Gasoline Price Analysis: Mean, Confidence Intervals & Trends

AAA Gasoline Price Report 1 AAA Gasoline Price Report Andree Redekosky Cal State University Fullerton ISDS 361A Business Analytics 1 Panos Skordi 11/20/2022

AAA Gasoline Price Report 2 Introduction and Problem Background In statistics we have many methods on finding data that can be used to analyze and react to what we discover. We can find the mean, median and mode to help develop a better understanding of the data we collect. To find the mean we must first gather all of the numerical values we have and divide it by the number of numerical values that are present. The median is simply the value that is in the middle of the list of the numerical values when it goes from smallest to largest value. Lastly to find the mode we must find which numerical value is occurring the most. In order to get the best analysis of our data there are other methods to finding what we want to know. Box plots and lower and upper limits are crucial to analyzing data in the best and most accurate ways possible. Box plots are graphs that demonstrate spread and skewness and the groups within the graphs through quartiles of the plot. Within the box plot, we can find the lower limit as well as the upper limit. The lower limit is the lowest possible value within the box plot and the upper limit is the highest possible value. In the box plot there are outliers as well so we can analyze our data efficiently. Using confidence intervals are another way we can analyze data properly and accurately. A confidence interval is a range of numerical vales that we have collected and are then put into a range of a parameter. In confidence intervals we mostly use the 95% confidence interval. But there are some cases that we use other intervals such as 99%. Because of the information we have here, we can now use these methods on the following problem. AAA has reported that the average price of gasoline in the state of Pennsylvania on Memorial Day was $2.65 per gallon. AAA has then gathered prices of 15 randomly selected gas stations in that state. We must calculate the mean, lower and upper limits, and create a 95% confidence interval with that data given.

AAA Gasoline Price Report 3 Data Description As we gather our data and use our methods to calculate our solutions, the data in the graph below will say what each one is. The mean is the average of our numerical values, so $2.64 (2.6413) is the average price of gas in the random sample of 15 gas stations on that specific day. Box Plot As we can see on the box plot that we created, the skewness of the data is to the left. Since it is to the left, we can confer the data is mostly on the right side of the median. When we look closely to the graph, we see most of the numerical values are well within the range and are near the median of the data. Once we plug in our values to create the box plot, we can now move on to calculating the Lower and Upper limits. To calculate these limits the calculation is as followed. Lower Limit = Q1-1.5*(Q3-Q1) = 2.585-1.5*(2.72-2.585) = 2.3825. Upper Limit = Q3+1.5*(Q3-Q1) = 2.72+1.5*(2.72-2.585) = 2.9225 .

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AAA Gasoline Price Report 4 Now that we found our lower and upper limits, anything outside of the two are now considered outliers. Since we can see that none of our numerical values fall outside of the plot and there are no outliers, we can confer the gas prices given are accepted. Confidence Interval To find the confidence interval at 95% confidence, we must know the normal standard distribution. The distribution at a 95% confidence interval has to lie between -1.96 and 1.96. To find the interval the following calculation using the t test must take place: CI = 2.6413±1.96*0.0870/sqrt(15), =2.6413±1.96*0.0870/3.8730 = CI= 2.6413±0.482 Similarities and Differences The difference of the box plot and the confidence interval is that we can see in the box plot where most of the values are being placed and where they are skewed to. We can see in the box plot where all values can be shown and as well as the outliers. As for the CI we can see where the values are at 95% of the time. The similarity of the two show if the sample means are shown in between the two points. Conclusion and Results In conclusion we can see that the results from the sample validate AAA’s findings that the average price of gasoline was $2.65. With the mean being $2.64, the CI and the box plot can both confer it is within range of 95% and will not go lower than them.

AAA Gasoline Price Report 5

AAA Gasoline Price Report

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