Arithmetic mean is the sum of the values divided by the number of values in the raw data. Arithmetic mean is also called simple mean because of its wide usage as a measure of central tendency. There is slight difference in the formulas in case of population data (grouped and ungrouped) and sample data (grouped and ungrouped). These formulas along with calculations are given below.
Population Ungrouped Data
In order to calculate the mean of population having ungrouped data, the formula will be
Sample Ungrouped Data
The mean of sample having ungrouped data can be calculated with the help of following formula.
Problem: Following are the number of hours of 10 people who work in same organization. 10, 17, 12, 10, 14, 9, 8, 3, 14, 16 Calculate Arithmetic Mean. (A) Treat data as a population (B) Treat data as a sample.
Population grouped Data
The formula for calculating the mean of population having grouped data is given below.
Sample grouped Data
The mean of sample having grouped data can be calculated with the help of following formula.
From the above calculations we conclude that the basic difference between population and sample formulas is only the various symbols used for calculating the means. For example in case of population, mean is represented by µ and number of observations by capital N. On the other hand in case of sample, number of observations is represented by small n while mean is represented by x bar.