Concept explainers
a.
Find the population standard deviation for 2012.
a.
Answer to Problem 36E
- The population standard deviation for 2012 is 96.23.
Explanation of Solution
Calculation:
The price of single family homes in United States for the first quarter of 2012 and 2013 are given.
Standard deviation:
Let
Population standard deviation:
Finding mean:
Software procedure:
Step-by-step procedure to find mean using the MINITAB software:
- Choose Stat > Basic Statistics > Display
Descriptive Statistics . - In Variables enter the columns 2012.
- Choose option statistics, and select Mean.
- Click OK.
Output using the MINITAB software is given below:
- From the MINITAB output the mean is 201.8.
The deviation, deviation’s squares are calculated below:
x | ||
87.8 | –114 | 12,996 |
218.1 | 16.3 | 265.69 |
311.5 | 109.7 | 12,034.09 |
157.2 | –44.6 | 1,989.16 |
112.5 | –89.3 | 7,974.49 |
84.9 | –116.9 | 13,665.61 |
148.2 | –53.6 | 2,872.96 |
226.4 | 24.6 | 605.16 |
152.1 | –49.7 | 2,470.09 |
122.1 | –79.7 | 6,352.09 |
182 | –19.8 | 392.04 |
147.3 | –54.5 | 2,970.25 |
363.8 | 162 | 26,244 |
193.5 | –8.3 | 68.89 |
129.9 | –71.9 | 5,169.61 |
208.6 | 6.8 | 46.24 |
174.3 | –27.5 | 756.25 |
103.7 | –98.1 | 9,623.61 |
359.5 | 157.7 | 24,869.29 |
448 | 246.2 | 60,614.44 |
265.4 | 63.6 | 4,044.96 |
131.9 | –69.9 | 4,886.01 |
311.6 | 109.8 | 12,056.04 |
Total |
Substituting
- Hence, the population standard deviation for 2012 is 96.23.
b.
Find the population standard deviation for 2013.
b.
Answer to Problem 36E
- The population standard deviation for 2013 is 115.99.
Explanation of Solution
Calculation:
Population standard deviation:
Finding mean:
Software procedure:
Step-by-step procedure to find mean using the MINITAB software:
- Choose Stat > Basic Statistics > Display Descriptive Statistics.
- In Variables enter the columns 2013.
- Choose option statistics, and select Mean.
- Click OK.
Output using the MINITAB software is given below:
- From the MINITAB output the mean is 230.6.
The deviation, deviation’s squares are calculated below:
x | ||
115.1 | –115.5 | 13,340.25 |
226.5 | –4.1 | 16.81 |
332.2 | 101.6 | 10,322.56 |
159.4 | –71.2 | 5,069.44 |
121 | –109.6 | 12,012.16 |
101 | –129.6 | 16,796.16 |
160.4 | –70.2 | 4,928.04 |
261.2 | 30.6 | 936.36 |
163.7 | –66.9 | 4,475.61 |
155.1 | –75.5 | 5,700.25 |
219.9 | –10.7 | 114.49 |
170.6 | –60 | 3,600 |
368.2 | 137.6 | 18,933.76 |
197.7 | –32.9 | 1,082.41 |
169 | –61.6 | 3,794.56 |
246.5 | 15.9 | 252.81 |
216.7 | –13.9 | 193.21 |
111 | –119.6 | 14,304.16 |
412.3 | 181.7 | 33,014.89 |
593.9 | 363.3 | 131,986.9 |
312.6 | 82 | 6,724 |
141.8 | –88.8 | 7,885.44 |
348.7 | 118.1 | 13,947.61 |
Total |
Substituting
- Hence, the population standard deviation for 2013 is 115.99.
c.
Explain whether the spread in house price has increased or not.
c.
Answer to Problem 36E
- The spreads in house price for 2012 has increased in 2013.
Explanation of Solution
- The house price has increased from 2012 to 2013.
- From part (a), the population standard deviation for 2012 is 96.23.
- From part (b), the population standard deviation for 2013 is 115.99.
- The standard deviation for 2012 is less than the population standard deviation of 2013.
- Thus, it can be concluded that the spreads in house price for 2012 has increased in 2013.
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Chapter 3 Solutions
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