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## The Mean, Mode, Median, and Range

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Title: The Mean, Mode, Median, and Range

1
The Mean, Mode, Median, and Range
• A Visual Approach

2
Imagine that there are five children of the
following ages
3 years
4 years
8 years
6 years
4 years
3
Each child can be represented as a tower.
3 years
4 years
8 years
6 years
4 years
4
3 years
4 years
8 years
6 years
4 years
5
3 years
4 years
8 years
6 years
4 years
6
3 years
4 years
8 years
6 years
4 years
7
3 years
4 years
8 years
6 years
4 years
8
3 years
4 years
8 years
6 years
4 years
9
3 years
4 years
8 years
6 years
4 years
10
Lets analyze this data by finding the range in
ages.
3 years
4 years
8 years
6 years
4 years
11
The range is the difference between the oldest
child and the youngest child.
3 years
4 years
8 years
6 years
4 years
12
The range is the difference between the oldest
child and the youngest child.
3 years
8 years
13
The range is the difference between the oldest
child and the youngest child.
3 years
8 years
14
The range is the difference between the oldest
child and the youngest child.
3 years
8 years
15
The range is the difference between the oldest
child and the youngest child.
3 years
8 years
16
The range is the difference between the oldest
child and the youngest child.
5 years
-
3 years 5 years
8 years
17
Now lets find the median age.
3 years
4 years
8 years
6 years
4 years
18
The median is the middle age.
3 years
4 years
8 years
6 years
4 years
19
Before we select the middle age, we must first
put the children in order from youngest to oldest.
3 years
4 years
8 years
6 years
4 years
20
Before we select the middle age, we must first
put the children in order from youngest to oldest.
3 years
4 years
6 years
8 years
4 years
21
Before we select the middle age, we must first
put the children in order from youngest to oldest.
3 years
4 years
6 years
4 years
8 years
22
Before we select the middle age, we must first
put the children in order from youngest to oldest.
3 years
4 years
4 years
6 years
8 years
23
The median age is 4 years.
3 years
4 years
4 years
6 years
8 years
24
The median divides the set of data in half.
3 years
4 years
4 years
6 years
8 years
25
The median divides the data into 2 equal groups.
3 years
4 years
4 years
6 years
8 years
26
The median strip in a highway divides the road in
half just like the median divides a set of data
in half.
27
Now lets find the mean.
3 years
4 years
8 years
6 years
4 years
28
The mean is also called the average.
3 years
4 years
8 years
6 years
4 years
29
The mean means equal distribution or everyone
has the same amount.
3 years
4 years
8 years
6 years
4 years
30
In order to find the mean, we must create 5
towers of equal height.
3 years
4 years
8 years
6 years
4 years
31
3 years
4 years
8 years
6 years
4 years
32
4 years
4 years
7 years
6 years
4 years
33
5 years
4 years
6 years
6 years
4 years
34
5 years
5 years
5 years
6 years
4 years
35
5 years
5 years
5 years
5 years
5 years
36
All towers have a height of 5. Therefore, the
mean is 5 years.
5 years
5 years
5 years
5 years
5 years
37
Now lets find the mode.
3 years
4 years
8 years
6 years
4 years
38
The mode is the number that appears most often.
3 years
4 years
8 years
6 years
4 years
39
In this case, there are two children who are 4
years old.
3 years
4 years
8 years
6 years
4 years
40
In this case, there are two children who are 4
years old.
4 years
4 years
41
In this case, there are two children who are 4
years old.
Therefore, the mode is 4.
4 years
4 years
42
Lets consider a different set of data
6 years
5 years
9 years
3 years
43
Lets make a tower to represent each childs age.
6 years
5 years
9 years
3 years
44
6 years
5 years
9 years
3 years
45
6 years
5 years
9 years
3 years
46
6 years
5 years
9 years
3 years
47
6 years
5 years
9 years
3 years
48
6 years
5 years
9 years
3 years
49
Lets analyze this data by finding the range in
ages.
6 years
5 years
9 years
3 years
50
The oldest child is 9 and the youngest is 3.
6 years
5 years
9 years
3 years
51
The oldest child is 9 and the youngest is 3.
9 years
3 years
52
The range is 6 years.
6 years
9 years -
3 years
53
Now lets find the median.
6 years
5 years
9 years
3 years
54
Now lets find the median.
6 years
5 years
9 years
3 years
55
Now lets find the median.
6 years
3 years
9 years
5 years
56
Now lets find the median.
3 years
6 years
9 years
5 years
57
Now lets find the median.
3 years
5 years
9 years
6 years
58
Remember, the median is the middle number the
number that splits the data in half.
3 years
5 years
9 years
6 years
59
Remember, the median is the middle number the
number that splits the data in half.
3 years
5 years
9 years
6 years
60
The median in this case will be 5 ½ .
5 ½
3 years
5 years
9 years
6 years
61
5 ½ is the average of the two middle numbers,
5 and 6.
5 ½
3 years
5 years
9 years
6 years
62
Now lets find the mean.
6 years
5 years
9 years
3 years
63
In order to find the mean we must make 4 towers
of equal height.
6 years
5 years
9 years
3 years
64
6 years
5 years
9 years
3 years
65
6 years
6 years
8 years
3 years
66
6 years
6 years
7 years
4 years
67
6 years
6 years
6 years
5 years
68
Is it possible to make 4 towers of equal height?
6 years
6 years
6 years
5 years
69
YES! It is possible, but the mean in this case
will not be a whole number.
6 years
6 years
6 years
5 years
70
Lets take these three squares and divide them
equally among the 4 towers.
5 years
5 years
5 years
5 years
71
5 years
5 years
5 years
5 years
72
5 years
5 years
5 years
5 years
73
5 years
5 years
5 years
5 years
74
5 years
5 years
5 years
5 years
75
3 ? 4 ¾
5 years
5 years
5 years
5 years
76
3 ? 4 ¾
5 years
5 years
5 years
5 years
77
3 ? 4 ¾
5¾ years
5 years
5 years
5 years
78
3 ? 4 ¾
5¾ years
5 ¾ years
5 years
5 years
79
3 ? 4 ¾
5¾ years
5 ¾ years
5¾years
5 years
80
3 ? 4 ¾
5¾ years
5 ¾ years
5¾years
5¾ years
81
We now have 4 equal towers. So the mean is 5 ¾
years.
5¾ years
5 ¾ years
5¾years
5¾ years
82
More often than not, the mean is a mixed number
and not a whole number.
5¾ years
5 ¾ years
5¾years
5¾ years
83
Now lets find the mode.
6 years
5 years
9 years
3 years
84
If no number is repeated most often, then there
is no mode.
6 years
5 years
9 years
3 years
85
Lets consider one more set of data
2 years
8 years
8 years
2 years
86
Each child can be represented by a tower.
2 years
8 years
8 years
2 years
87
2 years
8 years
8 years
2 years
88
2 years
8 years
8 years
2 years
89
2 years
8 years
8 years
2 years
90
2 years
8 years
8 years
2 years
91
2 years
8 years
8 years
2 years
92
Lets analyze this data by finding the range in
ages.
2 years
8 years
8 years
2 years
93
The oldest child is 8, and the youngest child is
2.
8 years
2 years
94
Therefore, the range is 6 years.
6 years
8 years -
2 years
95
Now lets find the median.
2 years
8 years
8 years
2 years
96
First, put the children in order from youngest to
oldest.
2 years
8 years
8 years
2 years
97
First, put the children in order from youngest to
oldest.
2 years
8 years
2 years
8 years
98
First, put the children in order from youngest to
oldest.
2 years
2 years
8 years
8 years
99
The median is the middle number that divides the
data into 2 equal groups.
2 years
2 years
8 years
8 years
100
We must average the two middle numbers to find
the median.
2 years
2 years
8 years
8 years
101
The average of 2 and 8 is 5.
5
2 years
2 years
8 years
8 years
102
Therefore, the median is 5.
5
2 years
2 years
8 years
8 years
103
Now lets find the mean.
2 years
8 years
8 years
2 years
104
We need to make 4 towers of equal height.
2 years
8 years
8 years
2 years
105
2 years
8 years
8 years
2 years
106
3 years
7 years
7 years
3 years
107
4 years
6 years
6 years
4 years
108
5 years
5 years
5 years
5 years
109
We have 4 towers that each have a height of 5.
5 years
5 years
5 years
5 years
110
Therefore, the mean is 5 years.
5 years
5 years
5 years
5 years
111
Now lets find the mode.
2 years
8 years
8 years
2 years
112
In this case, we have two numbers that are
repeated most often.
2 years
2 years
8 years
8 years
113
Therefore, we have 2 modes 2 years and 8 years.
2 years
2 years
8 years
8 years
114
SUMMARY
115
SUMMARY
1) The range is the difference between the
greatest value and the smallest value.
116
SUMMARY
2) The median is the middle number in the set.
You must first put the numbers in order before
selecting the middle number. If there are two
middle numbers, then the median is the average of
those two numbers.
117
SUMMARY
3) The mean is the average. To find the mean,
sum the numbers and divide by the number of
numbers. The mean means that everyone gets the
same amount. The mean is not always a whole
number.
118
SUMMARY
4) The mode is the number that appears most
often. It is possible to have more than one mode.
119
Practice Time
120
1) If the range in shoe size for a sixth grade
class is 9, then this means that everyone has
large feet.
A) True
B) False
121
1) If the range in shoe size for a sixth grade
class is 9, then this means that everyone has
large feet.
B) False
122
1) If the range in shoe size for a sixth grade
class is 9, then this means that everyone has
large feet.
A range of 9 means that the difference between
the largest shoe size and the smallest shoe size
is 9.
123
2) The median shoe size for a sixth grade class
is 6. There are as many students with a shoe
size of 6 or greater as there are students with a
shoe size of 6 or less.
A) True
B) False
124
2) The median shoe size for a sixth grade class
is 6. There are as many students with a shoe
size of 6 or greater as there are students with a
shoe size of 6 or less.
A) True
125
2) The median shoe size for a sixth grade class
is 6. There are as many students with a shoe
size of 6 or greater as there are students with a
shoe size of 6 or less.
Remember, the median divides the data into two
equal groups.
2
5
4
6
7
9
10
126
3) A survey was conducted on a sixth grade class
size. All of the responses were added together
to make a total of 140. What is the mean
(average)?
A) 6
B) 120
C) 7
D) 140
127
3) A survey was conducted on a sixth grade class
size. All of the responses were added together
to make a total of 140. What is the mean
(average)?
C) 7
128
3) A survey was conducted on a sixth grade class
size. All of the responses were added together
to make a total of 140. What is the mean
(average)?
The mean means everyone has the same amount.
Therefore, take the total and divide by the
number of students.
140 ? 20 students 7
129
4) A survey was conducted where students were
asked how many pets they have at home. What is
the mode?
130
4) A survey was conducted where students were
asked how many pets they have at home. What is
the mode?
131
There were 7 students who said that they have 2
pets. 2 was the most popular response in the
survey. Therefore, the mode is 2.
132
5) Find the mean number of calories.
• Quarter Pounder with Cheese 540 cal.
• Hamburger 280 cal.
• Big Mac 510 cal.
• Big N Tasty Burger 510 cal.
• Double Big Mac 700 cal.

133
5) Find the mean number of calories.
• Quarter Pounder with Cheese 540 cal.
• Hamburger 280 cal.
• Big Mac 510 cal.
• Big N Tasty Burger 510 cal.
• Double Big Mac 700 cal.

TOTAL CALORIES 2540MEAN 2540 5
508 cal.
134
6) Find the median number of calories.
• Quarter Pounder with Cheese 540 cal.
• Hamburger 280 cal.
• Big Mac 510 cal.
• Big N Tasty Burger 510 cal.
• Double Big Mac 700 cal.

135
6) Find the median number of calories.
• Quarter Pounder with Cheese 540 cal.
• Hamburger 280 cal.
• Big Mac 510 cal.
• Big N Tasty Burger 510 cal.
• Double Big Mac 700 cal.

First, put the numbers in order from least to
greatest.
136
6) Find the median number of calories.
• Hamburger 280 cal.
• Big N Tasty 510 cal.
• Big Mac 510 cal.
• Quarter Pounder with Cheese 540 cal.
• Double Big Mac 700 cal.

Now, pick out the middle number.
137
7) Find the range in the number of calories.
• Hamburger 280 cal.
• Big N Tasty 510 cal.
• Big Mac 510 cal.
• Quarter Pounder with Cheese 540 cal.
• Double Big Mac 700 cal.

138
7) Find the range in the number of calories.
• Hamburger 280 cal.
• Big N Tasty 510 cal.
• Big Mac 510 cal.
• Quarter Pounder with Cheese 540 cal.
• Double Big Mac 700 cal.

700 280 420
139
8) Find the mode.
• Hamburger 280 cal.
• Big N Tasty 510 cal.
• Big Mac 510 cal.
• Quarter Pounder with Cheese 540 cal.
• Double Big Mac 700 cal.

140
8) Find the mode.
• Hamburger 280 cal.
• Big N Tasty 510 cal.
• Big Mac 510 cal.
• Quarter Pounder with Cheese 540 cal.
• Double Big Mac 700 cal.

510 appears most often.
141
THE END!