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    In the following frequency distribution Height (in cm) 140–145 145–150 150–155 155–160 160–165 165–170 No. of students 13 15 9
    Question

    In the following frequency distribution

    Height (in cm)

    140–145

    145–150

    150–155

    155–160

    160–165

    165–170

    No. of students

    13

    15

    9

    10

    8

    5

    The sum of the upper limit of the modal class and the lower limit of the median class:

    A.

    310

    B.

    295

    C.

    305

    D.

    300

    Correct option is D

    Solution:
    Identify the Modal Class
    Modal class = class with highest frequency
    Frequencies: 13, 15, 9, 10, 8, 5
    Highest frequency = 15 => Modal class = 145–150
    Upper limit of modal class = 150
    Identify the Median Class
    Total number of students =
    13+15+9+10+8+5=60
    Median lies at the 602=30thitem \frac{60}{2} = 30^{th} item​​
    Compute cumulative frequency:
    • Up to 140–145: 13
    • Up to 145–150: 13 + 15 = 28
    • Up to 150–155: 28 + 9 = 37
    30th item lies in class 150–155
    Lower limit of median class = 150
    Add required limits
    Upper limit of modal class = 150
    Lower limit of median class = 150
    Sum = 150 + 150 = 300
    Correct answer is (d) 300

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