Question 1: Find the arithmetic mean of the following set of observations: 25, 32, 24, 38, 22, 25, 30, 34, 26, 30
Solution:
There are 10 observations given here. n =10
Arithmetic mean of the 10 observations given = $\frac{\sum x}{n}$
= $\frac{25+32+24+38+22+25+30+34+26+30}{10}$
= $\frac{286}{10}$ = 28.6
Question 2: The frequency distribution of the number of children participated under
each age in a local Sports event is given below. Find the arithmetic
mean of the distribution. What does AM represent here?
Solution:
Age in years x 
Number of Participants f 
8

15

9

20

10

25

11

22

12

18

Total 
100

To calculate the arithmetic mean of data given in frequency distribution we add one more column to the table given for fx.
Age in years x 
Number of Participants f  fx 
8

15
 120 
9

20
 180 
10

25
 250 
11

22
 242 
12

18
 216 
Total 
N = 100
 ∑fx = 1008 
Arithmetic Mean =
$\frac{\sum fx}{N}$ =
$\frac{1008}{100}$ = 10.08
The Arithmetic mean represents here the average age of participants in the sports event.