- A23
- B38
- C42
- D37
Step-by-Step Solution
Add the frequencies from 35–45 onwards: 23 + 14 + 5 = 42 patients. (38 = 6 + 11 + 21 is the number aged under 35, and 23 counts only the class 35–45.)
Answer: C) 42
The ages (years) of 80 patients are grouped as 5–15: 6, 15–25: 11, 25–35: 21, 35–45: 23, 45–55: 14, 55–65: 5. How many patients are 35 years old or more?
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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