Microsoft Office Tutorials and References
In Depth Information
is the Greek letter sigma, which stands for “sum.” It tells you to
add up all the scores that are indicated by the letter X, and then to divide your
answer by n (the number of numbers that you have).
Let’s give a simple example:
Suppose that you had these six biology test scores on an 7-item true-false quiz:
The symbol
S
6
4
5
3
2
5
To ﬁnd the mean of these scores, you add them up, and then divide by the
number of scores. So, the mean is: 25/6
¼
4.17
1.2 Standard Deviation
The standard deviation tells you “how close the scores are to the mean.” If the
standard deviation is a small number, this tells you that the scores are “bunched
together” close to the mean. If the standard deviation is a large number, this tells
you that the scores are “spread out” a greater distance from the mean. The formula
for the standard deviation (which we will call STDEV) and use the letter, S , to
symbolize is:
s
P X
2
X
ð
Þ
STDEV
¼
S
¼
(1.2)
n
1
The formula look complicated, but what it asks you to do is this:
X
1. Subtract the mean from each score X
.
2. Then, square the resulting number to make it a positive number.
3. Then, add up these squared numbers to get a total score.
4. Then, take this total score and divide it by n – 1 (where n stands for the number
of numbers that you have).
5. The ﬁnal step is to take the square root of the number you found in step 4.
ð
Þ
You will not be asked to compute the standard deviation using your calculator in
this topic, but you could see examples of how it is computed in any basic statistics
book. Instead, we will use Excel to ﬁnd the standard deviation of a set of scores.
When we use Excel on the six numbers we gave in the description of the mean
above, you will ﬁnd that the STDEV of these numbers, S , is 1.47.
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