1. 1 Press Ctrl-A ©G Dear 2009 – Not to be sold/Free to use StandardDeviation Stage 6 - Year 12 Applied Mathematics Preliminary

2. 2 Standard Deviation 10 20 30 40 50 60 70 80 90 100 We need a lot of data with a Bell shaped curve. The median, mean and mode will all have about the same value. We use the greek letter σ for standard deviation. In manufacturing a small standard deviation is required. In education a large standard deviation is required. Standard Deviation measures the spread of the scores.

3. 3 102030405060708090100 Standard Deviation Small Normal Large The measure of the spread of scores Mean

4. 4 102030405060708090100 Spread of Scores. mean+1σ+2σ+3σ-1σ-2σ-3σ -1σ  +1σ-2σ  +2σ-3σ  +3σ 68% 95% 99.7% -1σ  +1σ = 68% -2σ  +2σ = 95% -3σ  +3σ = 99.7% The spread of scores as a Percentage for a given range of standard deviations.

5. 5 Exercise When taking an IQ test it has been found that the General population have a mean of 100 and a standard deviation of 12. a) What percentage of scores lie between 88 and 112. mean 100 +1σ 112 +2σ 124 +3σ 136 -1σ 88 -2σ 76 -3σ 64 -1σ  +1σ = 68% -2σ  +2σ = 95% -3σ  +3σ = 99.7% 100 + 1 x 12100 + 2 x 12100 + 3 x 12100 - 1 x 12 100 - 2 x 12 100 - 3 x 12 68% b) What percentage of scores lie between 64 and 136. 99.7%