1. 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

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

3. 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

4. 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.)

5. 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 =
Standard Deviation
= √160.33
= 12.7 (to 1 d.p.)
180

6. 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