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Consider the following measures of central tendency for a set of N numbers:

1. Arithmetic mean.

2. Geometric mean.

Which of the above uses/use all the data?

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  1. 1 only.
  2. 2 only.
  3. Both 1 and 2.
  4. Neither 1 nor 2.

Answer (Detailed Solution Below)

Option 3 : Both 1 and 2.
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Detailed Solution

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Concept:

Arithmetic Mean (A. M.): The Arithmetic Mean of a set of n numbers is given by:

A. M. = \(\rm \frac{\sum a_i}{n}\).

Geometric Mean (G. M.): The Geometric Mean of a set of n numbers is given by:

G. M. = \(\rm \sqrt[n]{\prod a_i}\).

Calculation:

Both the Arithmetic and Geometric Means use all the data for their calculations.

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