Thursday, October 24, 2019
Price of Gasoline :: essays research papers
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 â€Å"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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