Question

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

• A. 7
• B. 6.54
• C. 6.32
• D. 6.89

Answer 1

Answer: (B)

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 $=\frac{\sum f_i}{\sum \frac{f_i}{x_i}}$
$=\frac{46}{7.0325}=6.54$