Measures of Central Tendency
Mean, Median & Mode
Number of Rawhide Bones
Chewed Each Week
8
Number of Bones
7
6
5
4
3
2
1
0
Bianca
Blackie
Bronte
Dog
Demi
Jessie
Mean
Number of Rawhide Bones
Chewed Each Week
8
Number of Bones
7
6
5
4
3
2
1
0
Bianca
Blackie
Bronte
Dog
Demi
Jessie
Mean
How many bones does each dog chew each week?
Number of Rawhide Bones
Chewed Each Week
8
Number of Bones
7
6
5
4
3
2
1
0
Bianca
Blackie
Bronte
Demi
Jessie
Dog
Bianca _____ Blackie _______ Bronte _______ Demi ______ Jessie _____
Mean
How many bones does each dog chew each week?
Number of Rawhide Bones
Chewed Each Week
8
Number of Bones
7
6
5
4
3
2
1
0
Bianca
Blackie
Bronte
Dog
Bianca:5 Blackie:7 Bronte:2 Demi:1 Jessie:5
To Find the Mean we:
Demi
Jessie
Mean
How many bones does each dog chew each week?
Number of Rawhide Bones
Chewed Each Week
8
Number of Bones
7
6
5
4
3
2
1
0
Bianca
Blackie
Bronte
Demi
Jessie
Dog
Bianca:5 Blackie:7 Bronte:2 Demi:1 Jessie:5
To Find the Mean we:
Add up all the data and divide by the number of
pieces of data
Mean
How many bones does each dog chew each week?
Number of Rawhide Bones
Chewed Each Week
8
Number of Bones
7
6
5
4
3
2
1
0
Bianca
Blackie
Bronte
Demi
Jessie
Dog
Bianca:5 Blackie:7 Bronte:2 Demi:1 Jessie:5
To Find the Mean we:
Add up all the data and divide by the number of
pieces of data
5 + 7 + 2 + 1 + 5 = _________ ÷ 5 (the number of dogs)
Mean
How many bones does each dog chew each week?
Number of Rawhide Bones
Chewed Each Week
8
Number of Bones
7
6
5
4
3
2
1
0
Bianca
Blackie
Bronte
Demi
Jessie
Dog
Bianca:5 Blackie:7 Bronte:2 Demi:1 Jessie:5
To Find the Mean we:
Add up all the data and divide by the number of
pieces of data
5 + 7 + 2 + 1 + 5 = 20 ÷ 5 = 4
Median
• Look at the data from the dogs and rewrite it
so that all your numbers are in order from
least to greatest
• 5, 7, 2, 1, 5 =
Median
• Look at the data from the dogs and rewrite it
so that all your numbers are in order from
least to greatest
• 5, 7, 2, 1, 5 = 1, 2, 5, 5, 7
• In order to find the Median we:
Median
• Look at the data from the dogs and rewrite it
so that all your numbers are in order from
least to greatest
• 5, 7, 2, 1, 5 = 1, 2, 5, 5, 7
• In order to find the Median we:
– Just need to find out which number is in the
middle.
• Remember – Use your fingers to help!
Median
• Look at the data from the dogs and rewrite it
so that all your numbers are in order from
least to greatest
• 5, 7, 2, 1, 5 = 1, 2, 5, 5, 7
• In order to find the Median we:
– Just need to find out which number is in the
middle.
• Remember – Use your fingers to help!
Median
• WHAT IF!!!
• What happens if there are an even number of
data?
– Let’s see… let’s add a new dog named Bubba and
say he eats 3 bones per week.
– Order the numbers again, this time including
Bubba.
Median
• WHAT IF!!!
• What happens if there are an even number of
data?
– Let’s see… let’s add a new dog named Bubba and
say he eats 3 bones per week.
– Order the numbers again, this time including
Bubba.
– 1, 2, 3, 5, 5, 7
Median
• WHAT IF!!!
• What happens if there are an even number of
data?
– Let’s see… let’s add a new dog named Bubba and
say he eats 3 bones per week.
– Order the numbers again, this time including
Bubba.
– 1, 2, 3, 5, 5, 7
– How do we find the median now?
Median
• WHAT IF!!!
• What happens if there are an even number of
data?
– Let’s see… let’s add a new dog named Bubba and say
he eats 3 bones per week.
– Order the numbers again, this time including Bubba.
– 1, 2, 3, 5, 5, 7
– How do we find the median now?
• We take the two middle numbers and add them together
then divide by two: 3+5=8
8÷2=4
Mode
• In order to find the mode we:
– Order all our numbers again: 1, 2, 5, 5, 7
– Then find which number occurs the most amount
of times.
– The mode of these numbers is: ________
Mode
• In order to find the mode we:
– Order all our numbers again: 1, 2, 5, 5, 7
– Then find which number occurs the most amount
of times.
– The mode of these numbers is: 5
Mode
• WHAT IF!!!
• What if there are two or more numbers that
appear an equal number of times?
• ie 1, 2, 5, 5, 7, 7, 8, 9
• The mode then is both 5 and 7
• What if all the numbers only appear once?
• ie 1, 2, 5, 7, 8, 9
• Then there is no mode.
Notes
• Mean - Add up all numbers and divide by how
many numbers you have.
• Median - First, place the numbers in order from
smallest to largest. Then find the middle number!
Note: If there are 2 numbers in the middle, find
the average of these two numbers.
• Mode - is the number used the most of all the
numbers. If there is a tie, all those numbers are
the mode. Note: If all numbers occur only once
there is NO Mode.
Practice
• 9 students took a quiz that was worth 10
points. There scores were as follows:
8, 4, 3, 7, 9, 10, 1, 7, 5
What is the Mean?
What is the Median?
What is the Mode?
Practice
• To find the mean we must add up all the
numbers first
8 + 4 + 3 + 7 + 9 + 10 + 1 + 7 + 5 =
Practice
• To find the mean we must add up all the
numbers first
8 + 4 + 3 + 7 + 9 + 10 + 1 + 7 + 5 = 54
Next we divide the number of pieces of data
(9 in this case as there were 9 students) by the
total number of points (54)
54 ÷ 9 =
Practice
• To find the mean we must add up all the
numbers first
8 + 4 + 3 + 7 + 9 + 10 + 1 + 7 + 5 = 54
Next we divide the number of pieces of data
(9 in this case as there were 9 students) by the
total number of points (54)
54 ÷ 9 = 6
Therefore the mean in this case is 6
Practice
• To find the median we need to sort all our
numbers in order from least to greatest:
8, 4, 3, 7, 9, 10, 1, 7, 5
Practice
• To find the median we need to sort all our
numbers in order from least to greatest:
8, 4, 3, 7, 9, 10, 1, 7, 5
1, 3, 4, 5, 7, 7, 8, 9, 10
Now we need to find which number is in the
middle of the series. Remember to use your
fingers if you need to!
Practice
• To find the median we need to sort all our
numbers in order from least to greatest:
8, 4, 3, 7, 9, 10, 1, 7, 5
1, 3, 4, 5, 7, 7, 8, 9, 10
Now we need to find which number is in the
middle of the series. Remember to use your
fingers if you need to!
Our median is 7
Practice
• To find the mode we need to see which
number occurs the most times.
8, 4, 3, 7, 9, 10, 1, 7, 5
7 occurs twice while all the others occur only
once so 7 is our mode.
Why do we need the 3?
• Read the top of page 152
Practice
• Pg 152 # 1, 2, 3