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If a is the GM of the product of r sets of observations with geometric means G1,G2, …Gr respectively, then G is equal to

  • Option 1)

    \frac{G_1}{G_2}

  • Option 2)

    logG_1-logG_2

  • Option 3)

    \frac{logG_1}{logG_2}

  • Option 4)

    log(G_1,G_2)

 

Answers (1)

best_answer

As we have learned

Geometric Mean -

In case of discrete frequency distribution. 

- wherein

G=e^{\left | \frac{\sum_{i=1}^{n}f_{i}log(n_{i})}{\sum f_{i}} \right |}

 

 

Let x1, x2,………xn and y1, y2,……., ybe two series of observations with geometric means G1 and G2 respectively. Then,

                G1 = (x1, x2 ………xn)1/n and G2 = (y1, y2….. yn)1/n

 

Since G is the geometric mean of the ratios of the corresponding observations, therefore

                G=\left ( \frac{x_1}{y_1}.\frac{x_2}{y_2}.....\frac{x_n}{y_n} \right )^{1/n}

                   = =\frac{(x_1,x_2......x_n)^{1/n}}{(y_1,y_2......y_n)^{1/n}}=\frac{G_1}{G_2}


Option 1)

\frac{G_1}{G_2}

Option 2)

logG_1-logG_2

Option 3)

\frac{logG_1}{logG_2}

Option 4)

log(G_1,G_2)

Posted by

Himanshu

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