Download psyc standard deviation worksheet doc file - IB-Psychology

The mean for a distribution of the sum of the scores divided by the number of scores.
The formula for the population mean is:
(Myoo)
First, sum all the scores in the population, and then divide by N. For a sample, the computation is done the same
way, but the formula uses symbols that signify sample values:
Sample Mean =
Where n = the number of scores in the sample.
scores: 60, 75, 73, 50, 88, 90, 62, 55.
Using the scores above calculate the sample mean:
Standard deviation (variance)
Deviation is distance from the mean:
Deviation score = X - µ
The first step in finding the standard distance from the mean is to determine the deviation, or distance from the
mean, for each individual score. By definition, the deviation for each score is the difference between the score
and the mean. You will have both + and – scores , the sign tells the direction of the score from the mean, whether
the score is above or below the mean.
Because our goal is to compute a measure of the standard distance from the mean, the next step is to calculate
the mean of the deviation scores. To compute this mean, you first add up the deviation scores and then divide by
N.
Using the scores from above calculate the following:
Where N =
∑X =
µ=
Now add up X - µ what do you get?
This is how you check your equation to make sure it is right. It also shows that in order to compute the standard
deviation you need to get rid of the + and – signs. The standard procedure for this is to square each deviation
score. Using the squared values, you then compute the mean squared deviation, which is called variance.
However, the number we need is now squared, so in order to correct this, take the square root of the variance.
Standard Deviation =
Variance is the mean squared deviation. This mean is computed exactly the same way. First find the sum, then
divide by the number of scores.
Variance = mean squared deviation =
This equation is called the sum of squares and is represented this way SS. There are 2 formulas used to compute
this, we only need to learn one of them 
SS = ∑
–
First square each score and then sum the squared values. The second part requires you to add up the scores and
square this total, and then divide the result by N. Using the scores from before:
X
______
______
N = ______
SS = ∑
-- ------
________________________________
∑X =
∑
=
SS = _______
With this math nightmare over, the equation for variance is simple:
Variance =
The standard deviation is the square root of variance, so the equation for standard deviation is:
Standard deviation =
Compute the Standard deviation: __________
Using the following data sets, compute the mean, variance, sum of squares, and standard deviation.
22, 45, 36, 10, 42, 30
µ=
Variance =
SS =
SD =
SS =
SD =
2, 6, 9, 3, 3, 6, 3, 6, 9
µ=
Variance =
30, 50, 30, 40, 34, 89, 54, 89, 45, 23, 56, 43, 23, 45
µ=
Variance =
SS =
SD =