Question

Consider the following data set:

5, 10, 24, 79, 103

If you were told to determine the mean which formula is most appropriate to use? What other formula could you use, although it is less desirable? What would you have to keep in mind if you used this second formula?

Answer 1

Solution:

1) To find mean of the dataset, the most appropriate is the usage of the simple mean formula, since it is raw data:

$M=\sum_{i=1}^5\frac{x_i}{n}$, where $n=5$ is the total number of elements in the dataset.

$M = \frac{5+10+24+79+103}{5}=44.2$

2) The other formula we can use is the geometric mean:

$M = \sqrt[n=5]{x_1x_2x_3x_4x_5} = \sqrt[5]{5*10*24*79*103} = 24.999373$

3) The things, we need to keep in mind, using this formula are as follows:

1. All the numbers in our data must be positive
2. There must not be any zeros in the dataset

Answer:

1) $44.2$

2) $24.999373$