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    What is the mode of the data given below? [Give your answer correct to 2 decimal places.] Age in years 15-25 25-35 35-45 45-55 55-65 65-
    Question

    What is the mode of the data given below? [Give your answer correct to 2 decimal places.]

    Age in years

    15-25

    25-35

    35-45

    45-55

    55-65

    65-75

    75-85

    No. of patients

    14

    32

    39

    38

    10

    36

    22

    A.

    40.86

    B.

    60.47

    C.

    43.75

    D.

    36.08

    Correct option is C

    Formula Used:

    In a grouped frequency distribution, the mode:

    Mode = L +(f1f02f1f0f2)×h \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h​​

    Where:

    L = lower boundary of modal class

    f1 = frequency of modal class

    f0 = frequency of class before modal class

    f2 = frequency of class after modal class

    h = class width

    Solution:

    From the table:

    Highest frequency = 39 → Modal class = 35 – 45

    L = 35

    f1 = 39

    f0 = 32 (frequency before 35 – 45)

    f2 = 38 (frequency after 35 – 45, i.e., 45 – 55)

    h = 10 (class width)

    Now, 

    Mode = 35 + (39322(39)3238)×10\left( \frac{39 - 32}{2(39) - 32 - 38} \right) \times 10​​

    = 35 + (77870)×10\left( \frac{7}{78 - 70} \right) \times 10​​

    = 35 + (78)×10 \left( \frac{7}{8} \right) \times 10​​

    = 35 + 8.75 = 43.75

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