Definition of Standard Deviation
Standard deviation is a measure about how much a number or a value is deviating from the mean of the whole data set. In other words, it tells us how much is data scattered. The formula for calculating the standard deviation is as follows:
Example of Standard Deviation:
Assume that in a class 10 students have scored the following marks in math test: 25, 35, 65, 75, 64, 43, 59, 71, 91 and 32. To calculate the standard deviation, first, calculate the mean.
Then we have to take the squares of the difference between mean and each student’ score.
|
Scores |
Mean |
Mean - Score |
(Mean - Score)2 |
|
25 |
56 |
31 |
961 |
|
35 |
56 |
21 |
441 |
|
65 |
56 |
-9 |
81 |
|
75 |
56 |
-19 |
361 |
|
64 |
56 |
-8 |
64 |
|
43 |
56 |
13 |
169 |
|
59 |
56 |
-3 |
9 |
|
71 |
56 |
-15 |
225 |
|
91 |
56 |
-35 |
1225 |
|
32 |
56 |
24 |
576 |
|
|
|
|
4112 |
Using the above formula the standard deviation will be as follows:
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