Question

Clothing Prices, The table lists the prices of a set of comparable items of women’s and men’s and men’s clothing in 9 different cities.

1. Make box-and-whisker plots for the women’s and men’s data.
2. How do the prices in Houston compare with the rest of the cities for both women’s and men’s clothing? Explain your reasoning.
3. Interpret, would you say women’s clothing prices or men’s clothing prices vary more in the cities in the survey? Explain your reasoning.

   City	Women’s	Men’s
   New York	\(690	\)1190
   Los Angeles	\(450	\)620
   Chicago	\(590	\)1100
   Houston	\(440	\)900
   Paris	\(430	\)700
   London	\(350	\)660
   Toronto	\(310	\)850
   Tokyo	\(760	\)1050
   Mexico City	\(380	\)620

Short answer

a.

Box-and-whisker plot for women’s data

Box-and-whisker plot for men’s data:

b. The prices in Houston is nearly equal or equal to the mean prices for both men’s and women’s clothing.

c. The clothing price of men vary much more than the women’s clothing price.

a.

Box-and-whisker plot for women’s data:

Box-and-whisker plot for men’s data:

Step-by-step solution

Given information. 

The following table is given.

City	Women’s	Men’s
New York	$690	$1190
Los Angeles	$450	$620
Chicago	$590	$1100
Houston	$440	$900
Paris	$430	$700
London	$350	$660
Toronto	$310	$850
Tokyo	$760	$1050
Mexico City	$380	$620

Calculation.

The women’s data is arranged in ascending order:

$310,350,380,430,440,450,590,690,760$

The median is 440.

The lower quartile and upper quartile are$365\text{and640}$respectively.

The lower limit and upper limit are$310\text{and760}$respectively.

The box-and-whisker for women’s data can be drawn as:

The men’s data is arranged in ascending order:

$620,620,660,700,850,900,1050,1100,1190$

The median is 850.

The lower quartile and upper quartile are$640\text{and1075}$respectively.

The lower limit and upper limit are$620\text{and1190}$respectively.

The box-and-whisker for men’s can be drawn as:

Part b. Step 1: Given information.

The following table is given:

City	Women’s	Men’s
New York	$690	$1190
Los Angeles	$450	$620
Chicago	$590	$1100
Houston	$440	$900
Paris	$430	$700
London	$350	$660
Toronto	$310	$850
Tokyo	$760	$1050
Mexico City	$380	$620

Explanation. 

For women’s clothing, it can be seen from the plot that, the price at Houston is the mean price.

For men’s clothing, it is seen that, the price at Houston is very close to the mean price.

Hence, the prices in Houston is nearly equal or equal to the mean prices for both men’s and women’s clothing.

Part c. Step 1: Given information.

The following box-and-whisker plot is given to compare the prices:

Box-and-whisker plot for women’s data:

Box-and-whisker plot for men’s data:

Explanation. 

As it is seen from the above plots, in men’s clothing price there is a large difference from the median to the upper and lower quartile limits as compared to women’s clothing price.

Hence, the clothing price of men vary much more than the women’s clothing price.