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Calculating the Standard Deviation
The standard deviation is a statistical formula used to determine the average difference
from the mean of the distribution. In other words, the standard deviation tells whether a
particular set of data is significantly different from a control set of data.
The following formula is used:
(Pinkney).
A bell-shaped curve is provided as an additional visual to help explain this relationship.
This curve represents a normal distribution.
(Standard Deviation, 2010).
Steps for calculating the standard deviation:
1.
2.
3.
4.
5.
6.
Find the average of your trials; in other words calculate the mean.
For each trial, compute the difference minus the mean.
Square that number.
Add all of the squared differences from step 3.
Divide the sum of the results by the number of trials minus 1.
Take the square root of that number. This number means that on a bell-shaped
curve, the scores are dispersed by that number.
Example:
Let’s say that the following data represents the height of 6 men in inches (I know this is
not metric). For you, this is where you plug in the data you collected from your trials.
Tom = 62”
John = 71”
Paul = 69”
Kevin = 78”
Rick = 73”
Jim = 61”
1.
T1 + T2 + T3 + T4 + T5 + T6 / 6
Total = 414” / 6 = 69” Average height = 69”
2. Subtract 69 from each of the men’s heights.
62 – 69 = -7
71 – 69 = 2
69 – 69 = 0
78 – 69 = 9
73 – 69 = 4
61 – 69 = -8
3. As the formula states, each of these numbers must be squared to get rid of any
negative numbers.
(-7)2
22
02
92
42
(-8)2
=
49
4
= 0
= 81
= 16
= 64
=
4. Add all of the squared differences.
5. 49 + 4 + 0 + 81 + 16 + 64 = 214
214 / 5 = 42.8 ~ 43 (Remember divide total by the number of trials minus 1).
6. √ 43 = 6.5
This means that on a bell-shaped curve, the numbers would be dispersed by 6.5
Back to our example. The average height of the 6 men = 69”
This means that the normal curve would show heights from 62.5” to 75.5”.
Approximately 69% of the population would fall within this range.