1. Statistics 2 Lesson 2.7
Standard Deviation 2

2. Learning Objectives:- Compare distributions and make inferences,
using the shapes of distributions and measures of average and spread,
including median and quartiles. Calculate standard deviation.

3. The table below shows the scores obtained in 20 netball matches by year 11.
Score x
Frequency f 4 5 6 7 3 8 2 9 1 10 20
Calculate the mean and standard deviation.
The standard deviation is given by the formula.  =
fx2 n x2 x =
fx n

4. We use this table. x f x2 fx
fx2 4 5 6 7 3 8 2 9 1 10 20

5. We use this table. x f x2 fx fx2 4 16 5 25 6 36 7 3 49 8 2 64 9 1 8110
100 20

6. We use this table. x f x2 fx fx2 4 16 5 25 6 36 24 7 3 49 21 8 2 64 981 10
100 20
121

7. We use this table. x f x2 fx fx2 4 16 64 5 25 125 6 36 24 144 7 3 4921
147 8 2
128 9 1 81 10
100 20
121
789

8. x f x2 fx
fx2 4 16 64 5 25
125 6 36 24
144 7 3 49 21
147 8 2
128 9 1 81 10
100 20
121
789 x =
fx n

9. x f x2 fx
fx2 4 16 64 5 25
125 6 36 24
144 7 3 49 21
147 8 2
128 9 1 81 10
100 20
121
789 x =
fx n
121 20 = =
6.05

10. x f x2 fx
fx2 4 16 64 5 25
125 6 36 24
144 7 3 49 21
147 8 2
128 9 1 81 10
100 20
121
789 =
fx2 n x2 

11. x f x2 fx
fx2 4 16 64 5 25
125 6 36 24
144 7 3 49 21
147 8 2
128 9 1 81 10
100 20
121
789 =
fx2 n x2 =
789 20
6.052  =
1.69

12. The table below shows the scores obtained in 30 netball matches by year 10.
Score x
Frequency f 4 6 5 7 8 3 9 2 10 30
Calculate the mean and standard deviation.
The standard deviation is given by the formula.  =
fx2 n x2 x =
fx n

13. We use this table. x f x2 fx
fx2 4 6 5 7 8 3 9 2 10 30

14. We use this table. x f x2 fx fx2 4 6 16 5 25 36 7 49 8 3 64 9 2 81 10
100 30

15. We use this table. x f x2 fx fx2 4 6 16 24 5 25 36 30 7 49 8 3 64 9 281 18 10
100 20
190

16. We use this table. x f x2 fx fx2 4 6 16 24 64 5 25 125 36 30 180 7 49
343 8 3
192 9 2 81 18
162 10
100 20
200
190
1266

17. x f x2 fx
fx2 4 6 16 24 64 5 25
125 36 30
180 7 49
343 8 3
192 9 2 81 18
162 10
100 20
200
190
1266 x =
fx n

18. x f x2 fx
fx2 4 6 16 24 64 5 25
125 36 30
180 7 49
343 8 3
192 9 2 81 18
162 10
100 20
200
190
1266 x =
fx n
190 30 = =
6.33

19. x f x2 fx
fx2 4 6 16 24 64 5 25
125 36 30
180 7 49
343 8 3
192 9 2 81 18
162 10
100 20
200
190
1266 =
fx2 n x2 

20. x f x2 fx
fx2 4 6 16 24 64 5 25
125 36 30
180 7 49
343 8 3
192 9 2 81 18
162 10
100 20
200
190
1266 =
fx2 n x2 =
1266 30
6.332  =
1.46

21. Year 11 Mean = 6.05 Standard Deviation = 1.69
The means are very similar but year 10 have a slightly better mean. Year 10 also have a slightly lower standard deviation so the dispersion from the mean is slightly smaller. Overall year 10 are a little better and a little more consistent.

22. Key Words
Spread
Mean
Standard Deviation

23. Copy these formulae into your books.x =
fx n  =
fx2 n x2

24. What are the headings for this table?

25. What are the headings for this table?x f x2 fx
fx2
Set the pupils some examples to do.