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Question

# Find mean, median, mode, and range. Which measure best describes each group of data? Explain. resting heart rate in beats per minute: 79 72 80 81 40 72

Solution

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Given:

79, 72, 80, 81, 40, 72

The $\textbf{mean}$ is the sum of all values divided by the number of values:

\begin{align*} \overline{x}&=\dfrac{\sum_{i=1}^n x_i}{n} \\ &=\dfrac{\begin{matrix}79+72+80+81+40+72\end{matrix}}{6} \\ &=\dfrac{424}{6} \\ &\approx 70.7 \end{align*}

Sort the data values from smallest to largest:

40, 72, 72, 79, 80, 81

The $\textbf{median}$ is the middle value of the sorted data set. Since the data set contains 6 values, the median is the average of the 3rd and 4th data value.

$m=\frac{72+79}{2}=\frac{151}{2}=75.5$

The $\textbf{mode}$ is the data values that occurs most often in a dataset. If there are no repeated data values, then the mode does not exist.

The data value 72 is repeated twice, while no other data values in the data set are repeated and thus the mode is 72.

$\text{Mode}=72$

Thus the minimum is 40 and the maximum is 81.

The $\textbf{range}$ is the difference between the highest and lowest data value:

$\text{Range}=\max-\min=81-40=41$

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