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.