What is the Mean?
The mean (also known as the average) is a measure of central tendency that calculates the sum of all values in a dataset divided by the number of values.
Formula:
Mean = (Sum of all values) / (Number of values)
Example:
Suppose we have a set of exam scores for 5 students:
Student A: 80
Student B: 90
Student C: 70
Student D: 85
Student E: 95
To calculate the mean, we add up all the scores and divide by the number of students (5):
Mean = (80 + 90 + 70 + 85 + 95) / 5
= 420 / 5
= 84
Interpretation:
The mean score for these 5 students is 84. This means that if we were to take the sum of all their scores and divide it by the number of students, we would get an average score of 84.
Why is the Mean Important?
The mean is a useful measure in descriptive statistics because it:
- Gives a quick sense of the "middle" value in a dataset
- Is easy to calculate and interpret
- Can be used as a baseline for comparing other statistical measures, such as standard deviation
However, the mean has some limitations, such as being sensitive to outliers (very large or very small values) and not accounting for skewness (asymmetry) in the data.