Basic Mathematics for College Students

Find the weighted mean of a set of values.

When a value in a set appears more than once, that value has a greater “influence” on
the mean than another value that only occurs a single time. To simplify the process of
finding a mean, any value that appears more than once can be “weighted” by
multiplying it by the number of times it occurs. A mean that is found in this way is
called a weighted mean.

2

7.2 Mean, Median, and Mode 611

WHYWe do not have to find the sum of the miles driven each day in January. That
total is given in the problem as 4,805 miles.

Solution

Do the division.

On average, the trucker drove 155 miles per day.

 155

This is given.

 January has 31 days.





4,805

31

155

(^31) 4,805
 31
170
 155
155
 155
0



the total miles driven

the number of days

Average number of

miles driven per day

EXAMPLE (^3) Hotel Reservations
A hotel electronically recorded the number of
times the reservation desk telephone rang
before it was answered by a receptionist. The
results of the week-long survey are shown in
the table on the right. Find the average
number of times the phone rang before a
receptionist answered.
StrategyFirst, we will determine the total
number of times the reservation desk telephone
rang during the week before it was answered.
Then we will divide that result by the total number of calls received.
WHYTo find the average of a set of values, we divide the sum of the values by the
number of values.
Solution
To find the total number of times the reservation desk telephone rang during the
week before it was answered, we multiply each number of rings (1, 2, 3, 4, and 5) by
the number of times it occurred and add those results to get 450. The calculations
are shown in blue in the “Weighted number of rings” column.
Number Number
of rings of calls
111
246
345
428
520
Self Check 3
QUIZ RESULTSThe class results
on a five-question true-or-false
Spanish quiz are shown in the
table below. Find the average
number of incorrect answers on
the quiz.
Now TryProblem 45
Total number
of incorrect
answers on Number
the quiz of students
08
18
25
315
43
51
Number of rings Number of calls Weighted number of rings
111
246
345
428
5+20
Totals 150 450
5  20 → 100
4  28 → 112
3  45 → 135
2  46 → 92
1  11 → 11