Question

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?

Answer 1

Answer:

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