Question

While the housing market was in recession and was not likely to emerge anytime soon, real estate investment in college towns continued to promise good returns (The Wall Street Journal, September 24, 2010). Michele Gibellino worked for an investment firm in Michigan. Her assignment was to analyze the rental market in Ann Arbor, which is home to the University of Michigan. She gathered data on monthly rent for 2011 for a sample of 40 homes. The data is shown in the accompanying table.

Monthly Rent Monthly Rent Monthly Rent Monthly Rent

645 905 1084 1518

675 929 1100 1600

760 960 1100 1635

800 975 1185 1635

820 990 1245 1650

850 995 1275 1750

855 1029 1275 1950

859 1039 1400 1975

900 1049 1450 2200

905 1050 1500 2400

Tell me about the monthly rents. Choose the appropriate description.

a.	The shape of the distribution of monthly rentals is symmetric. The typical monthly rent is $1223. The spread is given by the standard deviation, $425. The monthly rents do not vary much.
	b.	The shape of the distribution of monthly rentals is right skewed. The typical monthly rent is 1067. The spread is given by the Five Number Summary: Minimum        645 Q1                  905 Median          1067 Q3                 1504.5 Maximum      2400 The monthly rents don't vary much.
	c.	The shape of the distribution of monthly rentals is symmetric. The typical monthly rent is $1223. The spread is .35 The monthly rents do not vary much.
	d.	The shape of the distribution of monthly rentals is right skewed. The typical monthly rent is $1067. The spread is given by the Five Number Summary: Minimum $645 Q1    $905 Median $1067 Q3 $1505 Maximum $2400 The monthly rents vary a lot.

Answer 1

For this question i will be using the Minitab software. it can also be done by excel

1st we plot a histogram of the data given on monthly rent to see if the data is symmetric or skewed

Steps to create Histogram in Minitab :

1. Enter the data in a column and name the column lets say C1
2. Go to "graph" then select "histogram"
3. There will be different options of customization of histogram for different purposes
4. Here we select "simple"
5. Now a dialog box is opened select the variables (by double clicking)for which you want the histogram.Here we select the C1
6. Then enter ok we will get the histogram

So looking at the graph we can say that the data of monthly rents has long tail toward the right side of the peak value(values with highest frequency) and most of the data falls in the right side of the peak value.

There we can say that the data is rightly skewed (also known as positively skewed)

Now looking at above conclusion we can say that the data is not symmetric so, we can say that the

option a. The shape of the distribution of monthly rentals is symmetric.The typical monthly rent is $1223.The spread is given by the standard deviation, $425.The monthly rents do not vary much.

&

option c. The shape of the distribution of monthly rentals is symmetric.The typical monthly rent is $1223.The spread is .35.The monthly rents do not vary much.

are not true.

Now to see which description is true we find the five point summary of the data of monthly rent.

can be computed with both minitab and excel as excel is more user friendly we will use excel

Five point summary :-

Minimum = $645 (use the function "=MIN(Select the column of data)" in excel)

Quartile 1 = $905 (use the function "=QUARTILE(Select the column of data,1)" in excel)

Median = $1067 = (use the function "=MEDIAN(Select the column of data)" in excel)

Quartile 3 = $1504.5 = $1505 (use the function "=QUARTILE(Select the column of data,3)" in excel)

Maximum = $2400 (use the function "=MAX(Select the column of data)" in excel)

Now both option b. and option d. have same values of the five point summary. Now we see that our answer is option d. because by looking at the maximum and minimum values of the data we can say that the rents vary a lot but in option b. it says that the rent do not vary much and in option d. the values of five point summary is given with the unit of rent (in dollars) so we can reject option b.

Therefore required option is d. The shape of the distribution of monthly rentals is right skewed.The typical monthly rent is $1067.The spread is given by the Five Number Summary:Minimum $645, Q1    $905,Median $1067, Q3 $1505, Maximum $2400.The monthly rents vary a lot. [answer]

Histogram of the given data Frequency 750 1000 1250 1500 1750 2000 2250 2500 C1