• 2021 December(E23) Math Question 59

    Statistics

    - Mean, Median

    Statistics (Mean, Median, Mode, Standard Deviation)
    Choice A

    We have two sets, with the terms ordered from the least to the largest:

    A=a1,a2,a3,a4,a5A=a_1,a_2,a_3,a_4,a_5

    And

    B=b1,a2,a3,a4,a5B=b_1,a_2,a_3,a_4,a_5

    And

    b1>a1b_1>a_1

    Then the median (a3a_3) will be same.

    Since b1>a1b_1>a_1, the range of B (a5−b1a_5-b_1) < the range of A (a5−a1a_5-a_1).

    Since b1>a1b_1>a_1,

    Mean  of  B={b1+a2+a3+a4+a5}{5}Mean\; of\; B=\frac\{b_1+a_2+a_3+a_4+a_5\}\{5\}
    Mean  of  A={a1+a2+a3+a4+a5}{5}Mean\; of\; A=\frac\{a_1+a_2+a_3+a_4+a_5\}\{5\}
    Mean  of  A−Mean  of  B={a1+a2+a3+a4+a5−(b1+a2+a3+a4+a5)}{5}Mean\; of\; A-Mean\; of\; B=\frac\{a_1+a_2+a_3+a_4+a_5-(b_1+a_2+a_3+a_4+a_5)\}\{5\}
    ={a1−b1}{5}<0=\frac\{a_1-b_1\}\{5\}<0
    =>Mean  of  A−Mean  of  B<0=> Mean\; of\; A-Mean\; of\; B<0
    ∴Mean  of  A<Mean  of  B\therefore Mean\; of\; A<Mean\; of\; B

    Only the mean must be greater for set B than for set A. Therefore A is correct.

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