Statistics 2 Lesson 2.7 Standard Deviation 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.

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

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

We use this table. x f x2 fx fx2 4 16 5 25 6 36 7 3 49 8 2 64 9 1 81 10 100 20

We use this table. x f x2 fx fx2 4 16 5 25 6 36 24 7 3 49 21 8 2 64 9 81 10 100 20 121

We use this table. 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 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

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

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 

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

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

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

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

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

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

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

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

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 

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

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.

Key Words Spread Mean Standard Deviation

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

What are the headings for this table?

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