Question

1. which data point(s) in the box - 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{|(mean value using all data)-(mean value excluding anomalous data)|}{mean value using all data}\times100
a. what is the percent deviation in the female data set when the outlying value of 1^n 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 4.5 is excluded?
% deviation=\frac{|9.20 - 8.72|}{9.20}\times100 = 5.25%
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 box - widths in males and females? explain your answer in a complete sentence.

Explanation:

Step1: Recall the given percentage - deviation formula

The formula for percentage deviation is $\text{\% deviation}=\frac{|(\text{mean value using all data})-(\text{mean value excluding anomalous data})|}{\text{mean value using all data}}\times100$.

Step2: Analyze the female data - set

For the female data - set, the percentage deviation when the outlying value is included is calculated as $\text{\% deviation}=\frac{|8.28 - 7.29|}{8.28}\times100=\frac{0.99}{8.28}\times100\approx11.96\%$ (the given calculation of $11.7\%$ may be due to rounding differences in intermediate steps).

Step3: Analyze the male data - set

For the male data - set, the percentage deviation when the outlying value is excluded is $\text{\% deviation}=\frac{|9.20 - 9.72|}{9.20}\times100=\frac{0.52}{9.20}\times100\approx5.65\%$.

Step4: Compare the percentage deviations

Since $11.96\%>5.65\%$, the female data - set has the largest percentage deviation.

Step5: Answer the question about the best - representing value

Outliers can greatly affect the mean. The median is less affected by outliers because it is the middle - value of a sorted data set. The mode is the most frequently occurring value and may not represent the overall data well if there are outliers or a non - uniform distribution. So, the median is likely to better represent the overall data set of box widths in males and females as it is more robust to outliers.

Answer:

1. The female data set has the largest percent deviation.
2. The median better represents the overall data set of box widths in males and females because it is less affected by outliers compared to the mean, and the mode may not capture the overall distribution well in the presence of outliers.