A vendor offers various t-shirts for sale on an Internet commerce site.Some of his t-shirts sell quite well, others have yet to find an interested customer.The summary $$\begin{array} { | l | c | }
\hline \bar { x } & 23 \
\hline \text { Median } & 15 \
\hline \text { Min } & 0 \
\hline \text { Q1 } & 3 \
\hline \text { Q3 } & 21 \
\hline \text { Max } & 82 \
\hline \text { sd } & 7.84 \
\hline
\end{array}$$
statistics are listed on right, based on the number of sales
per month for each of 80 different t-shirt designs.
A.What is the shape of this distribution? Explain how you know.
B.If the vendor spends $2 per t-shirt in shipping costs, what is his average monthly costs
per t-shirt sold? What is the standard deviation of this cost? Show work.
c.As time passes, the vendor has simplified his profit calculation.He estimates that he has
monthly flat costs of $35, with a gain of $3.50 per t-shirt sold.What is the median of his
profit? The IQR?
d.What are the mean and standard deviation of his profit?
e.What is more appropriate in this case: using mean and standard deviation, or using
median and IQR?

Question

A vendor offers various t-shirts for sale on an Internet commerce site.Some of his t-shirts sell quite well, others have yet to find an interested customer.The summary $$\begin{array} { | l | c | } 
\hline \bar { x } & 23 \
\hline \text { Median } & 15 \
\hline \text { Min } & 0 \
\hline \text { Q1 } & 3 \
\hline \text { Q3 } & 21 \
\hline \text { Max } & 82 \
\hline \text { sd } & 7.84 \
\hline
\end{array}$$ 
statistics are listed on right, based on the number of sales
per month for each of 80 different t-shirt designs.
A.What is the shape of this distribution? Explain how you know.
B.If the vendor spends $2 per t-shirt in shipping costs, what is his average monthly costs
per t-shirt sold? What is the standard deviation of this cost? Show work.
c.As time passes, the vendor has simplified his profit calculation.He estimates that he has
monthly flat costs of $35, with a gain of $3.50 per t-shirt sold.What is the median of his
profit? The IQR?
d.What are the mean and standard deviation of his profit?
e.What is more appropriate in this case: using mean and standard deviation, or using
median and IQR?

Quizplus · Accepted Answer

The Answer is a. The distribution is clearly skewed to the right. The mean is much larger than the median. The max is to be an outlier and is likely a part of a long tail of the most popular t-shirts. The min and Q1 are very close together, while the spread increases between the median, Q3, and the max.
b.

ext { mean } = 23 * \$ 2 = \$ 46 ; \quad \mathrm { sd } = 7.84 * \$ 2 = \$ 15.68

c.

ext { median } = 3.5 * 15 - 35 = \$ 17.50 ; \quad \mathrm { IQR } = 3.5 * ( 21 - 3 ) = \$ 63

d.

ext { mean } = 3.5 ^ { * } 23 - 35 = \$ 45.50 ; \mathrm { sd } = 3.5 ^ { * } 7.84 = \$ 27.44

e.
The distribution is strongly right skewed, thus mean and standard deviation are not appropriate.

A Vendor Offers Various T-Shirts for Sale on an Internet