Q.From the following frequency distribution of candidates' ages in an entrance examination, find the median: | Class Interval | 1–5 | 6–10 | 11–15 | 16–20 | 21–25 | 26–30 | 31–35 | |----------------|-----|------|-------|-------|-------|-------|-------| | Frequency | 2 | 3 | 6 | 7 | 5 | 4 | 3 |

The given frequency distribution table has class intervals in inclusive form. After converting them to exclusive form, the updated table is: | Class Boundaries | Frequency | Cumulative Frequency (Less than type) | |------------------|-----------|---------------------------------------| | 0.5–5.5 | 2 | 2 | | 5.5–10.5 | 3 | 5 | | 10.5–15.5 | 6 | 11 | | 15.5–20.5 | 7 | 18 | | 20.5–25.5 | 5 | 23 | | 25.5–30.5 | 4 | 27 | | 30.5–35.5 | 3 | \(n = 30\) | Here, \(n = 30\) So, \(\cfrac{n}{2} = \cfrac{30}{2} = 15\) The cumulative frequency just greater than 15 lies in the class (15.5–20.5) Therefore, the median class is (15.5–20.5) Now, the median is calculated using the formula: \[ \text{Median} = l + \left[\cfrac{\cfrac{n}{2} - cf}{f}\right] \times h \] Where: \(l = 15.5\), \(n = 30\), \(cf = 11\), \(f = 7\), \(h = 5\) \[ = 15.5 + \left[\cfrac{15 - 11}{7}\right] \times 5 = 15.5 + \cfrac{4}{7} \times 5 = 15.5 + \cfrac{20}{7} = 15.5 + 2.86 = 18.36 \text{ (approx.)} \]
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