Katie earned $15, $20, $10, $12, $20, $16, $80, and $18 for eight babysitting jobs. How much did she earn the ninth time if the mean of the data set is $24?

Question

Katie babysat 9 times. What did she earn on the ninth one if the mean is $24?

Answer 1

The mean is the arithmetic average.

Let x = the ninth earning

 

Mean = (Sum of values) / (number of values)

  (15+20+10+12+20+16+80+18+x)/9  = 24

  (15+20+10+12+20+16+80+18+x) = 216                [multiply both sides by 9]

  191 + x = 216                                                  [collect terms]

    x = 25                                             [subtract 191 from both sides]

 

Note that 80 is an “outlier.”  That is, a number that does not fit with the others.  In fact, if you plot values, you would see:

15  ***

20  ****

10  **

12  **

20  ****

16  ***

80  ****************

18  ***

 

As an alternative method, you may add shortfalls and overages like this:

 

Shortfall:     -9    -4  -14  -12   -4   -8            -6   -0       -57

Value:          15   20   10   12   20   16   80   18    x   

Overage:                                                +56          +1      +57

 

                                     [x needs +1 to balance, so x=25)

Answer 2

(15+20+10+12+20+16+80+18+x)/9     = 24

 

(191 + x) = 216

 

x= 25