Title: The Mean, Mode, Median, and Range
1The Mean, Mode, Median, and Range
2Imagine that there are five children of the
following ages
3 years
4 years
8 years
6 years
4 years
3Each child can be represented as a tower.
3 years
4 years
8 years
6 years
4 years
43 years
4 years
8 years
6 years
4 years
53 years
4 years
8 years
6 years
4 years
63 years
4 years
8 years
6 years
4 years
73 years
4 years
8 years
6 years
4 years
83 years
4 years
8 years
6 years
4 years
93 years
4 years
8 years
6 years
4 years
10Lets analyze this data by finding the range in
ages.
3 years
4 years
8 years
6 years
4 years
11The range is the difference between the oldest
child and the youngest child.
3 years
4 years
8 years
6 years
4 years
12The range is the difference between the oldest
child and the youngest child.
3 years
8 years
13The range is the difference between the oldest
child and the youngest child.
3 years
8 years
14The range is the difference between the oldest
child and the youngest child.
3 years
8 years
15The range is the difference between the oldest
child and the youngest child.
3 years
8 years
16The range is the difference between the oldest
child and the youngest child.
5 years

3 years 5 years
8 years
17Now lets find the median age.
3 years
4 years
8 years
6 years
4 years
18The median is the middle age.
3 years
4 years
8 years
6 years
4 years
19Before 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
20Before 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
21Before 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
22Before 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
23The median age is 4 years.
3 years
4 years
4 years
6 years
8 years
24The median divides the set of data in half.
3 years
4 years
4 years
6 years
8 years
25The median divides the data into 2 equal groups.
3 years
4 years
4 years
6 years
8 years
26The median strip in a highway divides the road in
half just like the median divides a set of data
in half.
27Now lets find the mean.
3 years
4 years
8 years
6 years
4 years
28The mean is also called the average.
3 years
4 years
8 years
6 years
4 years
29The mean means equal distribution or everyone
has the same amount.
3 years
4 years
8 years
6 years
4 years
30In order to find the mean, we must create 5
towers of equal height.
3 years
4 years
8 years
6 years
4 years
313 years
4 years
8 years
6 years
4 years
324 years
4 years
7 years
6 years
4 years
335 years
4 years
6 years
6 years
4 years
345 years
5 years
5 years
6 years
4 years
355 years
5 years
5 years
5 years
5 years
36All towers have a height of 5. Therefore, the
mean is 5 years.
5 years
5 years
5 years
5 years
5 years
37Now lets find the mode.
3 years
4 years
8 years
6 years
4 years
38The mode is the number that appears most often.
3 years
4 years
8 years
6 years
4 years
39In this case, there are two children who are 4
years old.
3 years
4 years
8 years
6 years
4 years
40In this case, there are two children who are 4
years old.
4 years
4 years
41In this case, there are two children who are 4
years old.
Therefore, the mode is 4.
4 years
4 years
42Lets consider a different set of data
6 years
5 years
9 years
3 years
43Lets make a tower to represent each childs age.
6 years
5 years
9 years
3 years
446 years
5 years
9 years
3 years
456 years
5 years
9 years
3 years
466 years
5 years
9 years
3 years
476 years
5 years
9 years
3 years
486 years
5 years
9 years
3 years
49Lets analyze this data by finding the range in
ages.
6 years
5 years
9 years
3 years
50The oldest child is 9 and the youngest is 3.
6 years
5 years
9 years
3 years
51The oldest child is 9 and the youngest is 3.
9 years
3 years
52The range is 6 years.
6 years
9 years 
3 years
53Now lets find the median.
6 years
5 years
9 years
3 years
54Now lets find the median.
6 years
5 years
9 years
3 years
55Now lets find the median.
6 years
3 years
9 years
5 years
56Now lets find the median.
3 years
6 years
9 years
5 years
57Now lets find the median.
3 years
5 years
9 years
6 years
58Remember, the median is the middle number the
number that splits the data in half.
3 years
5 years
9 years
6 years
59Remember, the median is the middle number the
number that splits the data in half.
3 years
5 years
9 years
6 years
60The median in this case will be 5 ½ .
5 ½
3 years
5 years
9 years
6 years
615 ½ is the average of the two middle numbers,
5 and 6.
5 ½
3 years
5 years
9 years
6 years
62Now lets find the mean.
6 years
5 years
9 years
3 years
63In order to find the mean we must make 4 towers
of equal height.
6 years
5 years
9 years
3 years
646 years
5 years
9 years
3 years
656 years
6 years
8 years
3 years
666 years
6 years
7 years
4 years
676 years
6 years
6 years
5 years
68Is it possible to make 4 towers of equal height?
6 years
6 years
6 years
5 years
69YES! It is possible, but the mean in this case
will not be a whole number.
6 years
6 years
6 years
5 years
70Lets take these three squares and divide them
equally among the 4 towers.
5 years
5 years
5 years
5 years
715 years
5 years
5 years
5 years
725 years
5 years
5 years
5 years
735 years
5 years
5 years
5 years
745 years
5 years
5 years
5 years
753 ? 4 ¾
5 years
5 years
5 years
5 years
763 ? 4 ¾
5 years
5 years
5 years
5 years
773 ? 4 ¾
5¾ years
5 years
5 years
5 years
783 ? 4 ¾
5¾ years
5 ¾ years
5 years
5 years
793 ? 4 ¾
5¾ years
5 ¾ years
5¾years
5 years
803 ? 4 ¾
5¾ years
5 ¾ years
5¾years
5¾ years
81We now have 4 equal towers. So the mean is 5 ¾
years.
5¾ years
5 ¾ years
5¾years
5¾ years
82More often than not, the mean is a mixed number
and not a whole number.
5¾ years
5 ¾ years
5¾years
5¾ years
83Now lets find the mode.
6 years
5 years
9 years
3 years
84If no number is repeated most often, then there
is no mode.
6 years
5 years
9 years
3 years
85Lets consider one more set of data
2 years
8 years
8 years
2 years
86Each child can be represented by a tower.
2 years
8 years
8 years
2 years
872 years
8 years
8 years
2 years
882 years
8 years
8 years
2 years
892 years
8 years
8 years
2 years
902 years
8 years
8 years
2 years
912 years
8 years
8 years
2 years
92Lets analyze this data by finding the range in
ages.
2 years
8 years
8 years
2 years
93The oldest child is 8, and the youngest child is
2.
8 years
2 years
94Therefore, the range is 6 years.
6 years
8 years 
2 years
95Now lets find the median.
2 years
8 years
8 years
2 years
96First, put the children in order from youngest to
oldest.
2 years
8 years
8 years
2 years
97First, put the children in order from youngest to
oldest.
2 years
8 years
2 years
8 years
98First, put the children in order from youngest to
oldest.
2 years
2 years
8 years
8 years
99The median is the middle number that divides the
data into 2 equal groups.
2 years
2 years
8 years
8 years
100We must average the two middle numbers to find
the median.
2 years
2 years
8 years
8 years
101The average of 2 and 8 is 5.
5
2 years
2 years
8 years
8 years
102Therefore, the median is 5.
5
2 years
2 years
8 years
8 years
103Now lets find the mean.
2 years
8 years
8 years
2 years
104We need to make 4 towers of equal height.
2 years
8 years
8 years
2 years
1052 years
8 years
8 years
2 years
1063 years
7 years
7 years
3 years
1074 years
6 years
6 years
4 years
1085 years
5 years
5 years
5 years
109We have 4 towers that each have a height of 5.
5 years
5 years
5 years
5 years
110Therefore, the mean is 5 years.
5 years
5 years
5 years
5 years
111Now lets find the mode.
2 years
8 years
8 years
2 years
112In this case, we have two numbers that are
repeated most often.
2 years
2 years
8 years
8 years
113Therefore, we have 2 modes 2 years and 8 years.
2 years
2 years
8 years
8 years
114SUMMARY
115SUMMARY
1) The range is the difference between the
greatest value and the smallest value.
116SUMMARY
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.
117SUMMARY
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.
118SUMMARY
4) The mode is the number that appears most
often. It is possible to have more than one mode.
119Practice Time
1201) 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
1211) If the range in shoe size for a sixth grade
class is 9, then this means that everyone has
large feet.
B) False
1221) 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.
1232) 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
1242) 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
1252) 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
1263) 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
1273) 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
1283) 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
1294) A survey was conducted where students were
asked how many pets they have at home. What is
the mode?
1304) A survey was conducted where students were
asked how many pets they have at home. What is
the mode?
131There were 7 students who said that they have 2
pets. 2 was the most popular response in the
survey. Therefore, the mode is 2.
1325) 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.
1335) 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.
1346) 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.
1356) 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.
1366) 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.
1377) 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.
1387) 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
1398) 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.
1408) 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.
141THE END!