CCBC Math 081
Third Edition
Statistics: Mean, Median, and Mode
Section 2.3
7 pages
2.3 Statistics: Mean, Median, and Mode
You may have heard a news report about the average unemployment rate or the median income
or the average price of gasoline per gallon. Summarizing numerical data like this is common. On
an individual level, if the number of hours you work varies each week, you may want to say to
your friends, “I work about 30 hours a week.” This statement does not list how many hours you
actually work each week, but it gives your friends a general idea of how many hours you work.
In mathematics, there are three common ways that a list of numbers can be summarized. These
three averages are the mean, median, and mode. Each of these is described below, one at a
time. Study the definition of each, the procedure used to find each, and the examples.
MEAN (most common; often called the average)
Definition
Procedure
Sample
1. Add the numbers in the list.
The sum of a set of
data values divided by
the number of data
PROBLEM: 9, 7, 5, 8, 6
SOLUTION:
2. Count how many numbers
1. Add: 9  7  5  8  6  35
2. Count: 5 numbers in list
3. Divide: 35  5  7
are in the list.
values in the set.
3. Divide the sum by the count.
Example 1:
ANSWER: Mean = 7
A car dealer recorded the miles-per-gallon ratings of six cars and the results were
as follows: 20, 30, 22, 32, 25, and 21. Find the mean rating of the cars.
Sum  20  30  22  32  25  21  150
Add the numbers in the list.
Count the numbers in the list.
Divide the sum by the count.
Answer.
6 numbers
150  6  25
Mean = 25 miles per gallon
Practice 1:
A car dealer recorded the miles-per-gallon ratings of six cars and the results were
as follows: 18, 36, 21, 32, 27, and 34. Determine the mean of the miles-per-gallon
ratings.
Answer:
28 miles-per-gallon
Watch it:
http://youtu.be/js8bQ25bn2E
102
CCBC Math 081
Third Edition
Example 2:
Statistics: Mean, Median, and Mode
Section 2.3
7 pages
For a particular stock, an investor reported the following losses and gains during
the week: Monday – lost $3, Tuesday – gained $6, Wednesday – gained $2,
Thursday – lost $4, Friday – lost $6. Find the mean loss or gain per day.
First we need to list the numbers. A gain should be represented as a positive
number and a loss should be represented as a negative number.
3, 6, 2,  4,  6
Sum  3  6  2  4  6  5
5 numbers
5  5  1
Mean = $1 loss per day
List the numbers.
Add the numbers in the list.
Count the numbers in the list.
Divide the sum by the count.
Answer.
Practice 2:
The temperatures for the last six days were 18º, 5º, – 2º, – 4º, 9º, and 10º.
Determine the mean temperature for the last six days.
Answer:
6º
Watch it:
http://youtu.be/nbhKwM-li5E
MEDIAN
Definition
The middle
number in a set of
data values.
Example 3:
Procedure
Sample
1. Place the numbers in order
from smallest to largest.
2. Find the middle number.
PROBLEM: 4, 8, 1, 3, 6
SOLUTION:
1. Numbers in Order: 1, 3, 4, 6, 8
Note: If two numbers are in
the middle, compute the
mean of those numbers.
2. Middle Number: 1, 3, 4 , 6, 8
ANSWER: Median = 4
Your scores on five tests were 82, 79, 71, 73, and 90. Find the median score.
Place the numbers in order.
Find the middle number.
Answer.
71, 73, 79, 82, 90
71, 73, 79 ,82,90
Median = 79
103
CCBC Math 081
Third Edition
Statistics: Mean, Median, and Mode
Section 2.3
7 pages
Practice 3:
Your scores on five tests were 74, 89, 97, 65, and 95. Find the median score.
Answer:
89
Watch it:
http://youtu.be/hE1X95euIgo
Example 4:
The number of laptops sold each month was 17, 27, 12, 32, 28, 17, 31, and 19.
Find the median number of laptops sold each month.
Place the numbers in order.
12,17,17, 19, 27, 28, 31, 32
Find the middle number.
12,17,17, 19 , 27 , 28,31,32
Since there are two numbers in the middle, we need to compute the mean of the
two numbers. We do this by adding the middle numbers and then dividing by 2.
Compute the mean of the two middle numbers.
Answer.
(19  27)  2  46  2  23
Median = 23 laptops
Practice 4:
The number of passengers on six US Airways flights are as follows: 312, 294,
304, 298, 350, 523. Determine the median number of the passengers on the six
US Airways flights.
Answer:
308
Watch it:
http://youtu.be/yUQ1BIFkynU
Example 5:
One of the football players in the game ran for 5 yards, 3 yards, –2 yards, 6 yards,
10 yards, –1 yard, and 13 yards. What is the median number of yards he ran?
Place the numbers in order.
2, 1, 3, 5, 6,10,13
Find the middle number.
2, 1, 3, 5 , 6, 10, 13
Answer.
Median = 5 yards
Practice 5:
One of the football players in the game ran for 18 yards, -3 yards, 5 yards, -6
yards, 14 yards, –1 yard, and -5 yards. What is the median number of yards he
ran?
Answer:
-1 yards
Watch it:
http://youtu.be/ncURC6MHDHE
104
CCBC Math 081
Third Edition
Statistics: Mean, Median, and Mode
Section 2.3
7 pages
MODE
Definition
The number
that occurs
most often in
a set of data
values.
Example 6:
Procedure
Sample
1. Place the numbers in order from
smallest to largest.
PROBLEM: 5, 2, 7, 5, 1
SOLUTION:
2. Find the number that occurs most.
1. Numbers in Order: 1, 2, 5, 5, 7
Note: There may be more than
one mode or even no mode.
2. Number here Most: 1, 2, 5 , 5 , 7
ANSWER: Mode = 5
The number of students enrolled in the seven sections of Math 081 is as follows:
18, 21, 16, 19, 20, 17, and 20. Find the mode of this data set.
Place the numbers in order.
16,17,18,19, 20, 20, 21
Find the number that occurs most.
Answer.
16,17,18,19, 20 , 20 , 21
Mode = 20
Practice 6:
The numbers of cars sold per month at a dealership are as follows: 12, 21, 33,
21, 33, 21, 24, 31, 20, 27, 32, 24. Determine the mode of the numbers of cars
sold.
Answer:
21
Watch it:
http://youtu.be/1b6xozBpFys
Example 7:
The grades of the students were as follows: C, B, A, C, D, B, C, A, and A. Find
the mode of this data set.
Place the grades in order.
A, A, A, B, B, C, C, C, D
Find the grade that occurs most.
A, A, A,B,B, C, C, C,D
Grades A and C both occur three times, more than any other grade. So, there are
two modes here. Note: A data set that has two modes is called bimodal.
Answer.
Modes = A and C
105
CCBC Math 081
Third Edition
Statistics: Mean, Median, and Mode
Section 2.3
7 pages
Practice 7:
The makes of cars in a dealership are: Honda, Chevy, Ford, Honda, Toyota,
Chevy, Honda, Ford, Chevy. Determine the mode of the makes of the cars.
Answer:
Honda, Chevy
Watch it:
http://youtu.be/2ESDY116OiI
Example 8:
You made these transactions on your bank account: $20 deposit, $50 withdrawal,
$25 deposit, $100 deposit, $35 withdrawal, and $45 deposit. Find the mode.
First we should list the numbers. A deposit should be represented as a positive
number and a withdrawal should be represented as a negative number.
List the numbers.
Place the numbers in order.
Find the number occurring most.
20, 50, 25,100, 35, 45
50, 35, 20, 25, 45,100
50, 35, 20, 25, 45,100
No number occurs more than once. So, there is no mode.
Answer.
Mode = No mode (Do not write 0 as the answer)
Practice 8:
You made these transactions on your bank account: $225 deposit, $25
withdrawal, $20 deposit, $25 deposit, $35 withdrawal, and $15 deposit. Find the
mode.
Answer:
No Mode
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106
CCBC Math 081
Third Edition
Statistics: Mean, Median, and Mode
Section 2.3
7 pages
2.3 Statistics: Mean, Median, and Mode Exercises:
1.
Find the median of the values: -7, -5, 2, -3, 0
2.
Find the mode of the values: 9, -1, 0, 4, -6, -2
3.
Find the mean of the values: 3, 4, 4, 5, 7, 8, 9, 9, 10, 11
4.
Find the mean of the values: -9, 8, 13, 8
5.
Find the mode of the values: 4, -5, 6, -3, -3, 5, 6, -4, -3, -5
6.
Find the mean of the values: $100, $200, $700, $600, $500, $300, $400
7.
Find the median of the values: 432, 563, -303, -749, -803, 64, -59
8.
Find the mean of the values: $24, $4, $10, $16, $11
9.
Find the median of the values: 17, 5, 13, 54, 4, 27
10.
Find the mode of the values: -5, 4, 8, 11, 9, -8, 16
11.
Selling prices of houses recently sold are shown below. Find the median selling price.
$230000, $180000, $190000, $300000, $200000, $160000
12.
The ages of the work study employees recently hired are shown below. Find the mode.
18, 24, 21, 19, 18, 23, 20, 25, 21
13.
The colors of the cars on the lot are shown below. Find the mode of the colors.
Blue, Red, Green, Green, Blue, Blue, White, Black
14.
The number of passengers on yesterday’s JetAir flights is shown below. Find the median.
309, 295, 311, 302, 400, 488, 344
15.
The salesman sold cars for the prices shown below. Find the mean car price.
$32000, $35000, $22000, $38000, $14000, $19000, $22000, $25000
16.
The salaries of the employees are shown below. Find the mean salary.
$18000, $19700, $18600, $20410, $21780
17.
The salaries of the employee are shown below. Find the median salary.
$18000, $19700, $18600, $20410, $21780
18.
The number of items in stock is shown below. Find the mode.
35 units, 35 units, 65 units, 66, units, 33 units, 60 units, 36 units, 66 units
19.
The daily temperatures are shown below. Find the mean temperature.
-4º, 7 º, 3 º, -6 º, 8 º, -2 º, -9 º, 3 º
20.
Recent bank transactions are shown below. Find the mean transaction amount.
$63 deposit, $54 withdrawal, $32 deposit, $35 deposit, $26 withdrawal
107
CCBC Math 081
Third Edition
Statistics: Mean, Median, and Mode
2.3 Statistics: Mean, Median, and Mode Exercise Answers:
1.
-3
11. $195000
2.
None
12.
18 and 21
3.
7
13.
Blue
4.
5
14.
311
5.
-3
15.
$25875
6.
$400
16.
$19698
7.
-59
17.
$19700
8.
$13
18.
35 units and 66 units
9.
15
19.
0º
10.
None
20.
$10
108
Section 2.3
7 pages