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Question

# For each data set, find the median, midrange, and geometric mean. (b) Are they reasonable measures of central tendency? Explain.Exam scores ($9$ students) $\quad 42,55,65,67,68,75,76,78,94$

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The median is the number in the middle of a set of numbers if $n$ is odd and the average of the two middle terms' values if $n$ is even. Keep in mind that the data need to be sorted in increasing order.

The midrange is defined as the average of the lowest and highest values, i.e.,

$\text{Midrange} = \frac{x_{\text{min}} + x_{\text{max}}}{2}, \tag{1}$

where

• $x_{\text{min}}$ is the lowest value,
• $x_{\text{min}}$ is the highest value.

The geometric mean, denoted by $G$, is a multiplicative average, calculated by multiplying the data values and then taking the $n$th root of the result, i.e.,

$G = \sqrt[n]{x_1 \cdot x_2 \cdots x_n}. \tag{2}$

This can be computed only if all the values are positive.

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