Q.
The harmonic mean of the following distribution
C .I
4.5 - 5.5
5.5 - 6.5
6.5 - 7.5
7.5 - 8.5
8.5 - 9.5
f
8
10
18
6
4
| C .I | 4.5 - 5.5 | 5.5 - 6.5 | 6.5 - 7.5 | 7.5 - 8.5 | 8.5 - 9.5 |
| f | 8 | 10 | 18 | 6 | 4 |
Statistics
Solution:
Construct the following table:
C . I
$x_i$
$f_i $
$\frac{f_i}{ x_i}$
4.5 - 5.5
5
8
1.6000
5.5- 6.5
6
10
1.6667
6.5 -7.5
7
18
2.5714
7.5 - 8.5
8
6
0.7500
8.5 - 9.5
9
4
0.4444
Total
46
7.0325
$\therefore $ The harmonic mean $ = \frac{\sum f_i}{\sum \frac{f_i}{x_i}}$
$ = \frac{46}{7.0325} = 6.54$
| C . I | $x_i$ | $f_i $ | $\frac{f_i}{ x_i}$ |
|---|---|---|---|
| 4.5 - 5.5 | 5 | 8 | 1.6000 |
| 5.5- 6.5 | 6 | 10 | 1.6667 |
| 6.5 -7.5 | 7 | 18 | 2.5714 |
| 7.5 - 8.5 | 8 | 6 | 0.7500 |
| 8.5 - 9.5 | 9 | 4 | 0.4444 |
| Total | 46 | 7.0325 |