First slide

Introduction to statistics

Question

If harmonic mean of first 5 observations is $\frac{5}{2}$ and harmonic mean of another 5 observations is $\frac{9}{2}$ then harmonic mean of all 10 observations is

Moderate

A

7
B

$\frac{45}{14}$
C

$\frac{101}{36}$
D

None of these

Solution

Let H₁, and n₁, are the harmonic mean and number of
observations of first group and H₂and n₂ are the
harmonic mean and number of observations of another
group.
$∴$ By using combined harmonic mean formula, we get
combined harmonic mean $\begin{array}{l} = \frac{n_{1} + n_{2}}{\frac{n_{1}}{H_{1}} + \frac{n_{2}}{H_{2}}} = \frac{5 + 5}{\frac{5}{5} + \frac{5}{9}} \\ = \frac{10}{\frac{28}{9}} = \frac{90}{28} = \frac{45}{14} \end{array}$

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