Data arising from organising n observed values into a smaller number of disjoint groups of values, and counting the frequency of each group; often presented as a frequency table.
X = Individual score f = Frequency
To find the Arithmetic Mean of 1,2,3,1,2,3,2. The arithmetic mean = 1+2+3+1+2+3+2/7 = 14/7 = 2 In this case there are two 1's, three 2's and two 3's. The number of times each number occurs is called its frequency. This can be clearly given in a table as below.
|1||2||1 * 2 = 2|
|2||3||2 * 3 = 6|
|3||2||3 * 2 = 6|
Find Σf. Σf = 7
Now, find ΣfX. ΣfX = ((1*2)+(2*3)+(3*2)) = 14
Now, Substitute in the above formula given Arithmetic mean = ΣfX/Σf = 14/7 = 2 The above example will lead you to calculate the Grouped data Arithmetic Mean manually.
This tutorial will help you dynamically to find the Grouped data Arithmetic Mean problems.