- A14%
- B20%
- C45%
- D35%
Step-by-Step Solution
"At least 60" covers the classes 60–80 and 80–100: 8 + 6 = 14 innings out of 40. That is 14/40 = 0.35, i.e. 35%. (14% confuses the count of innings with the percentage.)
Answer: D) 35%
The runs scored by a batter in 40 innings are grouped as 0–20: 6, 20–40: 11, 40–60: 9, 60–80: 8, 80–100: 6. In what percentage of the innings did the batter score at least 60 runs?
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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