Question

1. outlier cowboys (1.8): the roster of the dallas cowboys professional football team in a recent season included 7 defensive linemen. their weights (pounds) were 321, 285, 300, 285, 286, 293, and 298. identify any outliers in the distribution. show your work.

Explanation:

Step1: Order the data

First, order the weights: 285, 285, 286, 293, 298, 300, 321.

Step2: Find the median

Since there are 7 data - points, the median (Q2) is the 4th value. So, Q2 = 293.

Step3: Find Q1 and Q3

The lower half of the data is 285, 285, 286. The median of the lower half (Q1) is 285. The upper half of the data is 298, 300, 321. The median of the upper half (Q3) is 300.

Step4: Calculate the inter - quartile range (IQR)

IQR=Q3 - Q1. So, IQR = 300 - 285=15.

Step5: Calculate the fences

The lower fence is Q1−1.5×IQR = 285−1.5×15=285 - 22.5 = 262.5. The upper fence is Q3 + 1.5×IQR=300 + 1.5×15=300+22.5 = 322.5.

Step6: Identify outliers

Any data point less than the lower fence or greater than the upper fence is an outlier. Since all the data points 285, 285, 286, 293, 298, 300, 321 are between 262.5 and 322.5, there are no outliers.

Answer:

There are no outliers.