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Measures of Central Tendency and Dispersion

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Question : 61 of 211

Marks: +1, -0

The Harmonic mean of 5,6,10,15,20,24 is

$6.9$
$9.6$
$8.6$
$9.8$

Solution:

Concept:

Harmonic mean for ungrouped data is given by

H = \frac{n}{\sum \frac{1}{x_i}}

.

Explanation:

Given numbers:

5, 6, 10, 15, 20, 24

.

Number of terms:

n = 6

.

Sum of reciprocals:

\frac{1}{5} + \frac{1}{6} + \frac{1}{10} + \frac{1}{15} + \frac{1}{20} + \frac{1}{24}

.

Find common denominator

120

:

\frac{24}{120} + \frac{20}{120} + \frac{12}{120} + \frac{8}{120} + \frac{6}{120} + \frac{5}{120} = \frac{75}{120} = \frac{5}{8}

.

Thus,

H = \frac{6}{\frac{5}{8}} = 6 \times \frac{8}{5} = \frac{48}{5} = 9.6

.

Answer:

9.6

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