the box plots display the same data set for the number of touchdowns a quarterback threw in 10 seasons of…

the box plots display the same data set for the number of touchdowns a quarterback threw in 10 seasons of play. including outlier as minimum: excluding outlier as minimum: complete the statements describing the effect of the outlier on the measures of variability. the outlier of the data set is 5. the range of the data set including the outlier as the minimum is more than the one excluding the outlier as the minimum. the outlier has most effect on the range.

the box plots display the same data set for the number of touchdowns a quarterback threw in 10 seasons of play. including outlier as minimum: excluding outlier as minimum: complete the statements describing the effect of the outlier on the measures of variability. the outlier of the data set is 5. the range of the data set including the outlier as the minimum is more than the one excluding the outlier as the minimum. the outlier has most effect on the range.

Answer

Explanation:

Step1: Identify range formula

Range = Maximum - Minimum.

Step2: Analyze box - plots

Let's assume the maximum value in the data - set is (M). When the outlier (value (5)) is included as the minimum, the range is (R_1 = M - 5). When the outlier is excluded, let the new minimum be (m>5), and the range is (R_2 = M - m).

Step3: Calculate the difference in ranges

(R_1−R_2=(M - 5)-(M - m)=m - 5). Since (m>5), the range including the outlier as the minimum is larger than the range excluding it. The outlier has the most effect on the range because the range is directly affected by extreme values.

Answer:

The range of the data - set including the outlier as the minimum is larger more than the one excluding the outlier as the minimum. The outlier has the most effect on the range.