measures of central tendency jan sands 2007 mean, median, mode, range
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Measures ofCentral Tendency
Jan Sands2007
Mean, Median, Mode, Range
Definition of Mean
MeanMeans
Average
Definition of Mean•Mean – the average of a group of numbers.
2, 5, 2, 1, 5Mean = 3
Mean is found by evening out the
numbers.2, 5, 2, 1, 5
Mean is found by evening out the
numbers.2, 5, 2, 1, 5
mean = 3
How to Find the Mean of a Group of Numbers•Step 1 – Add all the numbers.
2, 5, 2, 1, 5
2+ 5+ 2+ 1+ 5 = 15
How to Find the Mean of a Group of Numbers• Step 2 – Divide the sum by
the number of items.
2, 5, 2, 1, 5How many total items are there?
How to Find the Mean of a Group of Numbers
•Step 2 – Divide the sum by the number of items.
sum15 ÷ 5 = 3
number of items
mean
Find the Mean of a Group of Numbers
The mean or average of these numbers is 3.
2, 5, 2, 1, 5
What is the mean of these numbers?
7, 10, 16
The mean is 11.
What is the mean of these numbers?
2, 9, 14, 27
The mean is 13.
What is the mean of these numbers?
1, 2, 7, 11, 19
The mean is 8.
What is the mean of these numbers?
26, 33, 41, 52The mean is 38.
Definition of Median
Medianis in theMiddle
Definition of Median•Median – the middle number in a set of ordered numbers.
1, 3, 7, 10, 13The median is 7.
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
How to Find the Median in a Group of
Numbers•Step 2 – Find the middle
number.
18, 19, 21, 24, 27
21 is the median number.
What is the median of these numbers?
16, 10, 7
The median number is 10.
7, 10, 16
What is the median of these numbers?
29, 8, 4, 11, 19
The median number is 11.
4, 8, 11, 19, 29
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, 29
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
46 ÷ 2 = 23
What is the median of these numbers?
31, 7, 2, 12, 14, 19
2, 7, 12, 14, 19, 31First Step
12 + 14 = 26
Second Step
26 ÷ 2 = 13The median is
13.
What is the median of these numbers?
53, 5, 81, 67, 25, 78
5, 25, 53, 67, 78, 81First Step
53 + 67 = 120
Second Step
120 ÷ 2 = 60The median is 60.
Definition of Mode
Modeis the most
Popular
Definition of Mode•Mode – the number that appears most frequently in a set of numbers.
1, 1, 3, 7, 10, 13The mode is 1.
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
How to Find the Mode in a Group of Numbers•Step 2 – Find the number that is repeated the most.
18, 18, 19, 21, 24
The mode is 18.
Which number is the mode?
29, 8, 4, 8, 19
The mode is 8.
4, 8, 8, 19, 29
Which number is the mode?
1, 2, 2, 9, 9, 4, 9, 10
The mode is 9.
1, 2, 2, 4, 9, 9, 9, 10
Which number is the mode?
22, 21, 27, 31, 21, 32
The mode is 21.
21, 21, 22, 27, 31, 32
Which number is the mode?
52, 21, 37, 31, 28, 42
There is no mode.
21, 28, 31, 37, 42, 52
Which number is the mode?
23, 25, 21, 31, 21, 25
There are two modes: 21 and 25.
21, 21, 23, 25, 25, 31
Definition of Range
Range is the distancebetween the least and greatest values in a set of numbers.
Definition of Range•Range – the difference between
the greatest and the least value in a set of numbers.
1, 1, 3, 7, 10, 13
The range is 12.
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
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
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.
What is the range?
29, 8, 4, 8, 19
29 – 4 = 25
4, 8, 8, 19, 29
The range is 25.
What is the range?
22, 21, 27, 31, 21, 32
32 – 21 = 11
21, 21, 22, 27, 31, 32
The range is 11.
What is the range?31, 8, 3, 11, 19
31 – 3 = 28
3, 8, 11, 19, 31
The range is 28.
What is the range?23, 7, 9, 41, 19
41 – 7 = 34
7, 9, 19, 23, 41
The range is 34.
Mean, Median, Mode, & Range
Review
Mean, Median, Mode, & Range
15, 19, 22, 25, 6, 15, 17
Mean
15, 19, 22, 25, 6, 15, 17
15 + 19 + 22 + 25 + 6 + 15 + 17 = 119
119 ÷ 7 = 17
The mean is 17.
Median
15, 19, 22, 25, 6, 15, 17
6, 15, 15, 17, 19, 22, 25
The mean is 17.
Mode
15, 19, 22, 25, 6, 15, 17
6, 15, 15, 17, 19, 22, 25
The mode is 15.
Range
15, 19, 22, 25, 6, 15, 17
6, 15, 15, 17, 19, 22, 25
The range is 19.
25 – 6 = 19
Mean, Median, Mode, & Range
Find the mean, median, mode and range of…
2. 52, 55, 51, 59, 65, 55, 55
1. 28, 6, 9, 7, 14, 6, 5
3. 43, 43, 32, 38, 49
Mean, Median, Mode, & Range
Answers
1. 29, 6, 9, 7, 15, 6, 5
1. Mean is 11. 2. Median is 7.
3. Mode is 6. 4. Range is 24.
Mean, Median, Mode, Range - answers continued
3. 43, 43, 32, 38, 49
2. 52, 55, 51, 59, 65, 55, 55
1. Mean is 56. 2. Median is 55.
3. Mode is 55. 4. Range is 14.
1. Mean is 41. 2. Median is 43.
3. Mode is 43. 4. Range is 17.