Let n observation be x1, x2……….xn and their frequencies be f1, f2, f3…….fn respectively. We define the mean as
Mean = 
is the Greek letter Sigma and shows Summation. While represents the mean
Example : 12
Find the mean of the following.
| xi |
10 |
15 |
20 |
25 |
30 |
35 |
40 |
fi |
4 |
6 |
8 |
18 |
6 |
5 |
3 |
Solution:
We will rewrite the table in the following form.
Mean of Group Data
If a class interval is given we take the xi value as the class mark value and use the same formula
Example : 13
The table shows the weight or 50 persons in a group.
| Weight in Kg |
40 - 43 |
44 - 47 |
48 - 51 |
52 - 55 |
56 - 59 |
Number of persons |
8 |
12 |
9 |
16 |
5 |
Find the mean weight.
Solution :
| Weight in kg |
Frequency fi |
Class Mark |
fi xi |
40 – 43 |
8 |
|
|
44 – 47 |
12 |
|
|
48 – 51 |
9 |
|
|
52 – 55 |
16 |
|
|
56 – 59 |
5 |
|
|
|
 50
|
|
 2467
|
Try these problems
The age of 50 players in a school are given below.
| Age (in years) |
14 |
15 |
16 |
17 |
Number of players |
16 |
14 |
12 |
8 |
Answer:
i) Find the mean of the following grouped frequency distribution.
| Class interval |
0 -9 |
10 - 19 |
20 –29 |
30 - 39 |
40 - 49 |
Frequency |
11 |
7 |
9 |
5 |
8 |
Answer :
| Class Interval |
Frequency |
Class Mark |
fixi |
0 – 9 |
11 |
|
|
10 – 19 |
7 |
|
|
20 – 29 |
9 |
|
|
30 – 39 |
5 |
|
|
40 – 49 |
8 |
|
|
|
|
|
|
Mean =