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# Statistics - Computing Price Index

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1. Suppose the following data are prices of market goods involved in household
transportation for the years 1994 through 2002. Using 1998 as a base year, compute
aggregate transportation price indexes for this data.

Year Items 1994 1995 1996 1997 1998 1999 2000 2001 2002
Gasoline (per gal.) 1.06 1.21 1.09 1.13 1.10 1.16 1.23 1.23 1.08
Oil (per qt.) 1.47 1.65 1.60 1.62 1.58 1.61 1.78 1.77 1.61
Transmission fluid(per qt.) 1.70 1.70 1.80 1.85 1.80 1.82 1.98 1.96 1.94
Radiator coolant (per gal.) 6.65 6.90 7.50 8.10 7.95 7.96 8.24 8.21 8.19.

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Solution:
Index Number of price for 1994 = ...

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## Median, Model, Numerical Measures

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17. A home theater in a box is the easiest and cheapest way to provide surround sound for a hoem entertainment center. A sample of prices is shown here (Consumer Reports Buying Guide,2004). The prices are for models with a DVD player and for models without a DVD player.
*Models with DVD Player *Price(\$)
Sony HT-1800DP 450
Pioneer HTD-330DV 300
Sony HT-C800DP 400
Panasonic SC-HT900 500
Panasonic SC-MTI 400

*Models without DVD player *Price(\$)
Pioneer HTP-230 300
Sony HT-DDW750 300
Kenwood HTB-306 360
RCA RT-2600 290
Kenwood HTB-206 300
a. Compute the mean price for models with a DVD player and the mean price for models without DVD player. What is the additional price paid to have a DVD player included in a home theater unit?
b. Compute the range, variance, and standard deviation for the two samples. What does this information tell you about the prices for models with and without a DVD player.
19. The Los Angeles Times regularly reports the air quality index for various areas of Southern California. A sample of air quality index values for Ponoma provided the following data: 28,42,58,48,45,55,60,49 and 50.
a. Compute the range and interquartile range.
b. Compute the sample variance and sample standard deviation.
c. A sample of air quality index radings for Anaheim provided a sample mean of 48.5, a sample variance of 136, and a sample standard deviation of 11.66. What comarions can you make between the air quality in Ponoma and that in Anaheim on the basis of these desciptove statistics?
21. How do grocery costs compare across the country? Using a market basket of 10 items including meat, milk, bread, eggs, coffee, potatoes, cereal and orange juice, Where to Retire magazine calculated the cost of the market basket in six cities and in six retirement areas across the country (Where to Retire magazine),November/December 2003). The data with market basket cost to the nearest dollars are as follows:

City Cost(\$) Retirement area Cost(\$)
Buffalo,NY 33 Biloxi-Gulfport,MS 29
Des Moines,IA 27 Asheville,NC 32
Hartford,CT 32 Flagstaff,AZ 32
Los Angeles,CA 38 Hilton Head,SC 34
Miami,FL 36 Fort Myers,FL 34
Pittburgh,PA 32 Santa Fe,MN 31
a. Compute the mean, variance and standard deviation for the sample of cities and the sample of retirement areas.
b. What observations can be made based on the two samples?

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