Mean
The arithmetic mean is the most common measure of central tendency. It is computed by summing all the scores (sigma or Σ) and dividing by the number of scores (N):
Where X is the mean, ∑x is the addition or summation of all scores, and N is the number of cases.
 Example of calculating mean with formula:
Given the scores of first year students in a Statistics test, calculate the mean.
10 5 9 8 6 5 9 8 7 6 5 6
1. To calculate the mean, first add all scores; that is, 10+5+9+8++6+5+9+8+7+6+5+6= 84
2. Then divide the result by the number of cases (the number of scores): 12
3.
Applying the formula:
X= 84/12= 7
Thus, the mean or average score of this Statistics test is 7.
 Example of calculating the mean using a frequency table.
In this example, you are given a table of frequencies of the scores obtained in a Statistics test. The column on the left gives you test scores, and the column on the right the frequency (how many students obtained that score).
X (score)

Frequency

10

1

5

3

8

2

2

5

4

5

1. First, multiply each score by its frequency to calculate the sum of all scores:
10X1+5x3+8x2+2x5+4X5= 71
2. Then divide by the number of scores, which is the sum of all the frequencies: 1+3+2+5+5= 16
3. Applying the formula: 71/16= 4.43
The mean is sensitive to outliers (that is, unusually large or small observations). A 5% trimmed mean is calculated when there are outliers in the distribution, as it calculates the mean of the distribution when the top and bottom 5% scores are removed.
In this example, the 5% trimmed mean and the arithmetic mean are very similar. Thus, there are no extreme scores or outliers in this distribution that may be affecting the mean.
In this example, the 5% trimmed mean is different from the arithmetic mean. This implies that there are outliers in the distribution.