- A16–24
- B18–22
- C20–28
- D12–20
Step-by-Step Solution
The class width is the gap between consecutive marks: h = 20 − 12 = 8. Each class runs from mark − h/2 to mark + h/2, so the mark 20 belongs to 20 − 4 up to 20 + 4, that is 16–24.
Answer: A) 16–24
The class marks of a continuous frequency distribution are 12, 20, 28 and 36. The class interval whose class mark is 20 is ____.
Class 10StatisticsStatistics and Probability
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.
**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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