1. Support for English, maths and ESOL Module 7: Developing the personal maths skills of teachers and assessors Master class 4: Handling data

2. Session aim
To review and extend participants’ personal mathematics relating to statistics and probability
To apply concepts of statistics and probability to solve problems

3. 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

4. What’s the difference?

5. Measures of dispersion
Range
Interquartile range
Variance
Standard deviation

6. Box and whisker plots Group A Group B
Group A: mean = 3.5, median = 3.5, mode = 3 & 4, range = 3
Group B: mean = 3.5, median = 3.5, mode = 4, range = 5

7. 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

8. Frequency diagram

9. Grouped frequency distribution
Score
0-10
11-20
21-30
31-40
41-50
51-60
61-70
Frequency 10 60
230
420
250 28 2
450
400
350
300
250
200
150
100 50

10. Cumulative frequency table
Score
0-10
11-20
21-30
31-40
41-50
51-60
61-70
Frequency 10 60
230
420
250 28 2
Score
10
20
30
40
50
60
70
Cumulative frequency 10 70
300
720
970
998
1000

11. Cumulative frequency graph
Score
10
20
30
40
50
60
70
Cumulative frequency 10 70
300
720
970
998
1000

12. Box and whisker plot
Lower quartile
Upper quartile
Median

13. What’s misleading? Score 0-10 11-20 21-30 31-50 51-100 101-150
Frequency 20 38 42 18 6 1
Frequency 45 40 35 30 25 20 15 10 5
Score

14. Frequencies proportional to area of bars
Score
0-10
11-20
21-30
31-50
51-100
Frequency 20 38 42 18 6 1
Frequency 45 40 35 30 25 20 15 10 5
Score

15. Correlation

16. Negative correlation

17. P(a) = No. successful outcomes Total possible outcomes
Probability
P(a) = No. successful outcomes
Total possible outcomes

18. 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

19. 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%

20. 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
450
400
350
300
250
200
150
100 50
Frequency
Score