In the following frequency distribution table ages of 300 patients and number of patients in a hospital is given. Find the median age of the patients :Age (In years)Number of patients10–206020–304230–405540–507050–605360–7020

Q.4 (iii) In the following frequency distribution table ages of 300 patients and number of patients in a hospital is given. Find the median age of the patients :

Age (In years)	Number of patients
10–20	60
20–30	42
30–40	55
40–50	70
50–60	53
60–70	20

Doubtly Asked 25 Oct 2026 ssc 10th Save WhatsApp Report

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Answer: Median age ≈ 38.73 years

Age	Number of patients (f_i)	Cumulative frequency (cf)
10–20	60	60
20–30	42	102
30–40	55	157
40–50	70	227
50–60	53	280
60–70	20	300

\(N = 300\), so \(\dfrac{N}{2} = 150\). The cumulative frequency first exceeds 150 in the class 30–40, so 30–40 is the median class.

\(L = 30\), \(cf\) of the preceding class = 102, \(f = 55\), \(h = 10\).

Median \(= L + \left( \dfrac{\frac{N}{2} - cf}{f} \right) h = 30 + \dfrac{150 - 102}{55} \times 10\)

\(= 30 + \dfrac{480}{55} = 30 + 8.73 = 38.73\) years (approximately).

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report

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In the following frequency distribution table ages of 300 patients and number of patients in a hospital is given. Find the median age of the patients :Age (In years)Number of patients10–206020–304230–405540–507050–605360–7020

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