Question

Three sets of data contain 8, 7 and 5 observations and their gemometric means are 8.52, 10.12 and 7.75, respectively. Find the combined geometric mean of these 20 observations​

Answer 1

A geometric mean is defined as:

¯

x=(x_1⋅x_2⋅...xn)1/n

We need to find the product of each of the groups of observations in order to form a pooled single group.

¯

x_1 = P_1/8¹ = 8.52

P_1 = 8.52⁸

¯

x_2 = P_1/7² = 10.12

P_2 = 10.12⁷

x_3 = P_1/5²= 7.75

P_3 = 7.75⁵

The new geometric mean of the pooled group is

x = (P_1⋅P_2.P_3) ^1/20

= (8.52⁸⋅ 10.12⁷ ⋅ 7.75⁵)^1/20

= 8.837

So the geometric mean of the 20 observations in the single group formed by pooling the three groups is: b. 8.837

Answer 2

Answer:

Three groups of observations contain 8, 7, and 5 observations. Their geometric means are 8.52, 10.12, and 7.75. Find the geometric mean of the 20 observations in the single group formed by pooling the three groups.

a. 7.831

b. 8.837

c. 9.643

d. 6.438

Step-by-step explanation: