1. Statistics Exam Revision Summer 2019
Edexcel GCSE Statistics Higher

2. Formula you NEED to learn
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑖𝑠𝑒𝑑 𝑠𝑐𝑜𝑟𝑒= 𝑠𝑐𝑜𝑟𝑒 −𝑚𝑒𝑎𝑛 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
𝑇𝑜 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 𝑡ℎ𝑒 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑐𝑜𝑚𝑝𝑎𝑟𝑎𝑡𝑖𝑣𝑒 𝑝𝑖𝑒 𝑐ℎ𝑎𝑟𝑡𝑠 𝑟 2 𝑟 1 = 𝐹 𝐹 1
Geometric mean = 𝑛 𝑣𝑎𝑙𝑢𝑒 1 × 𝑣𝑎𝑙𝑢𝑒 2 ×… ×𝑣𝑎𝑙𝑢𝑒 𝑛

3. Formula at the front of the exam

4. Thursday 13th June - Afternoon
Paper 1 Paper 2
Tuesday 18th June - Morning

5. Venn diagrams Probability ‘given that’ 5 3 6 𝑃(𝐵) 4 B A
𝑃(𝐵) 4
The probability B occurs, the whole B circle is included.
𝑃 𝐴 𝐵 means the probability A occurs, given that B has already occurred.
From the venn diagram above, there are 9 in the B circle so that is the fraction denominator. From that 9, 3 are A. So 𝑃 𝐴 𝐵 = 3 9 = 1 3 B A
𝑃(𝐴∩𝐵)
A and B both occur. B A
𝑃(𝐴∪𝐵)
A and B both occur or A happens, or B happens.
𝑃 𝐵 𝐴 means the probability B occurs, given that A has already occurred.
From the venn diagram above, there are 8 in the A circle so that is the fraction denominator. From that 8, 3 are B. So 𝑃 𝐵 𝐴 = 3 8

6. Venn diagrams

7. Sampling Types
These are all types of non random sampling.

8. Sampling Types – Stratified Sampling
A stratified sample contains members of each sample in proportion to the size of that stratum.
The table shows employees in different salary bands. There are 160 employees in total.
The company wants a sample of 30 employees stratified by salary band. How many employees should be included from the £ £45000 band?
Salary band
£ £25 000
£ £45 000
Over £45 000
Employees 80 64 16
×30=12
64 people out of 160 altogether, multiplied by the sample size of 30.
Exam Question

9. Comparative pie charts
The area of the pie chart (or sector) compares the frequency shown on each chart. The bigger the area, the higher the frequency.
The angle shows the proportions of each pie chart. If the angles are the same, the proportion of people is the same, however the number of people will be different if the pie charts are different sizes.
Exam Question

10. Comparative pie charts
𝑇𝑜 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 𝑡ℎ𝑒 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑐𝑜𝑚𝑝𝑎𝑟𝑎𝑡𝑖𝑣𝑒 𝑝𝑖𝑒 𝑐ℎ𝑎𝑟𝑡𝑠 𝑟 2 𝑟 1 = 𝐹 𝐹 1
Learn this!!
In 1991 the number of people who got married was
In 2005 the number of people who got married was
Ed used a radius of 4cm for his 1991 pie chart. What length of radius should he use for 2005?
𝑈𝑠𝑒 𝑟 2 𝑟 1 = 𝐹 𝐹 1
𝑟 2 4 =
𝑟 2 =4×
𝑟 2 =3.5𝑐𝑚
Put the values you have into the formula
Rearrange and put in your calculator
The radius of the 2005 pie chart is 3.5cm

11. Index numbers Exam Question
Simple index numbers use a base year to compare percentage increases and decreases (usually in prices).
Each year is compared back to the base year.
Chain base index numbers compare the percentage increases and decreases to the previous year.
Exam Question
The table shows the index numbers for the cost of takeaways in Glasgow and London taking 2008 as the base year.
2009
2010
2011
London Simple Index
104.2
107.8
114.6
London Chain base Index
103.5
106.3
Glasgow Simple Index
101.8
106.2
116.5
Glasgow Chain Base index
104.3
109.7
Interpret the 2009 London simple index number.
A takeaway cost £20 in Glasgow in Use the appropriate index number to work out the cost in 2011.
By calculating the appropriate geometric means, compare and interpret the yearly average change in takeaway prices in Glasgow and London

12. Normal Distribution Key features: - bell shaped curve - symmetrical
- can be used to calculate probabilities if the data is normally distributed
Mean 𝜇
standard deviation 𝜎
Percentages give probabilities
On this distribution, 50% of the graph is shaded.
On tis distribution 34% of the graph is shaded. (Half of 68%).

13. Normal Distribution Exam Question
The table shows the mean and standard deviation of Maths and English scores. The scores are normally distributed.
(a) Use the values to sketch a diagram of the distribution of the curves.
Mean
Standard deviation
English 46 3
Maths 55 2 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63
(b) One student who took the English test is selected at random. What is the probability they scored above 49?
(c) Use your curves to compare the English and Maths scores, interpret your conclusions in context.

14. Quality Control charts
Quality control charts are for quality assurance in production.
Control charts are used once a sample is taken to decide whether or not any action needs to be taken.
Action limits are 3 standard deviations from the target value.
Warning lines are 2 standard deviations from the target value.
If a sample taken is above or below the warning line, then another sample should be taken first.
If this sample is over the action line, then the machine should be reset.
ALWAYS take another sample before taking action.

15. Quality Control charts
The target mean on a quality control chart is set higher than the expected weight of the product. For example, if you had a cake you expected to weigh 34g and you set the target mean line to 34g, 50% of your cakes would fall below this line. Therefore the target weight would be set slightly higher to ensure most cakes were at least 34g.
The standard deviation of any sample you take will be smaller than the standard deviation of the whole population. Consider a school, the standard deviation of students heights from year 7 to year 11 would be high as there is a big difference in heights. If I took a sample of 3 students, the standard deviation would be much smaller of those 3 students.
Exam Question
A company is making car parts. If the part is found to be below 4cm, the company cannot legally sell it. (a) Why should the company not set the target level on its control chart to 4cm?
The mean length of the car part is 4.5cm and the standard deviation 0.3cm.
(b) What can be deduced about the mean and standard deviation of all car parts made on the production line?

16. Standard Deviation
THE FORMULA IS AT THE FRONT OF YOUR EXAM….USE IT!!!!!!!!!!
Exam Question

17. Standard Deviation
THE FORMULA IS AT THE FRONT OF YOUR EXAM….USE IT!!!!!!!!!!
Exam Question

18. Scatter graphs and interpreting line of best fit
(also called regression line)
Exam Question
Plot the points on the scatter graph.
The mean cost is £5125. Use this information and the mean age to plot the mean point.
Draw a line of best fit that passes through this mean point.

19. Scatter graphs and interpreting line of best fit
Exam Question
Describe the correlation shown on the scatter graph.
The line of best fit goes through points (16,32) and (98,196). Calculate the gradient of the line.
Interpret this number in context.
The y intercept of the line is 0. Explain what this means.

20. Cumulative frequency and interpercentile range
To find the median, draw a line half way up the cumulative frequency axis and read the time from the x axis.
To find percentiles, imagine the data has been split into 100.
Calculate the 20th and 80th percentile.
The cumulative frequency here is 160 (where the curve ends).
20th percentile
0.2 x 160 = 32nd person
80th percentile
0.8 x 160 = 128th person
When comparing from cumulative frequency:
The median shows which group got the highest/lowest scores
The interquartile/interpercentile range shows how spread out the data is. A smaller range means more consistent data.
Remember to put comparisons in the context of the question.

21. Cumulative frequency and interpercentile range
Exam Question
1. Use statistical calculations to determine which population has the higher age and which population has the greater range in ages.
Population 1
10th percentile
Median
90th percentile 18 37 61
Second person is 19
90th person is 41
Median 30
Population 2

22. Standardised scores 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑖𝑠𝑒𝑑 𝑠𝑐𝑜𝑟𝑒= 𝑠𝑐𝑜𝑟𝑒 −𝑚𝑒𝑎𝑛 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑖𝑠𝑒𝑑 𝑠𝑐𝑜𝑟𝑒= 𝑠𝑐𝑜𝑟𝑒 −𝑚𝑒𝑎𝑛 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
Learn this!!
Exam Question

23. These may be given in the question
Rates of change
This is given for you
Crude rates tell you the number of births/deaths etc per 1000 people. They don’t include the age profile of the population.
Standard populations calculate the number of people in each age group in a population of 1000.
Standardised rates compare the same age group in different populations and allow comparisons to be made.
These may be given in the question
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛= 𝑛𝑢𝑚𝑏𝑒𝑟 𝑖𝑛 𝑎𝑔𝑒 𝑔𝑟𝑜𝑢𝑝 𝑡𝑜𝑡𝑎𝑙 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 ×1000
standardised rate = 𝑐𝑟𝑢𝑑𝑒 𝑟𝑎𝑡𝑒 1000 ×𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
Exam Question
A town with a population of recorded 375 deaths in one year. Calculate the crude death rate of the town.
The population of a city in 2016 is shown.
Find the standard population of this city.
Age
0-19
20-39
40-59
60-79
>79
Population
21 458
48 215
87 534
9781

24. Binomial distribution – using calculator to work out coefficient
A probability distribution given as B(14, 0.3) means an experiment is carried out 14 times and the probability of success is 0.3 each time. The B stands for a binomial distribution.
To find the mean of a binomial distribution, multiply the number of trials by the probability of success. Using the example above, 14 x 0.3 = 4.2.
You will need to be able to use your calculator (or pascals triangle) to work out the co efficient before the powers when using binomial.
For the distribution used above, work out the probability of 6 successes.
The powers will be 𝑝 6 𝑞 8 because there are 6 successes (p) and 8 failures (q). We need to find the number in front of p.
Use your calculator 14 C 6 (this means 14 choose 6). The C button is the nCr button above divide.
You should get 3003.
Then 𝑝 6 𝑞 8 = 3003 x 0.36 x 0.78 =

25. Binomial distribution – using calculator to work out coefficient
Exam Question
A probability distribution is described as B(8, 3 5 )
What does the 8 stand for?
The distribution describes an experiment with an unfair dice and the probability of rolling a 5.
Gina carries out the experiment 20 times and records the number of 5s she rolls.
She uses the distribution to estimate the number of times she will get a 5.
(b) Work out Gina’s estimate.
(c) Write down two assumptions that Gina has made for her model to be binomially distributed.

26. Revision Retrieval Quizzes and answers

27. Question 1 Question 2 Question 3 Solve Question 4 Lesson 1
Maximise what you gain from this activity by:
Completing this by yourself in silence
Avoid using notes
Question 1
Question 2
Question 3
Solve
Question 4
Lesson 1

29. Question 1 Question 2 Question 4
Maximise what you gain from this activity by:
Completing this by yourself in silence
Avoid using notes
Question 1
Question 2
Estimate the time taken for an 11 year old and an 18 year old. Which one would be more reliable?
There is also an image of a bar chart to go with this question but no space for it!
Question 4

31. Question 1 Question 2 Question 4 Question 3
Maximise what you gain from this activity by:
Completing this by yourself in silence
Avoid using notes
Question 1
Question 2
Question 3
The table shows the chain base index of average house prices in the 2 cities taking 2008 as the base year. By calculating appropriate geometric means, compare and interpret the change in yearly average house price from 2008 to 2011 in Birmingham and Manchester.
2009
2010
2011
Birmingham Chain base Index
104.2
103.5
106.3
Manchester Chain Base index
101.8
104.3
109.7
Question 4

33. Question 1 Question 2 Question 3 Solve Lesson 1
Maximise what you gain from this activity by:
Completing this by yourself in silence
Avoid using notes
Question 1
Question 2
Question 3
Solve
Lesson 1

35. Topics with a * are not included in this revision booklet.
Paper 1
Revised?
Paper 2
Venn diagrams including probability notation
Questionnaires*
Sampling types and stratified sampling
Box plots – drawing and interpreting *
Estimating the mean*
Scatter graphs and interpreting line of best fit
Frequency Polygon*
Capture recapture *
Comparative pie charts
Misleading graphs
Index numbers (simple and chain base)
Cumulative frequency and interpercentile range
Calculating geometric mean
Linear interpolation
Normal distribution drawing and interpreting
Standardised scores
Quality control charts
Crude rates
Standard deviation (formula given on formula sheet)
Binomial distribution – using calculator to work out coefficient
Topics with a * are not included in this revision booklet.

36. Your hard work this year will pay off!
Good luck!
Your hard work this year will pay off!