Grouped Data Arithmetic Mean Definition:
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..
Formula:
Grouped Data Arithmetic Mean :
Arithmetic Mean = ΣfX/Σf
where
X = Individual score
f = Frequency
Grouped Data
Arithmetic Mean Example: 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.
| X Value |
Frequency(f) |
ΣfX |
| 1 |
2 |
1 * 2 = 2 |
| 2 |
3 |
2 * 3 = 6 |
| 3 |
2 |
3 * 2 = 6 |
Step 1: Find Σf.
Σf = 7
Step 2: Now,
find ΣfX.
ΣfX = ((1*2)+(2*3)+(3*2)) = 14
Step 3:
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.
