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    Find the median of the data 11, 16, 33, 15, 51, 18, 71, 75, 22, 17.
    Question

    Find the median of the data 11, 16, 33, 15, 51, 18, 71, 75, 22, 17.

    A.

    18

    B.

    24

    C.

    20

    D.

    22

    Correct option is C

    Given:

    The data set is: 11, 16, 33, 15, 51, 18, 71, 75, 22, 17.

    Formula Used:

    If n is odd:

    Median = Value at positionn+12\text{Value at position}\frac{n+1}{2}​​

    If n is even:

    Median = Value at positionn2+Value at position(n2+1)2\frac{\text{Value at position}\frac{n}{2}+ \text{Value at position}(\frac{n}{2}+1)}{2}​​

    Solution:

    Arranging the data in ascending order:

    11,15,16,17,18,22,33,51,71,75

    So, n = 10 (even)

    Since n is even,​​

    Median = Value at position102+Value at position(102+1)2\frac{\text{Value at position}\frac{10}{2}+ \text{Value at position}(\frac{10}{2}+1)}{2}​​

    Median = Value at position 5th place+Value at position 6th place2\frac{\text{Value at position 5th place} + \text{Value at position 6th place}}{2}​​

    Median = 18+222=402=20\frac{18+22}{2} = \frac{40}{2} = 20​​

    Thus, The median of the data set is 20.

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