Question

Study the following stem-and-leaf plot, and calculate the center and outlier.

• A. Center: $8.7;$ outlier: $2.8$
• B. Center: $2.8;$ outlier: $8.7$
• C. Center: $3.4;$ outlier: $8.7$
• D. Center: $2.8;$ outlier: $1.3$

Answer 1

The correct option is B Center: $2.8;$ outlier: $8.7$

Let’s check each of the options.
Using the key, we can see that there are 15 data values: $1.3,1.5,1.7,1.9,2.2,2.3,2.4,2.8,3.4,3.5,3.6,3.7,4.3,4.4,$ and $\mathrm{8.7.}$
There are $7$ values to the left of $2.8$ and $7$ values to the right of $\mathrm{2.8.}$ So, the middle value of the data set is $\mathrm{2.8.}$ So, the center of the plot is $\mathrm{2.8.}$
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.
Using the key, we can see that there are 15 data values: $1.3,1.5,1.7,1.9,2.2,2.3,2.4,2.8,3.4,3.5,3.6,3.7,4.3,4.4,$ and $\mathrm{8.7.}$
All the values are close to each other except one value. The value that is numerically distant from the data set is $\mathrm{8.7.}$ Hence, the outlier is $\mathrm{8.7.}$