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Measures of Central Tendency and Dispersion

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Question : 186 of 211

Marks: +1, -0

The Geometric mean of 3,6,24 and 48 is

6
8
12
24

Solution:

Concept:

The geometric mean of

n

numbers is the

n

th root of their product.

Explanation:

For numbers

3, 6, 24, 48

:

Product

= 3 \times 6 \times 24 \times 48

= 3 \times 6 = 18

18 \times 24 = 432

432 \times 48 = 20736

Geometric mean

= \sqrt[4]{20736}

Alternatively, factor each number:

3 = 3^1

6 = 2 \times 3

24 = 2^3 \times 3

48 = 2^4 \times 3

Product

= 2^{0+1+3+4} \times 3^{1+1+1+1} = 2^8 \times 3^4

Fourth root

= 2^{8/4} \times 3^{4/4} = 2^2 \times 3 = 4 \times 3 = 12

Answer:

12

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