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19 May, 15:57

Suzanne owns a small business that employs 555 other people. Suzanne makes / $100{,}000$100,000dollar sign, 100, comma, 000 per year, and the other 555 employees make between / $40{,}000$40,000dollar sign, 40, comma, 000 and / $50{,}000$50,000dollar sign, 50, comma, 000 per year.

Suzanne decides to increase her salary by / $30{,}000$30,000dollar sign, 30, comma, 000 per year and leave the rest of the salaries the same.

How will increasing her salary affect the mean and median? How will increasing her salary affect the mean and median?

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  1. 19 May, 18:46
    0
    Mean increased

    Median remains same

    Step-by-step explanation:

    Suzanne make $ 100 k per year

    5 other employee $ 40 k to $ 50 K per year per employee

    data in ascending order

    $40000, $40000+a, $40000+b, $40000+c, $50000, $ 100000

    where 10000 ≥c ≥ b ≥ a ≥ 0

    Mean = ($40000 + $40000+a + $40000+b + $40000+c + $50000 + $ 100000) / 6

    Mean = $ (310000 + a + b + c) / 6

    Median = ($40000+b + $40000+c) / 2 = $40000 + (b+c) / 2

    Suzanne make now $ 100000 + $ 30000 = $ 130000 per year

    $40000, $40000+a, $40000+b, $40000+c, $50000, $ 130000

    Mean = ($40000 + $40000+a + $40000+b + $40000+c + $50000 + $ 130000) / 6

    Mean = $ (340000 + a + b + c) / 6

    Median = ($40+b k + $40+c k) / 2 = $40 + (b+c) / 2 k

    Mean increased by $ (340000 + a + b + c) / 6 - $ (310000 + a + b + c) / 6

    = $ 30000/6 = $ 5000

    Median Remains the same
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