Educational Psychology

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scores deviate from the mean. In the example in Exhibit 17 the standard deviations are 7.73 for School A and 2.01
for School B. In the exercise below we demonstrate how to calculate the standard deviation.

Calculating a standard deviation

Example: The scores from 11 students on a quiz are 4, 7, 6, 3, 10, 7, 3, 7, 5, 5, and 9

5. Order scores.


6. Calculate the mean score.


7. Calculate the deviations from the mean.


8. Square the deviations from the mean.


9. Calculate the mean of the squared deviations from the mean (i.e. sum the squared deviations from the
   mean then divide by the number of scores). This number is called the variance.


10. Take the square root and you have calculated the standard deviation.

Score

(Step 1, order)

Deviation

from the mean

Squared deviation

from the mean

3 -3 9

3 -3 9

4 -2 4 (Step 4-5, complete the calculations)

5 -1 1 Formula:

5 -1 1

Standarddeviation=∑Score−Mean

2

N

N = Number of scores

6 0 0

7 1 1

7 1 1

7 1 1

9 3 9

10 4 4

TOTAL = 66 40

(Step 2, calculate

mean)

MEAN 66 / 11 = 6

(Step 3, calculate

deviations)

Mean= 40 / 11 =3.64

(Step 6, find the standard deviation)

Standarddeviation=3.64=1.91

Exhibit 21: Calculating a standard deviation

The normal distribution

Knowing the standard deviation is particularly important when the distribution of the scores falls on a normal
distribution. When a standardized test is administered to a very large number of students the distribution of scores

Educational Psychology 295 A Global Text