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

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

3. 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. 20
Mean
When the standard deviation is high it means the scores
are spread out from the mean 20
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 =( ) / 6 = 13
We now construct a table to see how far each score differs
from the mean.

6. Score Deviation (Deviation )2
(3-13) =
(9-13) =
(12-13) =
(15-13) =
(19-13) =
(20-13) =
The mean square
deviation is
=34.7
Total
The standard deviation is

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

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

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

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

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.