Question

Given below are the center, spread, and outlier of the stem-and-leaf plot that shows Reuben’s scores in a game of darts.
$\begin{array}{cc}\text{Stem}& \text{Leaf}\\ 3& 05789\\ 4& 01567\\ 5& 07\\ 6& 023\end{array}$
Key: $\begin{array}{c}3\end{array}|0=30$
Select the incorrect option.

• A. Outlier: $40$
• B. Center: $45$
• C. Spread: $30$ to $63$

Answer 1

The correct option is A Outlier: $40$

Following the key, the data set of the given stem and leaf diagram is:
$30,35,37,38,39,40,41,45,46,47,50,57,60,62,63$

There are $15$ values in the given data set. There are $7$ values to the left of $45$ and $7$ values to the right of $45$. So, the middle value of the data set is $45.$ Thus, the center of the data is $45.$

The smallest observation in the plot is $30$ and the largest observation in the plot is $63.$ So, the spread is from $30$ to $63.$

An outlier is a data value that is numerically distant from the data set or it is a value that is very different from the rest of the values in the data set. Here, $40$ is very similar to the other data values. So, it is not an outlier.