Question

the following data give the margin of victory for a football championship over 15 years
15 4 4 10 11 31 3 25 6 4 3 4 6 14 6

a find the mean and median margin of victory
b identify the outlier in the data set. if the outlier is eliminated, what are the new mean and median?

(round to the nearest tenth as needed )

the median is
(type an integer or a decimal )
b which, if any, of the margins of victory would be considered the outlier? select the correct choice below and,
if necessary, fill in the answer box to complete your choice.

a. the outlier is 31
(type an integer or a decimal.)

b. none of the margins would be considered an outlier

find the mean with the outlier excluded. select the correct choice below and, if necessary, fill in the answer box to
complete your choice

a. the mean without the outlier is
(round to the nearest tenth as needed )

b. none of the weights would be considered an outlier

Explanation:

Step1: Identify the data set without outlier

The original data set is: 15, 4, 4, 10, 11, 31, 3, 25, 6, 4, 3, 4, 6, 14, 8. After removing the outlier (31), the new data set is: 15, 4, 4, 10, 11, 3, 25, 6, 4, 3, 4, 6, 14, 8.

Step2: Calculate the sum of the new data set

Sum = 15 + 4 + 4 + 10 + 11 + 3 + 25 + 6 + 4 + 3 + 4 + 6 + 14 + 8. Let's calculate step by step:
15 + 4 = 19; 19 + 4 = 23; 23 + 10 = 33; 33 + 11 = 44; 44 + 3 = 47; 47 + 25 = 72; 72 + 6 = 78; 78 + 4 = 82; 82 + 3 = 85; 85 + 4 = 89; 89 + 6 = 95; 95 + 14 = 109; 109 + 8 = 117.

Step3: Determine the number of data points without outlier

Original number of data points is 15, after removing 1 outlier, the number of data points (n) = 15 - 1 = 14.

Step4: Calculate the mean

Mean = $\frac{\text{Sum}}{\text{Number of data points}}$ = $\frac{117}{14}$ ≈ 8.4 (rounded to the nearest tenth).

Answer:

A. The mean without the outlier is 8.4