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Statistics
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Level F
Mean
Mean from a Frequency Table
Median and Mode
Range of a Set of Data
Grouped Frequency Table
28-Apr-17
Created by Mr. Lafferty
1
Starter
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Level F
Q1.
Round to 2 decimal places
(a)
52.567
(b)
Q2.
Add 2.34 + 5.03 + 7.2
Q3.
Solve for x
62.155
2x  20  8  x
28-Apr-17
Created by Mr. Lafferty
2
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Level E
Aims of the lesson
1. Explain the meaning of the keyword Mean
2. Calculate the mean for given data.
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Created by Mr. Lafferty
3
The mean
The mean is the most commonly used average.
To calculate the mean of a set of values we add together
the values and divide by the total number of values.
Mean =
Sum of values
Number of values
For example, the mean of 3, 6, 7, 9 and 9 is
28-Apr-17
3+6+7+9+9
34

5
5
 6.8
Created by Mr. Lafferty
4
Two dice were thrown 10 times and their scores were
added together and recorded. Find the mean for this
data.
7, 5, 2, 7, 6, 12, 10, 4, 8, 9
Mean  7 + 5 + 2 + 7 + 6 + 12 + 10 + 4 + 8 + 9
10
70

10
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7
Created by Mr. Lafferty
5
Average / Mean
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Level F
Now try Exercise 4
Ch5 (page 106)
28-Apr-17
Created by Mr. Lafferty
6
Lesson Starter
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Level F
Q1.
75% of £200
Q2.
How long between 8:40am to 1.20pm
Q3.
36.9 x 6
Q4.
34.7 x 20
Q5.
Find the mean for the set of numbers
-7, 10, 6, 3
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Created by Mr. Lafferty
7
Aims of the Lesson
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Level F
Find the mean for a set of data
without a calculator
using the mean difference
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Created by Mr. Lafferty
8
Two dice were thrown 10 times and their scores were
added together and recorded. Find the mean for this
data.
7, 5, 2, 4, 6, 12
Scores
7
5
2
4
6
12
Assumed
mean 5
2
0
-3
-1
1
7
2 + 0 + (-3) + (-1) + 1 + 7
Mean difference 
= 1
6
Mean =
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5 +1 = 6
Created by Mr. Lafferty
9
Find the mean for this data without a calculator.
112, 118, 121, 124, 129
Scores
112
118
121
124
129
Assumed mean 120
-8
-2
1
4
9
Mean difference
(-8) + (-2) + 1 + 4 + 9

5
= 0.8
Mean = 120 +0.8 = 120.8
28-Apr-17
Created by Mr. Lafferty
10
Average / Mean
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Level F
Now try Exercise 4.2
Ch5 (page 109)
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Created by Mr. Lafferty
11
Starter Questions
Level F
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1. Mutliply out 2y( y - 4)
2. Simplify the ratio 6 : 28
3.
10% of £22
4.
Tidy up the expression
7 - (-10) x 3
28-Apr-17
Created by Mr. Lafferty Maths Dept.
Frequency Tables
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Level F
Working Out the Mean
Learning Intention
1. To explain how to work
out the mean by adding in
a third column to a
Frequency Table.
Success Criteria
1. Add a third column to a
frequency table.
2. Work out the mean from a
frequency Table.
28-Apr-17
Created by Mr. Lafferty Maths Dept.
Frequency Tables
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Level F
Working Out the Mean
Example : This table shows the number
of coins in the pockets of some children.
Adding a third column to this table
will help us find the total number of
coins and the ‘Mean’.
Mean Number of coins =
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No of
Coins
(c)
Freq.
(f)
1
5
5 x 1 =5
2
5
5 x 2 = 10
3
1
1x3=3
4
3
3 x 4 = 12
5
2
2 x 5 = 10
Totals
16
40
40
= 2.5 coins
16
Created by Mr. Lafferty Maths Dept.
fxC
Frequency Tables
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Level F
Working Out the Mean
Example : This table shows the number
of brothers and sisters of pupils in an
S2 class.
No of
Sibling
s (S)
Adding a third column to this table
will help us find the total number of
siblings and the ‘Mean’.
Mean Number of siblings
=
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33
= 1.1 siblings
30
Sxf
0
9
1
13
1 x 13 = 13
2
6
2 x 6 = 12
3
1
3x1=3
5
1
5x1=5
Totals
Created by Mr. Lafferty Maths Dept.
Freq.
(f)
30
0 x 9 =0
33
Frequency Tables
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Working Out the Mean
Now try Exercise 5.1
Ch5 (page 111)
28-Apr-17
Created by Mr. Lafferty Maths Dept.
Lesson Starter
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Level E
Q1.
70% of £500
Q2.
How long between 8:12am to 2.09pm
Q3.
75.9 x 7
Q4.
Find arrow value
1200
Q5.
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1300
The answer to a question is 81. Write
down the question.
Created by Mr. Lafferty
17
Different Averages
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Level F
Learning Intention
1. To define the terms Mean
Median, Mode and Range
for a set of data.
Success Criteria
1. Know the terms Mean,
Median, Mode and Range.
2. Work out values of Mean,
Median, Mode and Range.
28-Apr-17
Created by Mr. Lafferty Maths Dept.
Different Averages
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Level F
Sum of all the numbers
The Mean =
No. of Number
Find the mean of the set of data 1, 1, 1, 1, 2, 3, 36
1 +1 +1 +1 +2 +3 +26
The Mean =
=5
7
Can you see that this is not the most suitable of averages since
five out of the six numbers are all below the mean of 5
28-Apr-17
Created by Mr. Lafferty Maths Dept.
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Different Averages
An average should indicate a
“measure of central tendency”
but should also indicate
what the distribution of data looks like.
This is why we have 3 different types of averages to consider
1. The Mean
2. The Median (put the data in order then find the MIDDLE value)
3. The Mode (the number that appears the most)
For the above data the Median or Mode is a better average = 1
28-Apr-17
Created by Mr. Lafferty Maths Dept.
Different Averages
Level F
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Example :
Find the median and mode for the set of data.
10, 2, 14, 1, 14, 7
Median = 1,2, 7,10,14,14
7 + 10 17
Median =
=
= 8.5
2
2
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Created by Mr. Lafferty Maths Dept.
Mode = 14
Different Averages
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Level F
Now try Exercise 6.1
Ch5 (page 115)
28-Apr-17
Created by Mr. Lafferty Maths Dept.
Lesson Starter
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Level F
Q1.
20% of £800
Q2.
12000 divided by 60
Q3.
Tidy up the following 2x + 5y – 3x – 6y
Q4.
A circle is divided into 10 equal pieces.
The whole circle represents 100%.
What value is one piece.
The answer to a question is 60. Write
down the question.
Q5.
28-Apr-17
Created by Mr. Lafferty
23
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Level F
Aims of the lesson
1. Explain the meaning of the keyword Range
2. Calculate the mean and range for given data.
28-Apr-17
Created by Mr. Lafferty
24
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; the values are similar in size.
When the range is large; the values vary widely in size.
28-Apr-17
Created by Mr. Lafferty
25
The Range
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Level F
Example : find the range for the following
(a)
3, 1, 4, 10
10 – 1 = 9
(b)
-3, 8, -6, 1, 7, 5
7 – (-6) = 13
– (-15.5)
(c) The highest and lowest every recorded35.3
temperature
= 50.8oC
for Glasgow are 35.3oC and -15.5oC respectively.
Find the value of the range.
28-Apr-17
Created by Mr. Lafferty
26
Statistics
Working Out Statistics
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Level F
Now try Ex7.1 & 7.2
Ch5 (page 117)
28-Apr-17
Created by Mr. Lafferty Maths Dept.
Starter Questions
Level F
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1.
Find the perimeter and area of the shape.
2a
6h
2. Calculate (a) (-3m) x (-4m)
3.
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(b) (2b) x (3a)
Find the mean of the data set
3,5,5,7,10
Created by Mr. Lafferty Maths Dept.
Grouped Frequency Tables
Frequency Tables
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Level F
Learning Intention
1. To explain how to
construct and interpret
Grouped Frequency
Tables.
28-Apr-17
Success Criteria
1. Construct Grouped
Frequency Table
2. Interpret Table.
Created by Mr. Lafferty Maths Dept.
Grouped Frequency Tables
Frequency Tables
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Level F
When a set of data is large, the numbers have to be
grouped into “class intervals”.
•
Each interval must have the same number of values
•
Ideally, there should be between 6 to 10 intervals
We will now construct a Frequency Table
28-Apr-17
Created by Mr. Lafferty Maths Dept.
Choose suitable
Class interval
Grouped Frequency Tables
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Level F
What is the
class
10modal
– 19, 40
– 49
Frequency Tables
interval
and
70 - 79
Example : The test scores for a class
Class
are given below. Construct a Frequency
Intervals
Table for the results.
10-19
12
15
21
71
55
56
78
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23
32
12
32
76
41
17
41
40
16
75
21
19
55
51
43
34
73
20
77
69
56
42
22
47
Created by Mr. Lafferty Maths Dept.
Tally
Frequency
6
20-29
5
30-39
3
40-49
6
50-59
5
60-69
1
70-79
6
Statistics
Working Out Statistics
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Level F
Now try Exercise 8.1
Ch5 (page 120)
28-Apr-17
Created by Mr. Lafferty Maths Dept.