Question

The geometric mean of 10 observations is 58.08. Later on it was discovered that a value 520 was misread as 250. What is the correct geometric mean​

Answer 1

Answer:

The corrected geometric mean = 62.49

Step-by-step explanation:

Please note that it is impossible to solve this sum without a scientific calculator!!

Geometric mean of "n" observations is the nth root of the product of the n observations.

Given:

Geometric mean of 10 observations = 58.08

Let product of 10 observations  = P

=> $\sqrt[10]{P}$ = 58.08

Taking logs on both sides

$\frac{1}{10} * log (P) =$ $log (58.08)$

$\frac{1}{10} *log (P) = 1.764$

$log (P) = 10 * 1.764$

$log(P) = 17.64$

P = antilog(17.64)

P = 4.367 * 10^17

This is the product of the original 10 numbers

We are given that one value 520 was misread as 250

=> Incorrect value: 250 and Correct value: 520

Correct Product = (Original Product / Incorrect Value) * Correct Value

Correct Product = (4.367 * 10^17 / 250)*520

                           = 9.085 * 10^17

Correct Geometric Mean = $\sqrt[10]{Correct Product}$

                                          = 62.49

The correct geometric mean = 62.49

Note:

Geometric mean deals with products. If we want to remove the effect of an incorrect value, we need to divide the incorrect product by the incorrect value. If we need to add the effect of the correct value, we need to multiply the correct value to the interim product. Thus, we will get the correct product.