Calculate the standard deviation of the following scores:
1, 2, 8, 9
Arrange the scores on a number line so that you can see if they are symmetrical enough to determine the mean just by looking at them.
__x_x___________x_x____
0 1 2 3 4 5 6 7 8 9 10
They are symmetrical ! The point in the middle is 5. Therefore, 5 is the mean.
What is the Sum of Squares? The sum of squares is the sum of all the squared deviations from the mean. How do the scores deviate from 5, and what are the squares of those deviations?
1 deviates by -4. The square is 16.
2 deviates by -3. The square is 9.
8 deviates by 3. The square is 9.
9 deviates by 4. The square is 16.
The sum of the squared deviations is 50.
What is the Variance? The variance is the average squared deviation, or the
sum of the squared deviations divided by n.
n is the number of scores, which is 4. 50 divided by 4is 12.5. Therefore,
the variance is 12.5.
What is the Standard Deviation? It is the square root of the variance. What is the square root of 12.5?
a.) 4.01
b.) 3.54
c.) 2.98
d.) 1.54
The answer you choose should equal 12.5 if you square it. Answer a.) would give you a number greater than 16. Answers c.) and d.) would give you a number less than 9.
Answer b.) is between 3 and 4. So squared, it should be between 9 and 16. To check, you could square 3.45. That would give you 12.5316. So the square root of 12.5 is about 3.54
Therefore, the Standard Deviation is 3.54