Standard deviation and the normal curve In most normal statistical situations, most scores occur near the mean, which is usually in the middle of the possible scores. The Normal Curve! x x x x  Lowest score possible Highest score possible (Mean) One standard deviation below Two standard deviations below Three standard deviations below Three standard deviations above Two standard deviations above One standard deviation above Middle score In fact, the following percentages of scores usually lie within, You will have to remember these percentages! 68% 95% 99.7% Anything further than 3 standard deviations is said to be an outlier!  Now for some practice questions…9:3

Worksheet 9:3 Q. 1 A normal distribution of scores has a mean of 25 and a standard deviation of 4. What percentage of scores lie between:  (a) 21 and 29 (b) 17 and 33 (c) 13 and 37 ALWAYS DRAW A NUMBER LINE WITH THE MEAN IN THE MIDDLE AND PLACES FOR 3 EVENLY SPACED STANDARD DEVIATION NUMBERS. 99.7% 95%  68% 13 17 21 25 29 33 37 Three standard deviations below Two standard deviations below One standard deviation below (Mean) One standard deviation above Two standard deviations above Three standard deviations above  All this has been preparation work . Now you are ready to answer parts a, b & c. The answer to part (a) is The answer to part (b) is The answer to part (c) is Some more questions…. 

The mean of a normally distributed set of scores if 15 and the standard deviation of 3.5. What percentage of scores lie: Q. 2 (a) between 8 and 22? (b) from 11.5 to 18.5? 95% 68% Three standard deviations below 4.5 Two standard deviations below 8 One standard deviation below 11.5 (Mean) 15 One standard deviation above 18.5 Two standard deviations above 22 Three standard deviations above 25.5 Once again, all this has been preparation work . Now you are ready to answer parts a, & b. The answer to part (a) is The answer to part (b) is One more……...

Q. 3 The standard deviation of a normally distributed set of scores if 12 and the mean is 60. What percentage of scores: (a) lie between 48 and 72? (b) are greater than 72? (c) lie between 36 and 84? (d) are less than 36? (e) are greater than 96? (c) are more than 48? (f) 95% (c) (d) (b) 68% (a) (e) (d) This is half of what remains after the 95% is accounted for (b) This is half of what remains after the 68% is accounted for (e) This is half of what remains after the 99.7% is accounted for Three standard deviations below 24 Two standard deviations below 36 One standard deviation below 48 (Mean) 60 One standard deviation above 72 Two standard deviations above 84 Three standard deviations above 96 Once again, all this has been preparation work . (f) This is all that remains except scores below 48 Now for the answers! Below 48 represents half of the 32%, i.e. 16% Which is (100% - 68%)  2 = 16% So all above 48 must be 100% - 16% = 84% Which is (100% - 95%)  2 = 2.5% Which is (100% - 99.7%)  2 = 0.15%