Standard Deviation Mean - the average of a set of data Median - the middle value of a set of data Mode – the most frequent piece of data Range - a measure of spread Deviation - How much the score differs from the mean A measure of spread which uses all the data is the STANDARD DEVIATION

Example 1 Find the Standard Deviation (S.D.) of 70, 72, 75, 78, 80

We can follow these 5 steps to calculate S.D. Step 1 – Calculate the mean Step 2 – Calculate the deviation of each score Step 3 – Square each deviation (removes any negatives) Step 4 – Add the squared deviations and divide by the number of scores (the MEAN SQUARE DEVIATION) Step 5 – Take the square root of this value

Step 5: Standard Deviation = √13.6 = 3.7 (to 1 d.p.) Score - Mean Step 3 Score Deviation (Deviation) ² 70 72 75 78 80 70-75 = -5 72-75 = -3 3 5 25 9 68 Step 1: Mean = 375/5 =75 Step 4: Mean Square Deviation = 68/5 = 13.6 375 Step 5: Standard Deviation = √13.6 = 3.7 (to 1 d.p.)

Example 2: Find the standard deviation of these 6 amounts of money; £12, £18, £27, £36, £37, £50 Score Deviation (Deviation) ² 12 18 27 36 37 50 324 144 9 36 49 400 962 -18 -12 -3 6 7 20 Mean = 180/6 = 30 Mean Square Deviation = 962/6 = 160.33 Standard Deviation = √160.33 = 12.7 (to 1 d.p.) 180

Example 3: Find the standard deviation of these 8 amounts of money; £42, £48, £37, £31, £28, £57, £47, £50 Score Deviation (Deviation) ² 42 48 37 31 28 57 47 50 -0.5 5.5 -5.5 -11.5 -14.5 14.5 4.5 7.5 0.25 30.25 132.25 210.25 20.25 56.25 690 Mean = 340/8 = 42.5 Mean Square Deviation = 690/8 = 86.25 Standard Deviation = √86.25 = 9.3 (to 1 d.p.) 340