First slide

Introduction to statistics

Question

The geometric mean G of the product of n sets of data with geometric means $G_{1}, G_{2}, \dots \dots \dots, G_{n}$ respectively, then

Easy

A

$\sqrt{G} = G_{1} G_{2} \dots \dots G_{n}$
B

$G = G_{1} G_{2} \dots \dots G_{n}$
C

$\sqrt{G} = - G_{1} G_{2} \dots \dots G_{n}$
D

None of these

Solution

Let $x_{1}, x_{2}, \dots \dots, x_{n}$ be the variates corresponding to n sets of data, each having the same number of observations say K
and x be their product. Then $x =$ $x_{1}, x_{2}, \dots \dots, x_{n}$
$\begin{array}{l} \log x = \log x_{1} + \log x_{2} + \dots + \log x_{n} \\ or \frac{Σlog x}{K} = \frac{Σlog x_{1}}{K} + \frac{Σlog x_{2}}{K} + \dots \dots + \frac{Σlog x_{n}}{K} \\ or \log G = \log G_{1} + \log G_{2} + \dots \dots + \log G_{n} \\ \Rightarrow G = G_{1} G_{2} \dots \dots G_{n} \end{array}$

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