2. Solution:

3. Statistics

4. Subject knowledge sessions
 Date
Time 
 Topic AM
Statistics
PTSA
Scott Yalden
Probability
Richard Whitehouse
Problem Solving and Numerical Methods
Donna Roughton
Higher Ability KS4
Tavistock
Bridging unit - introduction to A Level

5. 9-1 GCSE Mathematics - Statistics Content

7. Year 3

8. Year 4

9. Year 5

10. Year 6

12. Match the keyword with the definition.
Categorical Data
Data that is measured and can take a whole range of values
Bivariate Data
Data is counted i.e. can only take certain values
Discrete Data
Non – numerical data
Continuous Data
Data you have collected yourself e.g. by experiment or survey.
Primary Data
Data that has two variables
Secondary Data
Numerical data (numbers)
Quantitative Data
Data obtained from other sources e.g. internet or newspaper
Qualitative
Data that is grouped into categories

13. Solutions Categorical Data Data that is grouped into categories
Bivariate Data
Data that has two variables
Discrete Data
Data is counted i.e. can only take certain values
Continuous Data
Data that is measured and can take a whole range of values
Primary Data
Data you have collected yourself e.g. by experiment or survey
Secondary Data
Data obtained from other sources e.g. internet or newspaper
Quantitative Data
Numerical data (numbers)
Qualitative
Non – numerical data

14. Hypotheses
A good hypothesis is a statement not a question.

15. Types of sampling

16. Processing and representing data

17. Histograms

18. The area of the histogram represents area.
The histogram shows the times a sample of students spent on the internet one evening. (a) Copy and complete the frequency table, (b) Estimate how many students spent longer than 50 minutes on the internet.
Time, t, minutes
0 ≤ t < 20
20 ≤ t < 30
30 ≤ t < 35
35 ≤ t < 45
45 ≤ t < 60
Frequency
0.1 x 20 = 2
0.8 x 10 = 8
2.8 x 5 = 14
1.5 x 10 = 15
0.4 x 15 = 6
0.4
0.8
1.2
1.6
2.0
Frequency Density
2.4
2.8
50 Minutes or more
The area of the histogram represents area.
Area 50 ≤ t < 60
= 0.4 x 10 = 4
4 students spent longer than 50 minutes on the internet. 10 20 30 40 50 60
Time (Minutes)

22. Draw a histogram to represent this data.

23. Quartiles

24. Box Plots
A box plot is a way of illustrating key information about a set of data
They are also very useful for comparing the distribution of two sets of data (e.g. boys vs girls)

25. Box Plots To draw a box plot, you need FIVE pieces of information:
The minimum value
The lower quartile
The median
The upper quartile
The maximum value

26. Box Plots

27. Box Plots
Below are the midday temperatures for Ringwood over the past 11 days (in oC).
20, 22, 16, 17, 16, 18, 20, 18, 16, 21, 18
Below are the midday temperatures for Glasgow over the past 11 days (in oC).
17, 20, 20, 17, 16, 14, 13, 19, 21, 17, 18
Draw box plots for the data and write some comments on what they tell you about the temperatures in Ringwood and Glasgow over the past 11 days.

28. Cumulative Frequency and Box Plots
The table below shows the ages that men from two professions spotted their first grey hair.
Teachers
Doctors
Age, y, years
Frequency
Cumulative Frequency
20 < y ≤ 25 5
25 < y ≤ 30 15 14
30 < y ≤ 35 12 19
35 < y ≤ 40 6
40 < y ≤ 45 2 1 5 20 14 32 33 38 39 40 40
Calculate the cumulative frequencies
Draw cumulative frequency curves on the same axes
Use your cumulative frequency curves to draw box plots to compare the data
Write sentences to explain what your box plots show you.

29. Median = 40 ÷ 2 = 20th value
Median (T) = 30 years
Median (D) = 32 years
LQ = ¼ x 40 = 10th value
LQ (T) = 27 years
LQ (D) = 29 years
UQ = ¾ x 40 = 30th value
UQ (T & D) = 34 years 40
Cumulative Frequency 35 30 25
Teachers
Doctors 20 15 10 5
Age 20 25 30 35 40 45 50

30. 40
Cumulative Frequency 35 30
Teachers 25
Doctors 20
On average, teachers go grey at a younger age as their median is lower
However, doctors go grey at a more similar age as their range and interquartile range is smaller. 15 10 5 20 25 30 35 40 45 50
Teachers
Doctors

31. Box plot match
Here are six cumulative frequency graphs and six box plots of the same data. Can you match them up?

32. Average number of hours TV watched per week
Scatter graphs
Average number of hours TV watched per week IQ 42 89 14
103 22 94 16 91 2
116 26 3 15
106 95 8 10
115
100 27 6
102 90 9 88

33. Other types of chart

34. References:
Mathematics programmes of study: key stages 1 and 2 National curriculum in England NRICH M, M and M Histograms