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Support for English, maths and ESOL
Module 7: Developing the personal maths skills
of teachers and assessors
Master class 4: Handling data
Session aim
• To review and extend participants’
personal mathematics relating to statistics
and probability
• To apply concepts of statistics and
probability to solve problems
Outcomes
By the end of the session participants will have:
• Reviewed their understanding of mean, median, mode and range,
and their relationship to frequency distributions
• Examined and understood different measures of spread
• Explored features of grouped and cumulative frequency
distributions and their uses
• Used scatter diagrams to investigate correlation, and make
projections
• Reviewed key concepts of probability, including combined
probabilities
• Calculated probabilities from frequency data
• Applied understanding of statistics and probability to solve practical
problems
What’s the difference?
Measures of dispersion
• Range
• Interquartile range
• Variance
• Standard deviation
Box and whisker plots
Group A
Group B
Standard deviation
Use the population
standard deviation (σ)
when data is relates to
the entire population:
The standard deviation
of a sample of the
population (s) can be
estimated using:
Note:
•xi represents the individual values of x;
•μ is the mean of all the values of x
•N is the number of values
Frequency diagram
Grouped frequency distribution
Score
Frequency
450
400
350
300
250
200
150
100
50
0
0-10
11-20
21-30
31-40
41-50
51-60
61-70
10
60
230
420
250
28
2
Cumulative frequency table
Score
Frequency
0-10
11-20
21-30
31-40
41-50
51-60
61-70
10
60
230
420
250
28
2
Score
10
20
30
40
50
60
Cumulative
frequency
10
70
300
720
970
998
70
1000
Cumulative frequency graph
Score
10
20
30
40
50
60
70
Cumulative
frequency
10
70
300
720
970
998
1000
Box and whisker plot
Upper quartile
Median
Lower quartile
What’s misleading?
Score
Frequency
0-10
11-20
21-30
31-50
51-100
101-150
20
38
42
18
6
1
45
40
35
Frequency
30
25
20
15
10
5
0
0
10
20
30
40
50
60
70
80
Score
90
100
110 120 130 140 150
Frequencies proportional to area of bars
Score
Frequency
0-10
11-20
21-30
31-50
51-100
101-150
20
38
42
18
6
1
45
40
35
Frequency
30
25
20
15
10
5
0
0
10
20
30
40
50
60
70
80
Score
90
100
110 120 130 140 150
Correlation
Negative correlation
Probability
P(a) = No. successful outcomes
Total possible outcomes
Combined probabilities
When two coins are tossed there are
three possible outcomes:
•Two heads
•One head
•No heads
The probability of two heads is
therefore ⅓
Train punctuality data
Scheduled services running in the last month:
On time
84%
Up to 15 min. late
7%
15-30 min. late
4%
More than 30 min. late
2%
Cancelled
3%
Probability and frequency data
Score
0-10
11-20
21-30
31-40
41-50
51-60
61-70
Frequency
10
60
230
420
250
28
2
0
20
450
400
350
Frequency
300
250
200
150
100
50
0
10
30
40
50
Score
60
70
80
90
100