1. Created by Mr. Lafferty Maths Dept.
Statistics
S5 Int2
Quartiles from a Frequency Table
Quartiles from a Cumulative Frequency Table
Estimating Quartiles from C.F Graphs
Standard Deviation
Standard Deviation from a sample
Scatter Graphs
Probability
Relative Frequency & Probability
31-Mar-17
Created by Mr. Lafferty Maths Dept.

2. Created by Mr Lafferty Maths Dept
Starter Questions
S5 Int2
31-Mar-17
Created by Mr Lafferty Maths Dept

3. Created by Mr Lafferty Maths Dept
Statistics
Quartiles from Frequency Tables
S5 Int2
Learning Intention
Success Criteria
To explain how to calculate quartiles from frequency tables.
Know the term quartiles.
Calculate quartiles given a frequency table.
31-Mar-17
Created by Mr Lafferty Maths Dept

4. Created by Mr Lafferty Maths Dept
Statistics
Quartiles from Frequency Tables
S5 Int2
Reminder !
Range : The difference between highest and Lowest
values. It is a measure of spread.
Median : The middle value of a set of data.
When they are two middle values
the median is half way between them.
Mode : The value that occurs the most in a set
of data. Can be more than one value.
Quartiles : The median splits into lists of equal length.
The medians of these two lists are called quartiles.
31-Mar-17
Created by Mr Lafferty Maths Dept

5. Created by Mr Lafferty Maths Dept
Statistics
Quartiles from Frequency Tables
S5 Int2
To find the quartiles of an ordered list you consider its length. You need to find three numbers which break the list into four smaller list of equal length.
Example 1 : For a list of 24 numbers, 24 ÷ 6 = 4 R0
6 number Q1
6 number Q2
6 number Q3
6 number
The quartiles fall in the gaps between
Q1 : the 6th and 7th numbers
Q2 : the 12th and 13th numbers
Q3 : the 18th and 19th numbers.
31-Mar-17
Created by Mr Lafferty Maths Dept

6. Created by Mr Lafferty Maths Dept
Statistics
Quartiles from Frequency Tables
S5 Int2
Example 2 : For a list of 25 numbers, 25 ÷ 4 = 6 R1
6 number Q1
6 number
1 No.
6 number Q3
6 number Q2
The quartiles fall in the gaps between
Q1 : the 6th and 7th
Q2 : the 13th
Q3 : the 19th and 20th numbers.
31-Mar-17
Created by Mr Lafferty Maths Dept

7. Created by Mr Lafferty Maths Dept
Statistics
Quartiles from Frequency Tables
S5 Int2
Example 3 : For a list of 26 numbers, 26 ÷ 4 = 6 R2
6 number
1 No.
6 number Q2
6 number
1 No.
6 number Q1 Q3
The quartiles fall in the gaps between
Q1 : the 7th number
Q2 : the 13th and 14th number
Q3 : the 20th number.
31-Mar-17
Created by Mr Lafferty Maths Dept

8. Created by Mr Lafferty Maths Dept
Statistics
Quartiles from Frequency Tables
S5 Int2
Example 4 : For a list of 27 numbers, 27 ÷ 4 = 6 R3
6 number
1 No.
6 number
1 No.
6 number
1 No.
6 number Q1 Q2 Q3
The quartiles fall in the gaps between
Q1 : the 7th number
Q2 : the 14th number
Q3 : the 21th number.
31-Mar-17
Created by Mr Lafferty Maths Dept

9. Created by Mr Lafferty Maths Dept
Statistics
Quartiles from Frequency Tables
S5 Int2
Example 4 : For a ordered list of 34.
Describe the quartiles.
34 ÷ 4 = 8 R2
8 number
1 No.
8 number Q2
8 number
1 No.
8 number Q1 Q3
The quartiles fall in the gaps between
Q1 : the 9th number
Q2 : the 17th and 18th number
Q3 : the 26th number.
31-Mar-17
Created by Mr Lafferty Maths Dept

10. Created by Mr Lafferty Maths Dept
Statistics
Quartiles from Frequency Tables
S5 Int2
Now try Exercise 1
Start at 1b
Ch11 (page 162)
31-Mar-17
Created by Mr Lafferty Maths Dept

11. Created by Mr. Lafferty Maths Dept.
Starter Questions
S5 Int2
31-Mar-17
Created by Mr. Lafferty Maths Dept.

12. Created by Mr. Lafferty Maths Dept.
Statistics
S5 Int2
Quartiles from Cumulative Frequency Table
Learning Intention
Success Criteria
1. To explain how to calculate quartiles from Cumulative Frequency Table.
Find the quartile values from Cumulative Frequency Table.
31-Mar-17
Created by Mr. Lafferty Maths Dept.

13. Created by Mr. Lafferty Maths Dept.
Statistics
S5 Int2
Quartiles from Cumulative Frequency Table
Example 1 :
The frequency table shows the length
of phone calls ( in minutes) made from
an office in one day.
Time
Freq.
(f)
Cum. Freq. 1 2 2 2 3 5 3 5 10 4 8 18 5 4 22
31-Mar-17
Created by Mr. Lafferty Maths Dept.

14. Created by Mr. Lafferty Maths Dept.
Statistics
S5 Int2
Quartiles from Cumulative Frequency Table
We use a combination of quartiles from a frequency table
and the Cumulative Frequency Column.
For a list of 22 numbers, 22 ÷ 4 = 5 R2
5 number
1 No.
5 number Q2
5 number
1 No.
5 number Q1 Q3
The quartiles fall in the gaps between
Q1 : the 6th number Q1 : 3 minutes
Q2 : the 11th and 12th number Q2 : 4 minutes
Q3 : the 17th number. Q3 : 4 minutes
31-Mar-17
Created by Mr. Lafferty Maths Dept.

15. Created by Mr. Lafferty Maths Dept.
Statistics
S5 Int2
Quartiles from Cumulative Frequency Table
Example 2 :
A selection of schools were asked
how many 5th year sections they have.
Opposite is a table of the results.
Calculate the quartiles for the results.
No. Of Sections
Freq.
(f)
Cum. Freq. 4 3 3 5 5 8 6 8 16 7 9 25 8 8 33
31-Mar-17
Created by Mr. Lafferty Maths Dept.

16. Created by Mr. Lafferty Maths Dept.
Statistics
S5 Int2
Quartiles from Cumulative Frequency Table
We use a combination of quartiles from a frequency table
and the Cumulative Frequency Column.
Example 2 : For a list of 33 numbers, 33 ÷ 4 = 8 R1
8 number Q1
8 number
1 No.
8 number Q3
8 number Q2
The quartiles fall in the gaps between
Q1 : the 8th and 9th numbers Q1 : 5.5
Q2 : the 17th number Q2 : 7
Q3 : the 25th ad 26th numbers. Q3 : 7.5
31-Mar-17
Created by Mr. Lafferty Maths Dept.

17. Created by Mr Lafferty Maths Dept
Statistics
S5 Int2
Quartiles from Cumulative Frequency Table
Now try Exercise 2
Ch11 (page 163)
31-Mar-17
Created by Mr Lafferty Maths Dept

18. Created by Mr. Lafferty Maths Dept.
Starter Questions
S5 Int2
2cm
3cm
29o
4cm A
70o C
53o
8cm B
31-Mar-17
Created by Mr. Lafferty Maths Dept.

19. Quartiles from Cumulative Frequency Graphs
S5 Int2
Learning Intention
Success Criteria
1. To show how to estimate quartiles from cumulative frequency graphs.
Know the terms quartiles.
2. Estimate quartiles from cumulative frequency graphs.
31-Mar-17
Created by Mr. Lafferty Maths Dept.

20. Quartiles from Cumulative Frequency Graphs
S5 Int2
Number of sockets
Cumulative Frequency 10 2 20 9 30 24 40 34 50 39 60

21. Cumulative Frequency Graphs
New Term
Interquartile range
Semi-interquartile range
(Q3 – Q1 )÷2 = ( )÷2
=7.5
Cumulative Frequency Graphs
S5 Int2
Quartiles
40 ÷ 4 =10 Q3
Q3 =36 Q2
Q2 =27 Q1
Q1 =21

22. Quartiles from Cumulative Frequency Graphs
S5 Int2
Km travelled on 1 gallon (mpg)
Cumulative Frequency 20 3 25 11 30 35 53 40 69 45 76 50 80

23. Cumulative Frequency Graphs Cumulative Frequency Graphs
New Term
Interquartile range
Semi-interquartile range
(Q3 – Q1 )÷2 = ( )÷2
=4.5
Cumulative Frequency Graphs
Cumulative Frequency Graphs
S5 Int2 Q3
= 37
Quartiles
80 ÷ 4 =20 Q2
= 32 Q1
=28

24. Quartiles from Cumulative Frequency Graphs
S5 Int2
Now try Exercise 3
Ch11 (page 166)
31-Mar-17
Created by Mr. Lafferty Maths Dept.

25. Created by Mr. Lafferty Maths Dept.
Starter Questions
S5 Int2
31-Mar-17
Created by Mr. Lafferty Maths Dept.

26. Created by Mr. Lafferty Maths Dept.
Standard Deviation
S5 Int2
Learning Intention
Success Criteria
1. To explain the term and calculate the Standard Deviation for a collection of data.
Know the term Standard Deviation.
Calculate the Standard Deviation for a collection of data.
31-Mar-17
Created by Mr. Lafferty Maths Dept.

27. Standard Deviation For a FULL set of Data
S5 Int2
The range measures spread. Unfortunately any big
change in either the largest value or smallest score
will mean a big change in the range, even though only
one number may have changed.
The semi-interquartile range is less sensitive to a single number changing but again it is only really based on two of the score.
31-Mar-17
Created by Mr. Lafferty Maths Dept.

28. Created by Mr. Lafferty Maths Dept.
Standard Deviation
For a FULL set of Data
S5 Int2
A measure of spread which uses all the data is the
Standard Deviation
The deviation of a score is how much the score differs from the mean.
31-Mar-17
Created by Mr. Lafferty Maths Dept.

29. Standard Deviation For a FULL set of Data
Step 1 : Find the mean
375 ÷ 5 = 75
Step 5 :
Take the square root of step 4
√13.6 = 3.7
Standard Deviation is 3.7 (to 1d.p.)
Step 2 : Score - Mean
Step 4 : Mean square deviation
68 ÷ 5 = 13.6
Standard Deviation
For a FULL set of Data
Step 3 : (Deviation)2
S5 Int2
Example 1 : Find the standard deviation of these five
scores 70, 72, 75, 78, 80.
Score
Deviation
(Deviation)2 70 72 75 78 80
Totals
375 -5 25 -3 9 3 9 5 25 68
31-Mar-17
Created by Mr. Lafferty Maths Dept.

30. Standard Deviation For a FULL set of Data
Step 1 : Find the mean
180 ÷ 6 = 30
Step 5 :
Take the square root of step 4
√ = 12.7 (to 1d.p.)
Standard Deviation is £12.70
Step 2 : Score - Mean
Step 4 : Mean square deviation
962 ÷ 6 =
Step 3 : (Deviation)2
Standard Deviation
For a FULL set of Data
S5 Int2
Example 2 : Find the standard deviation of these six
amounts of money £12, £18, £27, £36, £37, £50.
Score
Deviation
(Deviation)2 12 18 27 36 37 50
Totals
180
-18
324
-12
144 -3 9 6 36 7 49 20
400
962
31-Mar-17
Created by Mr. Lafferty Maths Dept.

31. Standard Deviation For a FULL set of Data
S5 Int2
When Standard Deviation
is LOW it means the data
values are close to the
MEAN.
When Standard Deviation
is HIGH it means the data
values are spread out from
the MEAN.
Mean
Mean
31-Mar-17
Created by Mr. Lafferty Maths Dept.

32. Created by Mr. Lafferty Maths Dept.
Standard Deviation
S5 Int2
Now try Exercise 4
Ch11 (page 169)
31-Mar-17
Created by Mr. Lafferty Maths Dept.

33. Created by Mr. Lafferty Maths Dept.
Starter Questions
S5 Int2
Waist Sizes
Frequency
28” 7
30” 12
32” 23
34” 14
31-Mar-17
Created by Mr. Lafferty Maths Dept.

34. Created by Mr. Lafferty Maths Dept.
Standard Deviation
For a Sample of Data
S5 Int2
Learning Intention
Success Criteria
1. To show how to calculate the Standard deviation for a sample of data.
Construct a table to calculate the Standard Deviation for a sample of data.
2. Use the table of values to calculate Standard Deviation of a sample of data.
31-Mar-17
Created by Mr. Lafferty Maths Dept.

35. Standard Deviation For a Sample of Data
We will use this version because it is easier to use in practice !
S5 Int2
In real life situations it is normal to work with a sample
of data ( survey / questionnaire ).
We can use two formulae to calculate the sample deviation.
s = standard deviation
∑ = The sum of
x = sample mean
n = number in sample
31-Mar-17
Created by Mr. Lafferty Maths Dept.

36. Standard Deviation For a Sample of Data
Q1a. Calculate the mean :
592 ÷ 8 = 74
Step 1 :
Sum all the values
Step 3 :
Use formula to calculate sample deviation
Step 2 :
Square all the values and find the total
Q1a. Calculate the sample deviation
Standard Deviation
For a Sample of Data
S5 Int2
Example 1a : Eight athletes have heart rates
70, 72, 73, 74, 75, 76, 76 and 76.
Heart rate (x) x2 70 72 73 74 75 76
Totals
4900
5184
5329
5476
5625
5776
5776
5776
31-Mar-17
Created by Mr. Lafferty Maths Dept.
∑x = 592
∑x2 = 43842

37. Standard Deviation For a Sample of Data
Q1b(i) Calculate the mean :
720 ÷ 8 = 90
Q1b(ii) Calculate the sample deviation
Standard Deviation
For a Sample of Data
S5 Int2
Example 1b : Eight office staff train as athletes.
Their Pulse rates are 80, 81, 83, 90, 94, 96, 96 and 100 BPM
Heart rate (x) x2 80 81 83 90 94 96
100
Totals
6400
6561
6889
8100
8836
9216
9216
10000
31-Mar-17
Created by Mr. Lafferty Maths Dept.
∑x = 720
∑x2 = 65218

38. Standard Deviation For a Sample of Data
Q1b(iii) Who are fitter the athletes or staff.
Compare means
Athletes are fitter
Q1b(iv) What does the deviation tell us.
Staff data is more spread out.
Standard Deviation
For a Sample of Data
S5 Int2
Athletes
Staff
31-Mar-17
Created by Mr. Lafferty Maths Dept.

39. Created by Mr. Lafferty Maths Dept.
Standard Deviation
For a Sample of Data
S5 Int2
Now try Ex 5 & 6
Ch11 (page 171)
31-Mar-17
Created by Mr. Lafferty Maths Dept.

40. Created by Mr. Lafferty Maths Dept.
Starter Questions
S5 Int2
33o
31-Mar-17
Created by Mr. Lafferty Maths Dept.

41. Created by Mr Lafferty Maths Dept
Scatter Graphs
S5 Int2
Construction of Scatter Graphs
Learning Intention
Success Criteria
Construct and understand the Key-Points of a scattergraph.
To construct and interpret Scattergraphs.
2. Know the term positive and negative correlation.
31-Mar-17
Created by Mr Lafferty Maths Dept

42. Scatter Graphs www.mathsrevision.com Construction of Scatter Graph
This scattergraph shows the heights and weights of a sevens football team
Scatter Graphs
Write down height and weight of each player.
S5 Int2
Construction of Scatter Graph
Bob
Tim
Joe
Sam
Gary
Dave
Jim
31-Mar-17
Created by Mr Lafferty Maths Dept

43. Created by Mr Lafferty Maths Dept
Scatter Graphs
S5 Int2
Construction of Scatter Graph
When two quantities are strongly connected we say there is a
strong correlation between them.
Best fit line x x
Best fit line
Strong positive
correlation
Strong negative
correlation
31-Mar-17
Created by Mr Lafferty Maths Dept

44. Scatter Graphs www.mathsrevision.com Construction of Scatter Graph
S5 Int2
Construction of Scatter Graph
Key steps to:
Drawing the best fitting straight line to a scatter graph
Plot scatter graph.
Calculate mean for each variable and plot the
coordinates on the scatter graph.
3. Draw best fitting line, making sure it goes through
mean values.
31-Mar-17
Created by Mr. Lafferty Maths Dept.

45. Scatter Graphs www.mathsrevision.com Construction of Scatter Graph
Find the mean for theAge and Prices values.
Draw in the best fit line
Mean Age = 2.9
Mean Price = £6000
Scatter Graphs
S5 Int2
Construction of Scatter Graph
Is there
a correlation?
If yes, what kind?
Age
Price
(£1000) 3 1 2 4 5 9 8 7 6
Strong negative correlation
31-Mar-17
Created by Mr Lafferty Maths Dept

46. Scatter Graphs www.mathsrevision.com Construction of Scatter Graph
S5 Int2
Construction of Scatter Graph
Key steps to:
Finding the equation of the straight line.
Pick any 2 points of graph ( pick easy ones to work with).
Calculate the gradient using :
Find were the line crosses y–axis this is b.
Write down equation in the form : y = ax + b
31-Mar-17
Created by Mr. Lafferty Maths Dept.

47. Created by Mr Lafferty Maths Dept
Crosses y-axis at 10
Scatter Graphs
S5 Int2
Pick points
(0,10) and (3,6)
y = -1.33x + 10
31-Mar-17
Created by Mr Lafferty Maths Dept

48. Created by Mr. Lafferty Maths Dept.
Scatter Graphs
S5 Int2
Construction of Scatter Graph
Now try Exercise 7
Ch11 (page 175)
31-Mar-17
Created by Mr. Lafferty Maths Dept.

49. Created by Mr. Lafferty Maths Dept.
Starter Questions
S5 Int2
31-Mar-17
Created by Mr. Lafferty Maths Dept.

50. Created by Mr Lafferty Maths Dept
Probability
S5 Int2
Learning Intention
Success Criteria
To understand probability in terms of the number line and calculate simple probabilities.
Understand the probability line.
Calculate simply probabilities.
31-Mar-17
Created by Mr Lafferty Maths Dept

51. Probability Likelihood Line
S5 Int2 1
0.5
Impossible
Evens
Certain
Not very
likely
Very
likely
Seeing
a butterfly
In July
School
Holidays
Winning the
Lottery
Baby Born
A Boy
Go back
in time
31-Mar-17
Created by Mr Lafferty Maths Dept

52. Probability Likelihood Line
S5 Int2 1
0.5
Impossible
Evens
Certain
Not very
likely
Very
likely
It will
Snow in winter
Homework
Every week
Everyone getting
100 % in test
Toss a coin
That land
Heads
Going without
Food
for a year.
31-Mar-17
Created by Mr Lafferty Maths Dept

53. Probability We can normally attach a value
S5 Int2
We can normally attach a value
to the probability of an event happening.
To work out a probability
P(A) =
Probability is ALWAYS in the range 0 to 1
31-Mar-17
Created by Mr Lafferty Maths Dept

54. Probability Number Likelihood Line
S5 Int2 1 2 3 5 4 7 6 8 1
0.5
0.1
0.2
0.3
0.4
0.6
0.7
0.8
0.9
Impossible
Evens
Certain 8
P =
Q. What is the chance of picking a number between 1 – 8 ?
= 1 8 4
Q. What is the chance of picking a number that is even ?
P(E) =
= 0.5 8
Q. What is the chance of picking the number 1 ? 1
P(1) =
= 0.125
31-Mar-17
Created by Mr Lafferty Maths Dept 8

55. Probability Likelihood Line
S5 Int2
52 cards in a pack of cards 1
0.5
0.1
0.2
0.3
0.4
0.6
0.7
0.8
0.9
Impossible
Evens
Certain
Not very
likely
Very
likely 26
Q. What is the chance of picking a red card ?
P (Red) =
= 0.5 52 13
Q. What is the chance of picking a diamond ?
P (D) =
= 0.25 52 4
Q. What is the chance of picking ace ?
P (Ace) =
= 0.08 52
31-Mar-17
Created by Mr Lafferty Maths Dept

56. Created by Mr. Lafferty Maths Dept.
Probability
S5 Int2
Now try Ex 8
Ch11 (page 177)
31-Mar-17
Created by Mr. Lafferty Maths Dept.

57. Created by Mr Lafferty Maths Dept
Starter Questions
S5 Int2
31-Mar-17
Created by Mr Lafferty Maths Dept

58. Created by Mr Lafferty Maths Dept
Relative Frequencies
S5 Int2
Learning Intention
Success Criteria
To understand the term relative frequency.
Know the term relative frequency.
Calculate relative frequency from data given.
31-Mar-17
Created by Mr Lafferty Maths Dept

59. Relative Frequencies Relative Frequency www.mathsrevision.com
Relative Frequency always added up to 1
S5 Int2
Relative Frequency
How often an event happens compared
to the total number of events.
Example : Wine sold in a shop over one week
Country
Frequency
Relative Frequency
France
180
Italy 90
Spain
Total
180 ÷ 360 =
0.5
90 ÷ 360 =
0.25
90 ÷ 360 =
0.25
360 1
31-Mar-17
Created by Mr Lafferty Maths Dept

60. Relative Frequencies www.mathsrevision.com Example
S5 Int2
Example
Calculate the relative frequency for boys and girls
born in the Royal Infirmary hospital in December 2007.
Boys
Girls
Total
Frequency
300
200
Relative Frequency
Relative Frequency adds up to 1
500
0.6
0.4 1
31-Mar-17
Created by Mr Lafferty Maths Dept

61. Created by Mr. Lafferty Maths Dept.
Relative Frequencies
S5 Int2
Now try Ex 9
Ch11 (page 179)
31-Mar-17
Created by Mr. Lafferty Maths Dept.

62. Created by Mr. Lafferty Maths Dept.
Starter Questions
S5 Int2
31-Mar-17
Created by Mr. Lafferty Maths Dept.

63. Probability from Relative Frequency
S5 Int2
Learning Intention
Success Criteria
To understand the connection of probability and relative frequency.
Know the term relative frequency.
Estimate probability from the relative frequency.
31-Mar-17
Created by Mr Lafferty Maths Dept

64. Probability from Relative Frequency
When the sum of the frequencies is LARGE the relative frequency is a good estimate of the probability of an outcome
Probability from Relative Frequency
S5 Int2
Example 1
Three students carry out a survey to study left
handedness in a school. Results are given below
Number of Left - Hand Students
Total Asked
Relative
Frequency
Sean 2 10
Karen 3 25
Daniel 20
200
31-Mar-17
Created by Mr Lafferty Maths Dept

65. Probability from Relative Frequency
Who’s results would you use as a estimate of the probability of a house being alarmed ?
Megan’s
Probability from Relative Frequency
S5 Int2
Example 2
Three students carry out a survey to study how many
houses had an alarm system in a particular area.
Results are given below
What is the probability that a house is alarmed ?
0.4
Number of Alarmed Houses
Total Asked
Relative
Frequency
Paul 7 10
Amy 12 20
Megan 40
100
31-Mar-17
Created by Mr Lafferty Maths Dept

66. Probability from Relative Frequency
S5 Int2
Now try Ex 10
Ch11 Start at Q2 (page 181)
31-Mar-17
Created by Mr. Lafferty Maths Dept.