1. 1 Applications of Standard Deviation Press Ctrl-A G Dear ©2010 – Not to be sold/Free to use Stage 4 Year 9

2. Bell Curve Symmetrical 0 Mean + ve σ scores - ve σ scores Applications of Standard Deviation (1/11) End of Slide

3. 0 Mean 1  34%   34%   68%  1 Standard Deviation either side of mean (2/11) End of Slide What % of scores lie between …

4. 0 Mean 2σ2σ2σ2σ 47.5% -2σ 47.5% 95% 2 Standard Deviation either side of mean (3/11) What % of scores lie between … End of Slide

5. 0 Mean 3σ3σ3σ3σ -3σ 99.7% 3 Standard Deviation either side of mean (4/11) What % of scores lie between … End of Slide

6. 102030405060708090100 68% 95% 99.7% 68% of Scores lie between 40 and 6095% of Scores lie between 30 and 7099.7% of Scores lie between 20 and 80 0.04 0.03 0.02 0.01 0 01σ1σ2σ2σ3σ3σ-1σ-2σ-3σ Standard Deviation either side of mean (5/11) What % of scores lie between … End of Slide

7. 7 Standard Deviation either side of mean (6/11) 68% of scores lie within one standard deviation of the mean. 95% of scores lie within two standard deviation of the mean. 99.7% of scores lie within three standard deviation of the mean. What % of scores lie End of Slide

8. 8 Standard Deviation either side of mean (7/11) probably lie within one standard deviation of the mean. very probably lie within two standard deviation of the mean. almost certainly lie within three standard deviation of the mean. If a score is chosen it will: End of Slide

9. 01σ1σ 2σ2σ 3σ3σ-1σ-2σ -3σ 34% 13.5%2.35%0.15%13.5%2.35%0.15% 2 Other Percentages (8/11) What % of scores lie End of Slide

10. scoresmean Measures the distance of raw scores from the mean. unitstandard deviations It’s unit of measure is in standard deviations. zeromean Z scores equal zero at the mean. normal distributions Z scores only apply to normal distributions. bell shaped.Normal distributions are always bell shaped. Bell Shaped 1 z-score = 1 standard deviation (9/11) End of Slide

11. z scoredata So how do we calculate the z score for a data item? Z = x – x σ Zz scoreZ is the z score. xraw scorex is the raw score. xmeanx is the mean of the scores. σstandard deviationσ is the standard deviation. z-score formula (10/11) End of Slide

12. In the last test one student got a score of 84. If the mean was 70 and the standard deviation was 10. then calculate the z score of the score. z = x – x σ z = 84- 70 10 z = 1.4standard deviations above the mean. z-score calculation (11/11) End of Slide