While the housing market is in recession and is not likely to emerge anytime soon, real estate investment in college towns continues to promise good returns (The Wall Street Journal, September 24, 2010). Marcela Treisman works for an investment firm in Michigan. Her assignment is to analyze the rental market in Ann Arbor, which is home to the University of Michigan. She gathers data on monthly rent for 2011 along with the square footage of 40 homes. The data is shown in the accompanying table. Monthly Rent Square Footage 1163 1020 Monthly Rent Square Footage 645 500 1084 675 648 1100 760 700 1100 1150 800 903 1185 1225 817 820 1245 1368 850 920 1275 1400 855 900 1275 1350 1185 859 886 1400 900 1000 1450 1200 905 920 1500 1412 1700 905 876 1518 929 920 1600 1440 960 975 1635 1460 1635 1650 975 1100 1460 990 1170 940 1000 995 1750 1944 1029 1299 1950 2265 1039 1164 1975 1700 1049 1180 2200 4319 2700 1162 1050 2400
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
I have attached the data set. My only problem is finding the standard deviation for the set as it consists of multiple variables and it can be tedious. I have plugged in the numbers for both population values and sample values and can't seem to get the correct answer. I would just like to know if there is a simplier way to get the answer without having to work with every single value in the data set. Thank you.
a. Calculate the mean and the standard deviation for monthly rent. (Round your answers to 2 decimal places.)
b. Calculate the mean and the standard deviation for square footage. (Round your answers to 2 decimal places.)
c. Which sample data exhibit greater relative dispersion?
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