Basic Mathematics for College Students

1.9 Order of Operations 107

Solution

In the numerator, do the multiplication.

In the denominator, evaluate the exponential expression

within the parentheses.

In the numerator, do the subtraction.

In the denominator, do the multiplication.

 1 Do the division indicated by the fraction bar: 24 24 1.



24

24

2(13) 2

3( 23 )



26  2

3( 8 )

3 Find the mean (average) of a set of values.

The mean(sometimes called the arithmetic meanor average) of a set of numbers is

a value around which the values of the numbers are grouped. It gives you an

indication of the “center” of the set of numbers. To find the mean of a set of

numbers, we must apply the order of operations rule.

Finding the Mean

To find the mean (average) of a set of values, divide the sum of the values by

the number of values.

EXAMPLE (^10) NFL Offensive
Linemen The weights of the
2008–2009 New York Giants starting
offensive linemen are shown below.
What was their mean (average)
weight?
Self Check 10
NFL DEFENSIVE LINEMEN The
weights of the 2008–2009 New
York Giants starting defensive
linemen were 273 lb, 305 lb,
317 lb, and 265 lb. What was their
mean (average) weight? (Source:
nfl.com/New York Giants depth
chart)
Now TryProblems 51 and 113
© Larry French/Getty Images
StrategyWe will add and 319 and divide the sum by 5.
WHYTo find the mean (average) of a set of values, we divide the sum of the
values by the number of values.
Solution
Since there are 5 weights, divide the sum by 5.
In the numerator, do the addition.
 315 Do the indicated division: 1,5755.



1,575

5

Mean

327  317  302  310  319

5

327, 317, 302, 310,

315

(^5) 1,575
 15
7
 5
25
 25
0
32
2
7
317
302
310
 319
1,575
In 2008–2009, the mean (average) weight of the starting offensive linemen on the
New York Giants was 315 pounds.
(Source: nfl.com/New York Giants depth chart)
Right tackle
#67 K. McKenzie
327 lb
Right guard
#76 C. Snee
317 lb
Center
#60 S. O’Hara
302 lb
Left guard
#69 R. Seubert
310 lb
Left tackle
#66 D. Diehl
319 lb