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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
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
SLO:
To calculate the mean average
Sum
(you will need to know this word)
problem.
Copy into
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
Youtube video how to find mean average (Very strange man!)
SLO:
To find the Median Average
Copy into
Definition
Median
is in the
Middle
(List must be in order)
Copy into
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
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.
Copy into
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
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)
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
SLO:
To find the mode average
Copy into
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.
Copy into
Example 1
In a set of numbers the Mode is the
number that appears most often.
1, 1, 3, 7, 10, 13
Mode = 1
Copy into
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
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
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
(youtube clip to find mode average, deals with multiple modes)
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
Copy into
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.
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
• 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
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)
Range (Biggest – Smallest)
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
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
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
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)
(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
This power point has been put together using
power points, images, videos and games from
the net.
Thank you to all those who have placed their
work in the public domain. For others to use.
```
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