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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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