Question

1. which data point(s) in the foot width values in model 2 might be considered outliers? explain your choice(s).
2. the equation below allows you to calculate the amount of deviation (in percent) for the values within a data set. the percent deviation is reported as an absolute value.

% deviation = \\(\frac{|(\text{mean value using all data})-(\text{mean value excluding anomalous data})|}{\text{mean value using all data}}\times100\\)
a. what is the percent deviation in the female data set when the outlying value of 17 is excluded (i.e., considered to be anomalous data)?
% deviation = \\(\frac{|8.26 - 7.29|}{8.26}\times100 = 11.7\\%\\)
b. what is the percent deviation in the male data set when the outlying value of 45 is excluded?
% deviation = \\(\frac{|9.20 - 9.72|}{9.20}\times100 = 5.65\\%\\)
c. which data set (male or female) had the largest percent deviation?

1. given the outliers and amount of deviation in each data set, which value (mean, median, mode) best represents the overall data set of foot width in males and females? explain your answer in a complete sentence.

Explanation:

Step1: Analyze question 14

No data points for foot - width in Model 2 are given, so cannot answer this part.

Step2: Analyze question 15a

The formula for percent deviation is $\text{\% deviation}=\frac{\vert(\text{mean value using all data})-(\text{mean value excluding anomalous data})\vert}{\text{mean value using all data}}\times100$. Given values are plugged in: $\text{\% deviation}=\frac{\vert8.26 - 7.29\vert}{8.26}\times100=\frac{0.97}{8.26}\times100\approx11.7\%$.

Step3: Analyze question 15b

Using the percent - deviation formula with given values: $\text{\% deviation}=\frac{\vert9.20 - 9.72\vert}{9.20}\times100=\frac{0.52}{9.20}\times100\approx5.65\%$.

Step4: Analyze question 15c

Compare the percent deviations from 15a and 15b. Since $11.7\%>5.65\%$, the female data set has the largest percent deviation.

Step5: Analyze question 16

Outliers can greatly affect the mean. The median is less affected by outliers as it is the middle value when the data is ordered. The mode is the most frequently occurring value and may not represent the overall spread. So, the median best represents the overall data set of foot width in males and females because outliers have a minimal impact on it.

Answer:

1. Cannot be answered due to lack of data.

15a. $11.7\%$
15b. $5.65\%$
15c. Female data set

1. The median best represents the overall data set of foot width in males and females because outliers have a minimal impact on it.