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Business / Basic Statistics for Business and Economics 7 / Chapter 3 / Problem 65E

Basic Statistics for Business and Economics | 7th Edition | ISBN: 9780077384470 | Authors: Douglas Lind; William Marchal; Samuel Wathen

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U.S. housing prices reached their peak in July of 2006.

Chapter 3, Problem 65E

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QUESTION:

Problem 65E

U.S. housing prices reached their peak in July of 2006. The following data shows the ratio of the prices reported in a recent month to the July 2006 figure. These are to be used to represent typical amounts of decline from that peak for 20 cities.

Phoenix	Los Angeles	San Diego	San Francisco	Denver	Washington	Miami	Tampa	Atlanta	Chicago
0.760	0.784	0.764	0.802	0.909	0.828	0.786	0.792	0.933	0.915
Boston	Detroit	Minneapolis	Charlotte	Las Vegas	New York	Cleveland	Portland	Dallas	Seattle
0.902	0.792	0.855	1.025	0.756	0.922	0.865	0.981	0.939	0.999

a. Find the mean, median, and mode of these statistics.

b. What are the range and standard deviation of the values? (Assume this to be sample information.)

c. Use the Empirical Rule to determine an interval which contains approximately 95 percent of the observations.

Questions & Answers

QUESTION:

Problem 65E

U.S. housing prices reached their peak in July of 2006. The following data shows the ratio of the prices reported in a recent month to the July 2006 figure. These are to be used to represent typical amounts of decline from that peak for 20 cities.

Phoenix	Los Angeles	San Diego	San Francisco	Denver	Washington	Miami	Tampa	Atlanta	Chicago
0.760	0.784	0.764	0.802	0.909	0.828	0.786	0.792	0.933	0.915
Boston	Detroit	Minneapolis	Charlotte	Las Vegas	New York	Cleveland	Portland	Dallas	Seattle
0.902	0.792	0.855	1.025	0.756	0.922	0.865	0.981	0.939	0.999

a. Find the mean, median, and mode of these statistics.

b. What are the range and standard deviation of the values? (Assume this to be sample information.)

c. Use the Empirical Rule to determine an interval which contains approximately 95 percent of the observations.

ANSWER:

Answer:

Step 1 of 3:

(a)

The U.S. housing prices reached their peak in July of 2006.

The following data shows the ratio of the prices reported in a recent month to the July 2006 figure.

These are to be used to represent typical amounts of decline from that peak for 20 cities.

Phoenix	Los Angeles	San Diego	San Francisco	Denver	Washington	Miami	Tampa	Atlanta	Chicago
0.760	0.784	0.764	0.802	0.909	0.828	0.786	0.792	0.933	0.915
Boston	Detroit	Minneapolis	Charlotte	Las Vegas	New York	Cleveland	Portland	Dallas	Seattle
0.902	0.792	0.855	1.025	0.756	0.922	0.865	0.981	0.939	0.999

We are asked to find the mean, median, and mode of this data set.

$Sample\ mean\ \overline{X}\ =\frac{Sum\ of\ all\ the\ values\ in\ the\ sample}{Number\ of\ values\ in\ the\ sample}=\frac{\sum\limits_{i}^{\ }{X}_{i}}{n}$

$\ mean\ \overline{X}\ =\frac{\sum\limits_{i=1}^{20}{X}_{i}}{n}$

$\ mean\ \overline{X}\ =\frac{0.760+0.784.........+0.939+0.999}{20}=0.86545$

Since the number is even, then the median is the average of two middle sorted numbers.

$Median\ =\frac{0.855+0.865}{2}=0.86$ $\$

Mode: The value of the observation that appears most frequently.

$Mode\ =0.792$

Hence the mean, median, and mode of this data set are $0.86545,\ 0.86\ and\ 0.792$ respectively.

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