Mean

Of all the measures of central tendency, the mean is the most often used and can be defined in a variety of ways. It can be defined as the sum of all the scores in a data set divided by the number of observations, and can also be defined as the point about which the sum of the deviations is equal to zero.

The formula for the computation of the mean is as follows:

where

X¯ (also called “X bar” is the mean value of the group of scores or the mean;

Σ (sigma) is the summation sign, which directs you to add together what follows it;

X is each individual score in the group of scores;

n is the size of the sample from which you are computing the mean.

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Table 1 Sample Data for Computation of the Mean
Observation	Test Score 1	Test Score 2
1	7	14
2	8	13
3	6	15
4	7	21
5	5	31
6	6	27
7	4	28
8	7	21
9	6	32
10	8	25
11	9	23
12	7	24
13	8	21
14	9	18
15	7	19
16	6	25
17	6	22
18	7	23
19	4	27
20	5	31
21	6	21
22	5	25
23	4	29
24	8	34
25	7	20

For example, the data set in Table 1 consists of 25 cases with two variables, Test Score 1 and Test Score 2.

To compute the mean, follow these steps:

1.
List the entire set of values in one or more columns such as you see in the table. These are all the Xs.
2.
Compute the sum or total of all the values.
3.
Divide the total or sum by the number of values.

Applying the above formula to the sample data results in the following two means:

The mean is sometimes represented by the letter M and is also called the typical, average, or most central score.

More About the Mean

In the formula, a small n represents the sample size for which the mean is being computed. A large N represents the population size.

• The sample mean is the measure of central tendency that most accurately reflects the population mean.
• The mean is like the fulcrum on a seesaw. It's the centermost point where all the values on one side of the mean are equal in weight to all the values on the other side of the mean.
• The mean is very sensitive to extreme scores. An extreme score can pull the mean in one direction or another and make it less representative of the set of scores and less useful as a measure of central tendency.

Analysis Using SPSS

Figure 1 is a simple output using SPSS's descriptive feature.

Figure 1 Results of SPSS Descriptives

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