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Find the median from the following data. Age in years 20-30 30-40 40-50 50-60 60-70 70-80 80-90 No. of Patients 12 16 30 2
Question

Find the median from the following data.

Age in years

20-30

30-40

40-50

50-60

60-70

70-80

80-90

No. of Patients

12

16

30

20

17

38

15

A.

74 years

B.

49 years

C.

58 years

D.

46 years

Correct option is C

Formula Used:
Median=L+(N2CFf)×h\text{Median} = L + \left( \frac{\frac{N}{2} - CF}{f} \right) \times h​​
Where:
- L = lower boundary of median class
- N = total frequency
- CF = cumulative frequency before median class
- f = frequency of median class
- h = class width
Solution:

Age (in years)

Frequency (f)

Cumulative Frequency (CF)

20–30

12

12

30–40

16

28

40–50

30

58

50–60

20

78

60–70

17

95

70–80

38

133

80–90

15

148

Total frequency N = 148
N2\frac N2​= 74
The cumulative frequency just greater than 74 is 78, so the median class is 50–60
Now apply the formula:
L = 50
N = 148
CF = 58
f = 20
h = 10
Median = 50+(745820)×10=50+(1620)×10=50+8=5850 + \left(\frac{74 - 58}{20}\right) \times 10 = 50 + \left(\frac{16}{20}\right) \times 10 = 50 + 8 = 58​​

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