ANALYZING THE PRICE OF GASOLINE
The assignment this week presents a problem where the American Automobile Association (AA) generates a report on gasoline prices that it distributes to newspapers throughout the state. It further states that on February 18, 1999, the AAA called a random sample of fifty-one stations to determine that day’s price of unleaded gasoline. The following data (in dollars) was given in this report:
Table 1 - Prices of Unleaded Gasoline at 51 Stations
1.07 1.31 1.18 1.01 1.23 1.09 1.29 1.10 1.16 1.08
0.96 1.66 1.21 1.09 1.02 1.04 1.01 1.03 1.09 1.11
1.11 1.17 1.04 1.09 1.05 0.96 1.32 1.09 1.26 1.11
1.03 1.20 1.21 1.05 1.10 1.04 0.97 1.21 1.07 1.17
0.98 1.10 1.04 1.03 1.12 1.10 1.03 1.18 1.11 1.09
1.06
Create a data array with the gasoline price data
A data array is defined as “data that have been sorted in ascending or descending order” (Shannon, Groebner, Fry, & Smith, 2002, 72). The following section presents the data presented in Table 1 as a data array.
Data Array
0.96, 0.96, 0.97, 0.98, 1.01, 1.01, 1.02, 1.03, 1.03, 1.03, 1.03, 1.04, 1.04, 1.04, 1.04, 1.05, 1.05, 1.06, 1.07, 1.07, 1.08, 1.09, 1.09, 1.09, 1.09, 1.09, 1.09, 1.10, 1.10, 1.10, 1.10, 1.11, 1.11, 1.11, 1.11, 1.12, 1.16, 1.17, 1.17, 1.18, 1.18, 1.20, 1.21, 1.21, 1.21, 1.23, 1.26, 1.29, 1.31, 1.32, 1.66
Data Analysis
Given the data presented in the previous sections, the next few sections use two histograms to estimate the number of prices that are at least $1.15. The first histogram presents the data using five classes and the second uses fifteen.
Histogram #1
Data Used in Histogram #1 (5 classes)
Range 0.70
# of Classes 5
Class Width 0.1400
Bin # Classes Frequency Relative Frequency Cumulative Frequency Cumulative Relative Frequency
1 0.9600 < 1.1000 27 0.53 27 0.53
2 1.1000 < 1.2400 19 0.37 46 0.90
3 1.2400 < 1.3800 4 0.08 50 0.98
4 1.3800 < 1.5200 0 0.00 50 0.98
5 1.5200 < 1.6601 1 0.02 51 1.00
Histogram #1 (using 5 Classes)
Estimate of the Number of Prices that are at least $1.15
Using the histogram presented in the previous section, the estimate of the number of prices that are at least $1.15 is five. This is because the only values that can be counted fall into bins three, four, and five. Even though bin two may contain values that are above the $1.15 threshold, they can not be counted as they are not guaranteed to be above the stated value. Therefore the formula for the estimate is: Estimate = B3 + B4 + B5, where B3=4, B4=0 and B5=1.
Histogram #2
Data Used in Histogram #2 (15 classes)
Range 0.70
# of Classes 15
Class Width 0.0467
Bin # Classes Frequency Relative Frequency Cumulative Frequency Cumulative Relative Frequency
1 0.9600 < 1.0067 4 0.08 4 0.08
2 1.0067 < 1.0534 13 0.25 17 0.33
3 1.0534 < 1.1001 14 0.27 31 0.61
4 1.1001 < 1.1468 5 0.10 36 0.71
5 1.1468 < 1.1935 5 0.10 41 0.80
6 1.1935 < 1.2402 5 0.10 46 0.90
7 1.2402 < 1.2869 1 0.02 47 0.92
8 1.2869 < 1.3336 3 0.06 50 0.98
9 1.3336 < 1.3803 0 0.00 50 0.98
10 1.3803 < 1.4270 0 0.00 50 0.98
11 1.4270 < 1.4737 0 0.00 50 0.98
12 1.4737 < 1.5204 0 0.00 50 0.98
13 1.5204 < 1.5671 0 0.00 50 0.98
14 1.5671 < 1.6138 0 0.00 50 0.98
15 1.6138 < 1.6601 1 0.02 51 1.00
Histogram #2 (using 15 Classes)
Estimate of the Number of Prices that are at least $1.15
Using the histogram presented in the previous section, the estimate of the number of prices that are at least $1.
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0.000 7 63 106 55 74.7 1.245 9 70 135 90 98.3 1.638 11 85 135 70 96.8 1.613 [ IMAGE ] [ IMAGE ] Conclusion = = = =
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... middle of paper ... ... (1+1/5)5 = 1.25 = 2.4883 (1+1/10)10 = 1.110 = 2.5937 (1+1/100)100 =