The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

Suppose, for instance, that we revisit the coffee price example that we were considering

earlier. We had obtained the prices for five competing coffee shops, and wanted to get a

sense of the average price in the local market. We did not consider in either of our “aver-

age” calculations, though, how much business each of the coffee shops actually does. If

competitor A sells more coffee than the others, we might want to consider its price as more

important than the others. Suppose, for example, that we know the weekly sales for each

of these competitors. We might then want to give each coffee shop a different weight based

on the number of cups of coffee sold.

Competitor Price Estimated Weekly Sales (Cups)

A $1.49 850

B $1.59 550

C $1.25 700

D $3.75 500

E $1.50 1000

To calculate the weighted average price, we multiply each of the prices by its “weight”; in

this case the weight is the estimated sales. Then, we divide by the total of the weights. This

gives us a weighted average of:

Weighted average 

850($1.49)  550($1.59)  700($1.25)  500($3.75)  1,000($1.50)

____ 850  550  700  500  1,000

$1,266.50  $874.50  $875.00  $1875.00  $1,500.00

_____ 850  550  700  500  1,000

$6,391.00

__3,600

$1.78

Example 16.2.2 Suppose that a computer services company has fi ve part-time

workers. Each worker’s hourly wage and number of hours worked in a typical week are

listed in the table below. Calculate (a) the mean of the hourly rates, (b) the median,

and (c) the weighted average, weighted by hours worked.

Employee Hourly Wage Typical Weekly Hours

A $23.50 25

B $27.50 34

C $18.00 28

D $38.00 10

E $45.00 8

(a) The mean would be:

Mean 

$23.50  $27.50  $18.00  $38.00  $45.00

___ 5

$152

_____ 5
$30.40

(b) We put the hourly wages in order: $18.00, $23.50, $27.50, $38.00, $45.00. The mean

is the middle value of this list: $27.50.

(c) To fi nd the weighted average:

Weighted average 
 ____________________________________________________________25($23.50)  34($27.50)  28($18.00)  10($38.00)  8($45.00)

25  34  28  10  8

 _________________________________________________$587.50  $935.00  $504.00  $380.00  $360.00

25  34  28  10  8

16.2 Measures of Average 619