Multiple Choice Select the best answer for Exercises 123–126.

The stemplot shows the number of home runs hit by each of the 30 Major League Baseball teams in a single season. Home run totals above what value should be considered outliers?

(a) 173 (c) 222

(b) 210 (d) 229

(e) 257

The given information is:

The stemplot depicts how many home runs each of the 30 Major League Baseball teams hit in a single season.

We are provided with five options, we need to tell which statement is correct according to the given statement.

Data is:

91, 95, 103, 107, 108, 109, 114, 117, 121, 129, 148, 149, 153, 154, 154, 154, 155, 162, 163, 169, 172, 172, 173, 183, 185, 186, 191, 203, 210, 222

They are total 30 terms. Then the median is the average of 15th and 16th term.

$$\begin{gathered} M=\frac{154+154}{2} \\ =154 \end{gathered}$$

For the first quartile, the data values are 15. Then the first quartile is 117.

For the first quartile, the data values are 15. Then the first quartile is 173.

$$\begin{gathered} IQR=Q_3-Q_1 \\ =173-117 \\ =56 \\ {Q}_3+1.5IQR=173+1.5\left(56\right) \\ =256 \\ {Q}_1-1.5IQR=117-1.5\left(56\right) \\ =33 \end{gathered}$$

Observations that are more than 1.5 times the IQR above the third quarter or below the first quarter are considered outliers.

From the given data we can see that 257 is an outlier, therefore option (e) 257 is the correct option.