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Working with Data
Average
3 Averages
There are 3 types of average (central tendency)
• Mean
• Mode
• Median
Average is a way of comparing data.
SLO:
To understand what is Mean
Average
Mean is found by spreading out the
numbers evenly
2, 5, 2, 1, 5
How many beads would be in each pile if each of
the 5 piles had the same number of beads?
Mean average = 3 (3 in each pile)
A quicker way…..
To even out columns of numbers could take a
long time.
Here is a quicker method that does not involve
beads.
SLO:
To calculate the mean average
Sum
(you will need to know this word)
Sum – the answer to an addition
problem.
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your notes
To Find the Mean Average
• Step 1 – Add all the numbers.
2 + 5 + 2 + 5 + 1 = 15
1
2
3
4
5
Step 2 – Divide the sum by
the number of numbers.
15 ÷ 5 = 3
Mean average = 3
?5
Your Turn: What is the mean of these
numbers?
7, 10, 16
33 ÷ 3 = 11
Your Turn: What is the mean of these
numbers?
2, 9, 5, 4
5
Your Turn: What is the mean of these
numbers?
1, 2, 7, 11, 9
6
Your Turn: What is the mean of these
numbers?
4, 3, 1, 3, 2, 7, 1
3
Web resource
http://www.youtube.com/watch?v=UVnelMfhtrg
Youtube video how to find mean average (Very strange man!)
SLO:
To find the Median Average
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your notes
Definition
Median
is in the
Middle
(List must be in order)
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Median Example #1
Find the median of these five test scores.
10
1
6
3
5
Step 1: Put them in order.
1
3
5
6
10
Step 2: Find the middle number
1
3
5
6
10
The Median is 5
Your Turn:
Find the Median of the following
21, 18, 24, 19, 27
Step 1 – Arrange the numbers in order from least to greatest.
18, 19, 21, 24, 27
Step 2 – Find the middle number.
21 is your median number.
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Median Example #2
Find the median of an even number of test scores.
92
86
94
83
72
88
Step 1: put them in order
72 83 86 88 92 94
Step 2: There are two numbers in the middle, 86 and 88
72 83 86 88 92 94
Step 3: Find half way between these two numbers, by adding them and
dividing by two.
86+88= 174
174÷2= 87
The Median is 87
Your Turn:
Find the Median of the following
21, 25, 19, 28, 27, 18
Step 1 – Arrange the numbers in order from least to greatest.
18, 19, 21, 25, 27, 28
Step 2 – Find the middle number.
Step 3 – As there are two middle numbers, find the middle
of these two numbers. (46 ÷ 2)
23 is your median number.
Your Turn: What is the median of
these numbers?
16, 10, 7
7, 10, 16
10
Your Turn: What is the median of
these numbers?
29, 8, 4, 11, 19
4, 8, 11, 19, 29
11
Your Turn: What is the median of
these numbers?
31, 7, 2, 12, 14, 19
2, 7, 12, 14, 19, 31
13
12 + 14 = 26 2) 26
Your Turn: What is the median of
these numbers?
53, 5, 81, 67, 25, 78
5, 25, 53, 67, 78, 81
60
53 + 67 = 120 2) 120
Web resources
http://www.youtube.com/watch?v=loAAovIKLGw
(youtube video to find median)
SLO:
To find the mode average
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your notes
Definition
Mode
is the most
Popular
A little French….
• A la mode – the most popular or
that which is in fashion.
Baseball caps are a la mode today.
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Example 1
In a set of numbers the Mode is the
number that appears most often.
1, 1, 3, 7, 10, 13
Mode = 1
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Example 2
1, 1, 1, 3, 7, 7, 7, 10, 10, 13
There are 2 numbers to choose from
so there are 2 modes (bimodal)
Mode = 1 and 7
Your Turn:
Find the mode
21, 18, 24, 19, 18
Mode = 18
Your Turn: Which number is the
mode?
29, 8, 4, 8, 19, 4
Mode = 4 and 8
Your Turn: Which number is the
mode?
1, 2, 2, 9, 9, 4, 9, 10
Mode = 9
Your Turn: Which number is the
mode?
22, 21, 27, 31, 21, 32
Mode = 21
Your Turn:
Here is an list of temperatures for one week. Find the
mode temperature.
Mon. Tues. Wed. Thurs. Fri. Sat. Sun.
77° 79°
83°
77° 83° 77° 82°
77° is the most frequent number, so the mode= 77°
Your Turn: Which number is the
mode?
6, 8, 3, 8, 5, 4, 3, 9, 6
Mode = 3, 6 and 8
(Tri-modal)
Web Resources
http://www.youtube.com/watch?v=dam-TCRbkFw
(youtube clip to find mode average, deals with multiple modes)
Spread
Spread
Average looks at how data is grouped.
Spread looks at the distribution of the data.
SLO:
To find the range of a set of data
Difference
A word you will need to know
Difference – the answer to one number
subtracted from another.
E.g. the difference between 8 and 3 is 5
Definition
Range
is the difference
between the highest
and lowest
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To find the range we subtract the lowest value in the set
from the highest value.
Range = highest value – lowest value
When the range is small; the values are similar in size.
When the range is large; the values vary widely in size.
Copy into your notes:
E.g. Find the Range of
21, 18, 24, 19, 27
Step 1: Find the lowest and highest numbers.
Step 2: Find the difference between these 2 numbers.
27 – 18 = 9
The range is 9
Your Turn: Find the Range
• Find the range from the temperatures.
77° 77° 77° 79° 82° 83° 83°
The highest number is 83, and the lowest is 77.
83-77= 6
The Range is 6
Your Turn: Find the Range
1, 1, 3, 7, 10, 13
Range = 13 – 1 =
12
What is the range?
29, 8, 4, 8, 19
29 – 4 = 25
What is the range?
22, 21, 27, 31, 21, 32
32 – 21 = 11
What is the range?
31, 8, 3, 11, 19
31 – 3 = 28
What is the range?
23, 7, 9, 41, 19
41 – 7 = 34
SLO:
Not to mix up mean, median,
mode and range
In conclusion
Average:
Mean (sum ÷ #)
Mode (most)
Median (Middle)
Spread
Range (Biggest – Smallest)
Your Turn: find the Mean
Dad
Mum
34
33
Jack
Alex
Katie
5
5
1
The Mean
34+33+5+5+1= 80
Then, since there are 6 people in the family, we
next divide by 6.
78÷6= 13
Your Turn: Find the Median
Dad
Mum
34
33
Jack
Alex
Katie
5
5
1
The Median
first put all of the numbers in order.
34
33
5
5
1
The Mean in this case is 5
Mode
Dad
Mum
34
33
Jack
Alex
Katie
5
5
1
The Mode
See which number appears the most
34
33
5
5
1
The Mode in this case is 5
Your Turn: find the Range
Dad
Mum
34
33
Jack
Alex
Katie
5
5
1
The Range
The highest age is 34, and the lowest is 1
Now we need to subtract to find the difference
34-1= 33
The range is 33
Web resources
http://www.bbc.co.uk/bitesize/ks2/maths/data/mode_median_mean_range/play/
(individual game for mean, median and mode)
http://www.bbc.co.uk/schools/gcsebitesize/maths/statistics/measuresofaverageact.shtml
(Notes and individual interactive mean, median and mode questions)
http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.STAT&ID2=AB.MATH.JR.STA
T.CENT&lesson=html/object_interactives/central_tendency/use_it.html
(mean, mode, median game)
http://www.youtube.com/watch?v=oNdVynH6hcY
(Mean, median and mode song)
http://www.bbc.co.uk/bitesize/ks2/maths/data/mode_median_mean_range/quiz/q10083371/
(mean, mode, median, range quiz)
Extension:
Potential Problem with Means
Median
Mean
Median
Mean
Problems with Mode
• May not exist
• May not be unique
– E.g. “bi-modal” distribution
• Two values occur with same frequency
Thanks
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