3.2
Trade electrician plumber carpenter labourer
Totals
(12 3 7 1 9 3 11 1 6 3 24) 4 (12 1 9 1 6) 5 12.111…
Euan is a contractor. This chart shows how much he pays employees. What is the mean hourly wage of Euan’s employees?
Number of employees
2
2
6
20
30
Hourly wage
$38.25
$32.75
$39.50
$23.00
—
(
(
(
2
6
20
Total hourly wage
(2)($38.25)
5
$76.50
)($
)($
)($
32.75
39.50
23.00
) 5 $
) 5 $
65.50
237.00
) 5 $ 460.00
$ 839.00
1 Record the following in the chart:
• the total hourly wage for each trade
• the total number of employees
• the total hourly wage for all the employees
64
Why is this a better way to calculate a typical hourly wage than using the means for the four trades?
2 What is the mean hourly wage of Euan’s employees?
Mean hourly wage: total hourly wage 4 total number of employees
5 $ 839.00
4 30, or $ 27.97
The mean hourly wage of Euan’s employees is $
27.97
.
Jennifer assesses job applicants. Avery and
Bryn interviewed for a position. Their scores from 1 to 5 are in the chart. The score 5 is highest. Who should get the job?
Category education
Avery Bryn
4 3 experience 5 communication 2
2
2
4
3 Solution leadership
A. What is the mean score for each applicant?
Avery: (4 1 5 1 2 1 2) 4 4 5 13 4 4, or 3.25
Bryn:
(3 1 2 1 4 1 3) 4 4 5 12 4 4, or 3
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B. Jennifer assigns a weight to each category to show its importance. What is each weighted mean score?
Category education experience communication leadership
Totals
Weight
10
5
20
15
50
Avery’s score
4
5
2
2
Avery’s weighted score
(10)(4)
5
40
25
40
30
135
Bryn’s score
3
2
4
3
Bryn’s weighted score
(10)(3)
5
30
10
80
45
165
Weighted mean: sum of weighted scores 4 sum of weights
Avery:
Bryn:
135 4
165 4
50
50
5
5
2.7
3.3
C. Who should get the job, based on the scores?
Bryn weighted mean a mean that includes the relative importance of each piece of data
Hint
The highest score shows the best qualified applicant.
A Canadian survey asked the following question:
“If a noteworthy event happens within your circle of friends, how are you most likely to hear about it?”
What percent of all the people who answered said they were most likely to hear about the event on a social networking site?
18–29 46%
30–44 33%
45–59 14%
8% 60 1
Solution
A. The population of each age group as a percent of the total survey population is shown below. Complete the chart.
Age group
18 29
30 44
45 59
60 1
Totals
20%
7%
3%
1%
8%
18%
19%
27%
Percent of people who said social networking
46%
33%
14%
8%
Age group as percent of people surveyed
13.4%
28.2%
37.5%
20.9%
100 %
(
(
(
Weighted percent of people who said social networking
(0.46)(0.134)
5
0.33
)( 0.282
0.06164
, or 6.164
) 5 0.093 06 , or
%
9.306
0.14
0.08
)(
)(
0.375
0.209
) 5 0.0525
, or
) 5
0.016 72 , or
%
5.25
1.672
22.392%
%
%
B. What percent of all the people who answered said they were most likely to hear on a social networking site?
About
22.4
% of the people who answered said this.
NEL
Chapter 3 Statistics
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Class
A
B
C
D
Class size
26
29
22
24
Mean exam mark
82
Practice
1. Oakwood High School has four classes of Grade 12 math.
The size of each class and the mean exam mark for the class are given in the chart. What is the mean exam mark for all four classes, to one decimal place?
77
(26 3 82 29 3 77 22 75 1 24 3 4 (26 29 1 22 1 24)
75
70
5 7695 101, or 76.2 The mean exam mark is 76.2.
2. Vytas and Flynn are applying for a community college program.
Applicants get a score between 1 and 4 in four categories.
The score 4 is highest. Each category has a weighting. To be accepted, an applicant needs a weighted mean over 2.5.
Category academic achievement community service admission essay reference letter
Weighting
35
20
30
15
Vytas
3
2
4
2
Flynn
2
4
2
3
66 a) Which category has the greatest weighting in the mean?
Explain why this makes sense.
Academic achievement has the greatest weighting. e.g., The college wants to make sure that applicants will be able to handle the program.
b) Who will be accepted?
Vytas: (35 3 3 1 20 3 2 1 30 3 4 1 15 3 2) 4 100 5 2.95
Flynn: (35 3 2 1 20 3 4 1 30 3 2 1 15 3 3) 4 100 5 2.55
Both Vytas and Flynn will be accepted.
3. Colton got these marks in science.
a) Which piece of work has the greatest weighting in the final mark? Explain why this might be.
Work quiz essay project exam
Mark
68
75
70
78
Percent of final mark
5
25
20
50
The exam has the greatest weighting. e.g., The exam gives students a chance to show their knowledge of the whole course.
b) What was Colton’s final mark in science?
(5 3 68 1 25 3 75 1 20 3 70 1 50 3 78) 4 100
5 75.15 Colton’s final mark was 75.15%.
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4. Delia’s class organized a food drive. Delia calculated the weighted mean for the average number of items collected per student.
Food Items Collected for Food Bank
Number of students in class
Average number of items collected per student
25
4.4
14
3.0
35
4.8
32
5.5
36
5.5
18
5.0
Delia’s weighted mean: (4.4 1 3.0 1 4.8 1 5.5 1 5.5 1 5.0) 4 6 5 4.7
The average number of items collected per student was 4.7.
Delia’s error: e.g., She just added the averages per class and divided by the number of classes. She should have divided the total number of items by the total number of students.
Correct weighted mean:
(25 3 4.4 1 14 3 3.0 1 35 3 4.8 1 32 3 5.5
1 36 3 5.5 1 18 3 5.0) 4 160 5 4.9
5. This chart shows the percent of people who speak a language other than English or French at home.
City
Winnipeg
Regina
Calgary
Vancouver
Totals
Percent who do not speak
English or French at home
21.5%
10.8%
12.9%
26.1%
Population
753 600
215 100
1 242 600
2 391 300
4 602 600
Number of people who do not speak English or French at home
(0.215)(753 600) 5 162 024
(0.108)(215 100) 5 23 231
(0.129)(1 242 600) 5 160 295
(0.261)(2 391 300) 5 624 129
969 679 a) How many people in each city speak a language other than English or French at home? Complete the last column in the chart, and determine the totals.
b) What percent of the people who live in these cities speak a language other than English or French at home?
Number of people who speak another language 4 population
5 969 679 4 4 602 600, or 0.210…, or 21.068…%
About 21% speak a language other than English or French at home.
c) Suppose that you determined the mean of the percents in the chart. Would it match your answer for Part b)? Explain.
No. e.g., The mean would match only if each city had the same population.
When cities with more people have more weight, the mean changes.
NEL
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