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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 11 16 14 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

    11

    16

    14

    29

    40

    21

    17

    A.

    80 years

    B.

    59 years

    C.

    79 years

    D.

    61 years

    Correct option is D

    Formula Used:

    Median = L + (N2CFf)×h\left( \frac{\frac{N}{2} - CF}{f} \right) \times h​​

    Where:

    L = lower boundary of the median class

    N = total frequency

    CF = cumulative frequency before median class

    f = frequency of median class

    h = class width

    Solution:

    Class
    f
    CF
    20–30
    11
    11
    30–40
    16
    27
    40–50
    14
    41
    50–60
    29
    70
    60–70
    40
    110
    70–80
    21
    131
    80–90
    17
    148

    Total frequency N = 148

    N2=1482=74\frac{N}{2} = \frac{148}{2} = 74​​

    The median class is 60 – 70, because 74 lies between 70 and 110

    Now: L = 60, CF = 70, f = 40, h = 10

    Median = 60 + (747040)×10\left( \frac{74 - 70}{40} \right) \times 10​​

    = 60 + (440)×10\left( \frac{4}{40} \right) \times 10​​

    = 60 + 1 = 61

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