The Mean, Mode, Median, and Range

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The Mean, Mode, Median, and Range

• A Visual Approach

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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
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The range is the difference between the oldest
child and the youngest child.
5 years
-
3 years 5 years
8 years
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Now lets find the median age.
3 years
4 years
8 years
6 years
4 years
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The median is the middle age.
3 years
4 years
8 years
6 years
4 years
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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
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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
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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
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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
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The median age is 4 years.
3 years
4 years
4 years
6 years
8 years
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The median divides the set of data in half.
3 years
4 years
4 years
6 years
8 years
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The median divides the data into 2 equal groups.
3 years
4 years
4 years
6 years
8 years
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The median strip in a highway divides the road in
half just like the median divides a set of data
in half.
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Now lets find the mean.
3 years
4 years
8 years
6 years
4 years
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The mean is also called the average.
3 years
4 years
8 years
6 years
4 years
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The mean means equal distribution or everyone
has the same amount.
3 years
4 years
8 years
6 years
4 years
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In order to find the mean, we must create 5
towers of equal height.
3 years
4 years
8 years
6 years
4 years
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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
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Now lets find the mode.
3 years
4 years
8 years
6 years
4 years
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The mode is the number that appears most often.
3 years
4 years
8 years
6 years
4 years
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In this case, there are two children who are 4
years old.
3 years
4 years
8 years
6 years
4 years
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In this case, there are two children who are 4
years old.
4 years
4 years
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In this case, there are two children who are 4
years old.
Therefore, the mode is 4.
4 years
4 years
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Lets consider a different set of data
6 years
5 years
9 years
3 years
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Lets make a tower to represent each childs age.
6 years
5 years
9 years
3 years
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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
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Lets analyze this data by finding the range in
ages.
6 years
5 years
9 years
3 years
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The oldest child is 9 and the youngest is 3.
6 years
5 years
9 years
3 years
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The oldest child is 9 and the youngest is 3.
9 years
3 years
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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
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Now lets find the median.
6 years
3 years
9 years
5 years
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Now lets find the median.
3 years
6 years
9 years
5 years
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Now lets find the median.
3 years
5 years
9 years
6 years
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Remember, the median is the middle number the
number that splits the data in half.
3 years
5 years
9 years
6 years
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Remember, the median is the middle number the
number that splits the data in half.
3 years
5 years
9 years
6 years
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The median in this case will be 5 ½ .
5 ½
3 years
5 years
9 years
6 years
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5 ½ is the average of the two middle numbers,
5 and 6.
5 ½
3 years
5 years
9 years
6 years
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Now lets find the mean.
6 years
5 years
9 years
3 years
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In order to find the mean we must make 4 towers
of equal height.
6 years
5 years
9 years
3 years
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6 years
5 years
9 years
3 years
65
6 years
6 years
8 years
3 years
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6 years
6 years
7 years
4 years
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6 years
6 years
6 years
5 years
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Is it possible to make 4 towers of equal height?
6 years
6 years
6 years
5 years
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YES! It is possible, but the mean in this case
will not be a whole number.
6 years
6 years
6 years
5 years
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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
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3 ? 4 ¾
5 years
5 years
5 years
5 years
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3 ? 4 ¾
5¾ years
5 years
5 years
5 years
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3 ? 4 ¾
5¾ years
5 ¾ years
5 years
5 years
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3 ? 4 ¾
5¾ years
5 ¾ years
5¾years
5 years
80
3 ? 4 ¾
5¾ years
5 ¾ years
5¾years
5¾ years
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We now have 4 equal towers. So the mean is 5 ¾
years.
5¾ years
5 ¾ years
5¾years
5¾ years
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More often than not, the mean is a mixed number
and not a whole number.
5¾ years
5 ¾ years
5¾years
5¾ years
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Now lets find the mode.
6 years
5 years
9 years
3 years
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If no number is repeated most often, then there
is no mode.
6 years
5 years
9 years
3 years
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Lets consider one more set of data
2 years
8 years
8 years
2 years
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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
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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
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The oldest child is 8, and the youngest child is
2.
8 years
2 years
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Therefore, the range is 6 years.
6 years
8 years -
2 years
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Now lets find the median.
2 years
8 years
8 years
2 years
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First, put the children in order from youngest to
oldest.
2 years
8 years
8 years
2 years
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First, put the children in order from youngest to
oldest.
2 years
8 years
2 years
8 years
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First, put the children in order from youngest to
oldest.
2 years
2 years
8 years
8 years
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The median is the middle number that divides the
data into 2 equal groups.
2 years
2 years
8 years
8 years
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We must average the two middle numbers to find
the median.
2 years
2 years
8 years
8 years
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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
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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
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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
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Now lets find the mode.
2 years
8 years
8 years
2 years
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In this case, we have two numbers that are
repeated most often.
2 years
2 years
8 years
8 years
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Therefore, we have 2 modes 2 years and 8 years.
2 years
2 years
8 years
8 years
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SUMMARY
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SUMMARY
1) The range is the difference between the
greatest value and the smallest value.
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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.
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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.
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SUMMARY
4) The mode is the number that appears most
often. It is possible to have more than one mode.
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Practice Time
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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
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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.
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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
where 20 students were asked about their shoe
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
where 20 students were asked about their shoe
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
where 20 students were asked about their shoe
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?
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4) A survey was conducted where students were
asked how many pets they have at home. What is
the mode?
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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.
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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.

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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.
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THE END!