1. Statistics

2. Discrete or Continuous Data
Discrete data is data that has no in betweens
e.g. shoes sizes or hair colour
Continuous data can be a range of values
e.g. your weight or height

3. Averages There are different types of averages;
The Mean: is the most commonly used average
The Mode: is easy to work out (it is the number that appears the most times)
The Median is the middle value, when the numbers are grouped from smallest to biggest

4. The Mean
To get the mean you have to add all the values together and divide by the number of people
E.g. Here are the number of Olympic medals won by Italy from
18, 13, 15, 32, 14, 19, 34
The mean is:
= 145
There were 7 Olympics in this time so
145/7 = 20.7 medals were won
This looks right because it is between 13 and 34

5. Try these;
The mean weight of 8 people is 60 kg. Alex weighs 52 kg. What is the mean weight of the 9 people including Alex?
There are 29 pupils in 9x. Jason is away when there is a test. The mean test score for the other 28 pupils is Jason takes the test late and gets 86. What is the new mean score or 9x?
There are 33 pupils in set 1. When 32 of them take a test, their mean score is Rubina is absentfor the test and takes it late. The teacher tells her that the mean for the whole class is now 86 ⅔. How many marks did Rubina get in the test?

6. Answers
59.1 kg
76.8 92

7. The Mode
Mode is most
Here are the distances for the winners of the Olympic Javelin competitions
90, 90, 95, 91, 89, 84, 90
What is the modal length?
90 because it occurs three times
There can be more than one mode

8. Now try these; Find the mode of these sets of numbers;
90, 90, 95, 91, 89, 84, 90, 88
89, 90, 88, 90, 86, 84, 87, 87
87, 84, 87, 87, 84, 83, 83, 87

9. Answers 90
87 and 90 87

10. Median Median is the middle
Here are the number of Olympic medals won by Italy from
18, 13, 15, 32, 14, 19, 34
These first need to be sorted from smallest to biggest
13, 14, 15, 18, 19, 32, 34
18 is the middle number so it is the median
There can only be one median

11. Now try these; Find the median of these sets of values;
90, 90, 95, 91, 89, 84, 90, 88
89, 90, 88, 90, 86, 84, 87, 87
87, 84, 87, 87, 84, 83, 83, 87

12. Answers 90
87.5
85.5

13. Range This is the biggest number take away the smallest
What is the range for this question;
Here are the number of Olympic medals won by Italy from
18, 13, 15, 32, 14, 19, 34
34-13= 21
The range is 21

14. The Mid-Point
The following table shows how long it takes pupils to get to school
Time (mins)
1-5
6-10
11-15
16-20
21-25
26-30
31-50
Number of pupils 2 7 10 5 3 1
Mid-point 8 13 18 23 28 33
How can you find the mean time taken to get to school when the times are ranges e.g. 1-5
We take the middle of 1-5 which is 3 as our mid point!

15. The Mid-Point What is the average time taken to get to school?
Time (mins)
1-5
6-10
11-15
16-20
21-25
26-30
31-50
Number of pupils 2 7 10 5 3 1
Mid-point 8 13 18 23 28 33
Total 6 56
130 90 69
We add up our totals to get 440 and then divide by the total number of pupils
(30)
The mean time taken was 14.7 mins

16. Cumulative Frequency Tables
Cumulative means to add together or accumulate.
This means the values never get smaller
These are the marks scored by 750 GCSE students. They are percentages.
Mark
Frequency
1-10
11-20
21-30
31-40
41-50 20 48 65
124
157
51-60
61-70
71-80
81-90
91-100
147 84 64 24 17

17. Cumulative Frequency Tables
Mark
Frequency
1-10
11-20
21-30
31-40
41-50 20 48 65
124
157
51-60
61-70
71-80
81-90
91-100
147 84 64 24 17
The frequency is the number of people getting these results
To get the cumulative frequency you start at the lowest marks and add the others to it e.g.

18. Cumulative Frequency Tables
Mark
Frequency
Cumulative frequency
Less than 10
<20
<30
<40
<50 20 48 65
124
157 68
133
257
414
<60
<70
<80
<90
<100
147 84 64 24 17
561
645
709
733
750

19. Cumulative Frequency Graphs
They are always s-shaped
This is because the cumulative frequency always gets bigger
Except at the end where the values tail off

20. The Median Because the frequency goes up to 40 the median is 20
We draw across from 20 until we reach our graph
Then we draw a straight line down
The median length is mm

21. Inter quartile Range First we find the lower quartile (1/4 of 40)
10 = 23.5 mm
Then we find the upper quartile (3/4 of 40)
30 = 31.5 mm
Then we take them away from each other
31.5 – 23.5= 8 mm