class width (5), which is what using lower limits always costs.
Answer: C) 19.5

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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