Below are two data sets, one for the average retail price of gasoline in the State of California for each month in 2005, and the other for the average retail price of gasoline in the State of Texas for each month in 2005.This data is from the U.S. Department of Energy (units are dollars per gallon). California Texas Calif. + 3 Jan 2.016 1.773 Feb 2.163 1.841 Mar 2.346 2.008 Apr 2.596 2.169 May 2.52 2.088 Jun 2.41 2.101 Jul 2.559 2.227 Aug 2.721 2.446 Sept 3.032 2.843 Oct 2.926 2.72 Nov 2.57 2.204 Dec 2.319 2.161 SUM MEAN STDEV MEDIAN RANGE 1. Compare the sum, the mean, the standard deviation, the median, and the range of DATA SET B and DATA SET D. What happened to these summary statistics when you added 3 to each observation from the California data set? 2. In general, what happens to the the mean, the median, the standard deviation, and the range of a data set when a constant value is added to each value of any data set? Explain your reasoning. 3. Based on your graph, did the gas prices for the last few months of the year for both states appear to be increasing or decreasing? Explain your reasonig.
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.
Below are two data sets, one for the average retail price of gasoline in the State of California for each month in 2005, and the other for the average retail price of gasoline in the State of Texas for each month in 2005.This data is from the U.S. Department of Energy (units are dollars per gallon).
| California | Texas | Calif. + 3 | |
| Jan | 2.016 | 1.773 | |
| Feb | 2.163 | 1.841 | |
| Mar | 2.346 | 2.008 | |
| Apr | 2.596 | 2.169 | |
| May | 2.52 | 2.088 | |
| Jun | 2.41 | 2.101 | |
| Jul | 2.559 | 2.227 | |
| Aug | 2.721 | 2.446 | |
| Sept | 3.032 | 2.843 | |
| Oct | 2.926 | 2.72 | |
| Nov | 2.57 | 2.204 | |
| Dec | 2.319 | 2.161 | |
| SUM | |||
| MEAN | |||
| STDEV | |||
1. Compare the sum, the mean, the standard deviation, the median, and the range of DATA SET B and DATA SET D. What happened to these summary statistics when you added 3 to each observation from the California data set?
2. In general, what happens to the the mean, the median, the standard deviation, and the range of a data set when a constant value is added to each value of any data set? Explain your reasoning.
3. Based on your graph, did the gas prices for the last few months of the year for both states appear to be increasing or decreasing? Explain your reasonig.
4. Do the file conatining your data, calculations, and your grapgh.
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