Transcript Averages

Handling Data: AVERAGES
• Learning Objective:
To be able to calculate
the mode, median,
range and Mean
KEY WORDS:
MEDIAN, MODE,
RANGE, MEAN and
AVERAGES
Saturday, 09 April 2016
• All MUST be able
understand how to
calculate mode,
median, range and
Mean
• Some should be able
to know which
average is the best to
USE!
The mean
The mean is the most commonly used average. It can
only be used with numerical data.
To calculate the mean of a set of values we add together the
values and divide by the total number of values.
Sum of values
Mean =
Number of values
For example, the mean of 3, 6, 7, 9 and 9 is
3+6+7+9+9
5
=
34
5
= 6.8
Calculating the mean from a frequency table
The following frequency table shows the scores obtained
when a dice is thrown 50 times.
What is the mean score?
Score
1
2
3
4
5
6
Total
Frequency
8
11
6
9
9
7
50
Score ×
Frequency
8
22
18
36
45
42
171
171
The mean score =
50
= 3.42
Complete Questions:
• Page 84 Exercise 8.3 1-4
• Remember:
Sum of values
Mean =
Number of values
3+6+7+9+9
5
=
34
5
= 6.8
Finding the mode
The mode or modal value in a set of data is the data value
that appears the most often.
For example, the number of goals scored by the local
football team in the last ten games is:
2,
1,
2,
0,
0,
2,
3,
1,
2,
1.
The modal score is 2.
Is it possible to have more than one modal value?
Is it possible to have no modal value?
Yes
Yes
Finding the mode
The mode is the only average that can be used for
categorical or non-numerical data.
For example, 30 pupils are asked how they usually travel to
school. The results are shown in a frequency table.
Method of travel Frequency
Bicycle
6
8
On foot
Car
2
Bus
6
Train
3
What is the modal
method of travel?
Most children travel on foot.
Travelling on foot is
therefore the modal method
of travel.
Finding the mode from a bar chart
Number of pupils
This bar chart shows the scores in a science test:
9
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
Marks out of ten
What was the modal score?
6 is the modal score because it has the highest bar.
Finding the mode from a pie chart
This pie chart shows the favourite food of a sample of people:
23
78
55
18
chocolate
fruit
vegetables
sweets
other
What was the
modal food
type?
26
The biggest sector of the pie chart is for chocolate, so this
is the modal food type.
Finding the mode from a frequency table
This frequency table shows the frequency of different length
words in a given paragraph of text.
Word length 1
Frequency
3
2 3 4
16 12 16
5
7
6
3
7
11
8
6
9
2
10
1
What was the modal word length?
We need to look for the word lengths that occur most
frequently.
For this data there are two modal word lengths: 2 and 4.
Complete Questions
• Page 85 Exercise 8.4 Questions1-6
MODE MEANS MOST
Finding the median
The median is the middle value of a set of numbers
arranged in order. For example,
Find the median of
10,
7,
9,
12,
7,
8,
6,
Write the values in order:
6,
7,
7,
8,
The median is the middle value.
9,
10,
12.
Finding the median
To find the number that is half-way between 47 and 51 we
can add the two numbers together and divide by 2.
47 + 51
2
=
98
2
= 49
Alternatively, find the difference between 47 and 51 and add
half this difference to the lower number.
51 – 47 = 4
½ of 4 = 2
2 + 47 = 49
The median of 42, 43, 47, 51, 56 and 65 is 49.
Class Work
• Page 87 Exercise 8.5 1-4
• Remember:
Write the values in order:
6,
7,
7,
8,
The median is the middle value.
9,
10,
12.
Finding the range
The range of a set of data is a measure of how the data is
spread across the distribution.
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 it tells us that the values are similar
What does it mean if the range is small?
in size.
When the range is large it tells us that the values vary widely
What does it mean if the range is large?
in size.
Class Work
• Page 88 Exercise 8.7 1-8
• Remember:
Range = highest value – lowest value
1,2,3,8,9,4,5,7 ------------Range=9-1=8
Plenary
• Come up with ONE WORD TO describe
the 3 AVERAGES and RANGE
• Mode:
• Median:
• Mean:
• Range:
Remember the three averages and range
S
M
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MODE
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RANGE
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MEAN
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DIVIDE
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The three averages and range
There are three different types of average:
MEAN
MEDIAN
MODE
sum of values
number of values
middle value
most common
The range is not an average, but tells you how the data is
spread out:
RANGE
largest value – smallest value