The data set below consists of the scores of 15 students on a quiz. For this data set, which measure of variation do you think is more appropriate, the range or the standard deviation? Explain your thinking.
$\begin{array} { l l l l l } 90 & 90 & 91 & 91 & 89 \end{array}$ $\begin{array} { l l l l l } 90 & 89 & 91 & 91 & 90 \end{array}$ $\begin{array} { l l l l l } 60 & 90 & 89 & 90 & 91 \end{array}$

Question

The data set below consists of the scores of 15 students on a quiz. For this data set, which measure of variation do you think is more appropriate, the range or the standard deviation? Explain your thinking.  
$\begin{array} { l l l l l } 90 & 90 & 91 & 91 & 89 \end{array}$ $\begin{array} { l l l l l } 90 & 89 & 91 & 91 & 90 \end{array}$ $\begin{array} { l l l l l } 60 & 90 & 89 & 90 & 91 \end{array}$

Quizplus · Accepted Answer

The Answer is For this data set, the range is very misleading. The range depends only on the smallest and largest values and the remainder of the data contributes nothing to the range. In this case, the smallest value is an outlier. Thus even though all the values except one lie between 89 and 91, the range is 31. The standard deviation, while it will also be affected by the outlier, will be less misleading, as it depends on every piece of data.

The Data Set Below Consists of the Scores of 15 9090919189\begin{array} { l l l l l } 90 & 90 & 91 & 91 & 89 \end{array}90​90​91​91​89​

The Data Set Below Consists of the Scores of 15 $\begin{array} { l l l l l } 90 & 90 & 91 & 91 & 89 \end{array}$