Transcript Mean, Median, Mode & Range

Mean,
Median,
Mode
& Range
Outlier
• An outlier is a data item
that is much higher or
much lower than items in
a data set.
• 1, 2, 5, 27, 3, 4
Definition
• Mean – the average of a group
of numbers.
2, 5, 2, 1, 5
Mean = 3
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Mean is found by
evening out the numbers
2, 5, 2, 1, 5
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Mean is found by
evening out the numbers
2, 5, 2, 1, 5
BACK
Mean is found by
evening out the numbers
2, 5, 2, 1, 5
mean = 3
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How to Find the Mean of a
Group of Numbers
• Step 1 – Add all the numbers.
8, 10, 12, 18, 22, 26
8+10+12+18+22+26 = 96
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How to Find the Mean of a
Group of Numbers
• Step 2 – Divide the sum by
the number of addends.
8, 10, 12, 18, 22, 26
8+10+12+18+22+26 = 96
How many addends are there?
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How to Find the Mean of a
Group of Numbers
• Step 2 – Divide the sum by
the number of addends.
# of addends
16
6) 96
6
36
36
sum
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Definition
• Median – the middle number in
a set of ordered numbers.
1, 3, 7, 10, 13
Median = 7
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How to Find the Median in
a Group of Numbers
• Step 1 – Arrange the numbers
in order from least to greatest.
21, 18, 24, 19, 27
18, 19, 21, 24, 27
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How to Find the Median in
a Group of Numbers
• Step 2 – Find the middle
number.
21, 18, 24, 19, 27
18, 19, 21, 24, 27
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How to Find the Median in
a Group of Numbers
• Step 2 – Find the middle
number.
18, 19, 21, 24, 27
This is your median number.
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How to Find the Median in
a Group of Numbers
• Step 3 – If there are two middle
numbers, find the mean of these
two numbers.
18, 19, 21, 25, 27, 28
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How to Find the Median in
a Group of Numbers
• Step 3 – If there are two middle
numbers, find the mean of these
two numbers.
21+ 25 = 46
median
23
2) 46
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What is the median of
these numbers?
16, 10, 7
7, 10, 16
10
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Definition
• Mode – the number that
appears most often in a set
of numbers.
1, 1, 3, 7, 10, 13
Mode = 1
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How to Find the Mode in a
Group of Numbers
• Step 1 – Arrange the numbers
in order from least to greatest.
21, 18, 24, 19, 18
18, 18, 19, 21, 24
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How to Find the Mode in a
Group of Numbers
• Step 2 – Find the number that
is repeated the most.
21, 18, 24, 19, 18
18, 18, 19, 21, 24
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Definition
• Range – the difference between
the greatest and the least value
in a set of numbers.
1, 1, 3, 7, 10, 13
Range = 12
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How to Find the Range in
a Group of Numbers
• Step 1 – Arrange the numbers
in order from least to greatest.
21, 18, 24, 19, 27
18, 19, 21, 24, 27
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How to Find the Range in
a Group of Numbers
• Step 2 – Find the lowest and
highest numbers.
21, 18, 24, 19, 27
18, 19, 21, 24, 27
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How to Find the Range in
a Group of Numbers
• Step 3 – Find the difference
between these 2 numbers.
18, 19, 21, 24, 27
27 – 18 = 9
The range is 9
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What is the range?
29, 8, 4, 8, 19
4, 8, 8, 19, 29
29 – 4 = 25
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What is the range?
22, 21, 27, 31, 21, 32
21, 21, 22, 27, 31, 32
32 – 21 = 11
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What is the range?
31, 8, 3, 11, 19
3, 8, 11, 19, 31
31 – 3 = 28
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What is the range?
23, 7, 9, 41, 19
7, 9, 23, 19, 41
41 – 7 = 34
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17, 18, 19, 21, 24,26, 27
The lower quartile (LQ) is the median of the
lower half of the data.
The LQ is 18.
The upper quartile (UQ) is the median of
the upper half of the data.
The UQ is 26.
The interquartile range is UQ-LQ
26 18  8
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Even amounts divide in 2 equal halves.
13,15,18,19,22,25
L.Q.
U.Q.
Interquart ile Range 22  15  7
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TRY THIS
Key Skills
Use data to construct a histogram.
Jose bowled 11 games: 172, 152, 168, 157,143,
175,144, 164, 142, 172, 168.
Histogram:
Bowling scores
3.5
3
2.5
2
1.5
1
0.5
0
140's
150's
160's
170's
Find the median
76, 78, 82, 87, 88, 88, 89, 90, 91, 95
88
Find the median of this
segment
82
76,78, 82
1st
quartile
Find the median of this
segment.
90
88, 89,90
3rd quartile
Minimum
76, 78,
65
70
End of 1st
quartile
82,
75
End of 3rd
quartile
Median
87,
80
88,
88,
85
Maximum
89,
90,
90
95 100 105
Now for the box and whisker
91,
95
Find the median
142, 143, 144, 152, 157, 164, 168, 168, 172, 172 175.
164
Find the median of this
segment
Find the median of this
segment.
144
172
142, 143, 144
1st
quartile
168, 168, 172
3rd quartile
Mean,
Median,
Mode
& Range
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