Statistics

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Statistics
Level F
Mean
Mean from a Frequency Table
Median and Mode
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Range of a Set of Data
Grouped Frequency Table
2
Starter
Level F
Q1. Round to 2 decimal places
(a) 52.567 (b) 62.155
Q2. Add 2.34 5.03 7.2
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Q3. Solve for x
3
Aims of the lesson
Level E

• 1. Explain the meaning of the keyword Mean
• Calculate the mean for given data.

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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.
For example, the mean of 3, 6, 7, 9 and 9 is
5
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
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Average / Mean
Level F
Now try Exercise 4 Ch5 (page 106)
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Lesson Starter
Level F
Q1.
Q2. How long between 840am to 1.20pm
Q3. 36.9 x 6
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Q4. 34.7 x 20
Q5. Find the mean for the set of numbers
-7, 10, 6, 3
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Aims of the Lesson
Level F
Find the mean for a set of data without a
calculator using the mean difference
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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
Mean difference
1
5 1 6
Mean
10
Find the mean for this data without a
calculator. 112, 118, 121, 124, 129
Mean difference
0.8
Mean
120 0.8 120.8
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Average / Mean
Level F
Now try Exercise 4.2 Ch5 (page 109)
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Starter Questions
Level F
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Frequency Tables
Level F
Working Out the Mean
Learning Intention
Success Criteria

• Add a third column to a frequency table.

1. To explain how to work out the mean by
adding in a third column to a Frequency Table.
2. Work out the mean from a frequency Table.
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Frequency Tables
Level F
Working Out the Mean
Example This table shows the number of coins in
the pockets of some children.
f x C
Adding a third column to this table will help us
find the total number of coins and the Mean.
5
1
5 x 1 5
5
2
5 x 2 10
1
3
1 x 3 3
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3
4
3 x 4 12
2
5
2 x 5 10
16
Totals
40
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Frequency Tables
Level F
Working Out the Mean
Example This table shows the number of brothers
and sisters of pupils in an S2 class.
S x f
Adding a third column to this table will help us
find the total number of siblings and the Mean.
9
0
0 x 9 0
13
1
1 x 13 13
6
2
2 x 6 12
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1
3
3 x 1 3
1
5
5 x 1 5
33
Totals
30
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Frequency Tables
Working Out the Mean
Now try Exercise 5.1 Ch5 (page 111)
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Lesson Starter
Level E
Q1.
Q2. How long between 812am to 2.09pm
Q3. 75.9 x 7
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Find arrow value
Q4.
1300
1200
Q5. The answer to a question is 81. Write down
the question.
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Different Averages
Level F
Learning Intention
Success Criteria

• To define the terms Mean Median, Mode and Range
  for a set of data.

1. Know the terms Mean, Median, Mode and Range.
2. Work out values of Mean, Median, Mode and
Range.
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Different Averages
Level F
Find the mean of the set of data 1, 1, 1, 1, 2,
3, 36
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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
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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
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• The Mean
• 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
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Different Averages
Level F
Example
Find the median and mode for the set of data.
10, 2, 14, 1, 14, 7
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Different Averages
Level F
Now try Exercise 6.1 Ch5 (page 115)
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Lesson Starter
Level F
Q1.
Q2. 12000 divided by 60
Q3. Tidy up the following 2x 5y 3x 6y
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A circle is divided into 10 equal pieces. The
whole circle represents 100. What value is one
piece.
Q4.
Q5. The answer to a question is 60. Write down
the question.
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Aims of the lesson
Level F

• 1. Explain the meaning of the keyword Range
• Calculate the mean and range for given data.

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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.
When the range is small the values are similar
in size.
When the range is large the values vary widely
in size.
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The Range
Level F
Example find the range for the following
10 1 9
(a) 3, 1, 4, 10
7 (-6) 13
(b) -3, 8, -6, 1, 7, 5
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35.3 (-15.5) 50.8oC
(c) The highest and lowest every recorded
temperature for Glasgow are 35.3oC and -15.5oC
respectively. Find the value of the range.
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Statistics
Level F
Working Out Statistics
Now try Ex7.1 7.2 Ch5 (page 117)
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Starter Questions
Level F
2a
6h
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Grouped Frequency Tables
Level F
Frequency Tables
Learning Intention
Success Criteria

• Construct Grouped Frequency Table

1. To explain how to construct and interpret
Grouped Frequency Tables.
2. Interpret Table.
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Grouped Frequency Tables
Level F
Frequency Tables
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

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We will now construct a Frequency Table
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Choose suitable Class interval
Grouped Frequency Tables
What is the modal class interval
10 19, 40 49 and 70 - 79
Level F
Frequency Tables
Example The test scores for a class are given
below. Construct a Frequency Table for the
results.
6
10-19
12 23 41 55 77 15 32 40 51 69 21 12 16 43 56 71
32 75 34 42 55 76 21 73 22 56 41 19 20 47 78
17
5
20-29
3
30-39
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6
5
1
6
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Statistics
Level F
Working Out Statistics
Now try Exercise 8.1 Ch5 (page 120)
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