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Standard Deviation

Standard Deviation. Consider the following sets of data: 3,9,12,15,19,20. 0. 20. Range = 20-3 = 17 Mean = (3+9+12+15+19+20)/6=13. 0. 20. 0. 20. 11,12,13,13,14,15. 0. 20. Range = 15-11 = 4 Mean = (11+12+13+13+14+15)/6 = 13.

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Standard Deviation

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  1. Standard Deviation Consider the following sets of data: 3,9,12,15,19,20 0 20 Range = 20-3 = 17 Mean = (3+9+12+15+19+20)/6=13

  2. 0 20 0 20 11,12,13,13,14,15 0 20 Range = 15-11 = 4 Mean = (11+12+13+13+14+15)/6 = 13 Note: The two sets of data have the same mean i.e. 13 but are very different.

  3. Mean 0 0 20 20 Mean A measure of spread which uses all the data is the standard deviation. When the standard deviation is low it means the scores are close to the mean. When the standard deviation is high it means the scores are spread out from the mean

  4. Exercise 1 Look at the three sets of scores below and place the standard deviations for these scores in order, low to high 1 2 3 Mean Mean Mean

  5. Calculating the Standard Deviation of a set of scores The standard deviation or “root, mean, square deviation” is a measure of how far all the scores differ from the mean. It can be calculated from first principles or by the application of a formula. Consider the scores listed earlier: 3,9,12,15,19,20 Mean =(3+9+12+15+19+20) / 6 = 13 We now construct a table to see how far each score differs from the mean.

  6. The mean square deviation is 206 6 =34.7 The standard deviation is Score Deviation (Deviation )2 3 (3-13) = -10 100 9 (9-13) = -4 16 12 (12-13) = -1 1 15 (15-13) = 2 4 19 (19-13) = 6 36 20 (20-13) = 7 49 Total 206

  7. Standard Deviation by Formula All of the values can be found using a scientific calculator. You do not have to learn this formula as it is given on the exam paper cover.

  8. MODE 2nd F DRG Using the Sharp EL-531VH You need to be in STAT mode. The calculator display shows MODE ? 0 - 2 Press 1

  9. 3 9 12 15 19 20 M+ M+ M+ M+ M+ M+ RCL You are now in STATS mode and the calculator display shows S t a t x 0 The next task is to enter the data. We will use the example already covered: We will enter the numbers: 3,9,12,15,19,20 All the STATS keys are in green on the calculator. We can now pick out any values from the keyboard using

  10. These values are obtained by pressing first. RCL The values we require for the formula are laid out in the following key positions on the calculator: 8 9 7 x sx 4 5 6 1 2 3 n x x2 0 7 +/-

  11. = x2 1220. = x 78. = n 6. The values can now be obtained and entered into the formula:

  12. Note: There is a slight difference in answer between the two methods. The formula uses n-1 instead of n. This is because the data is treated as a sample.

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