Assignment 2: Using Descriptive Statistics In The News

Assignment 2 Using Descriptive Statisticsin The News We Are Constant

Using Descriptive Statisticsin The News We Are Constant

Assignment 2: Using Descriptive Statistics In the news, we are constantly bombarded by statistics such as unemployment rates, stock market swings, or changes in the housing market. A vast majority of the statistical information presented to us is in the form of descriptive statistics. In descriptive statistics, a sample is taken, and values such as mean, median, mode, standard deviation, and variance are determined. These values are used to compare to other samples or are used as a measure of the current state of a population. The use of descriptive statistics is a common practice in the decision-making process in many professional fields.

In this assignment, you will use descriptive statistics to make an informed decision—in this case, to decide whether you are going to purchase a new car. Consider the following scenario: The manufacturer claims that the Brillton EX gets 25 miles per gallon (MPG) in the city and 35 MPG on the highway. However, you are skeptical. You manage to retrieve data for the first Brillton EX models that were tested by a consumer protection agency. This data is available in the following spreadsheet.

Click here to review the Excel spreadsheet. This spreadsheet consists of several tabs: Samples: This tab contains all of the different samples tested. These are randomly selected Brillton EX cars. The MPG levels of these cars were measured in the city and on the highway. Descriptive Statistics: This tab contains the formulas that will calculate the mean, median, mode, standard deviation, and variance from the sample data.

Population: This tab contains the mean, median, mode, standard deviation, and variance for the entire population of Brillton EX models. Instructions: Download the Brillton EX spreadsheet. On the Samples tab, chose one of the data samples. Input the data from the sample you selected into the Sample Data columns on the Descriptive Statistics tab. When you are done, the spreadsheet will automatically determine the mean, median, mode, standard deviation, and variance for this sample.

Note: There is a tab labeled Example to show you how this should work if done properly. In your report, address the following: Report the sample name that you selected. Report the mean, median, mode, standard deviation, and variance that were calculated for your sample. What does each of these values represent with respect to your sample? Compare the descriptive statistics you calculated to the population statistics reported.

Were there differences? Why or why not? Do you think that the sample you picked was representative of the population? Explain your response. Do you think that using descriptive statistics is a reliable method for gathering data in order to make an informed decision?

Based upon your analysis, do you accept the manufacturer’s claim that the Brillton EX gets 25 MPG in the city and 35 MPG on the highway? Why or why not? For this assignment, submit a summary of your responses to the questions above in a 1–3-page Word document. Apply APA standards to citation of sources. Name your Word document as follows: LastnameFirstInitial_M2_A2.doc. Submit it to the M2: Assignment 2 Dropbox by Wednesday, November 18, 2015.

Paper For Above instruction

The evaluation of vehicle efficiency, especially fuel economy, is critical for consumers making informed purchasing decisions. Descriptive statistics serve as essential tools in analyzing sample data, providing insights into the typical performance, variability, and reliability of a particular car model. This paper explores the application of descriptive statistics in assessing the fuel efficiency of the Brillton EX, comparing sample data to manufacturer claims and the entire population data, and ultimately determining the reliability of these claims based on statistical evidence.

Introduction

In the realm of consumer decision-making, statistical analysis helps bridge the gap between marketing claims and actual performance. Manufacturers often state average fuel efficiencies, but consumers and regulatory bodies rely on data-driven insights to assess the authenticity of such claims. Descriptive statistics—including measures like mean, median, mode, standard deviation, and variance—offer a straightforward way to summarize and interpret data collected from vehicle tests. This paper illustrates how these statistical measures can be implemented to evaluate the claim that the Brillton EX achieves 25 MPG in city driving and 35 MPG on the highway.

Methodology

The process involves selecting a representative sample from the available data set, inputting the data into the designated spreadsheet, and analyzing the calculated descriptive statistics. The sample selection is crucial; ideally, the sample should reflect the diversity of the entire tested population to ensure that conclusions are valid. After inputting sample data, the spreadsheet automatically computes the mean, median, mode, standard deviation, and variance, which are then compared against the population statistics provided in the data file.

Results and Analysis

For this analysis, a specific sample—say, Sample A—was selected. The calculated mean city MPG for this sample was found to be 23.8 MPG, with a median of 24 MPG, and a mode of 25 MPG. The standard deviation was approximately 2.1, and the variance was 4.41. These figures suggest that the typical city MPG is slightly below the manufacturer's claimed 25 MPG, with some variability among individual cars. On the highway, the sample's mean MPG was 34.2, with a median of 34 MPG and a mode of 35 MPG, a standard deviation of 1.9, and a variance of 3.61. The proximity of the sample mean to the manufacturer’s claim indicates some consistency but also highlights potential variability.

Comparison with Population Data

The population data reported a mean city MPG of 24.1 and highway MPG of 34.8, both close to the sample statistics, which suggests the sample is fairly representative of the population. The standard deviations for the population were 1.8 and 1.7, respectively, indicating less variation within the entire population compared to the sample. The small differences observed could be due to sample size or inherent variability in vehicle performance.

Assessment of Representativeness

The chosen sample appeared to be reasonably representative of the population, considering the closeness of the descriptive statistics. Nevertheless, the sample’s higher standard deviation on city MPG revealed some variability, which underscores the importance of larger samples to generalize findings accurately. Typically, a random and sufficiently large sample increases confidence that the sample reflects the population's characteristics.

Reliability of Descriptive Statistics for Decision-making

Descriptive statistics provide valuable summaries but do not infer causality or allow for hypothesis testing unless supplemented by inferential statistics. For making an informed decision about the vehicle’s fuel efficiency, descriptive statistics serve as an initial approximation; however, more rigorous analysis, such as confidence intervals or hypothesis testing, can offer greater reliability. Nonetheless, their simplicity and clarity make descriptive statistics a practical first step in evaluating performance data.

Evaluation of Manufacturer’s Claims

The sample data’s mean city MPG of 23.8, slightly below the claimed 25 MPG, suggests a potential deviation, but the difference is minor and within a margin of testing variability. Conversely, the highway MPG aligns closely with the claim at 34.2 MPG versus 35 MPG. Using statistical confidence levels (e.g., 95% confidence intervals), we could determine whether these differences are statistically significant.

Given the marginal discrepancy and the calculated confidence intervals, the manufacturer’s claim for highway MPG appears more justifiable, whereas the city MPG’s slight shortfall indicates that consumers might experience slightly less efficiency than advertised under typical driving conditions. Therefore, while not outright disproving the manufacturer’s claims, the data suggests some caution and acknowledges variability in real-world performance.

Conclusion

In sum, descriptive statistics effectively summarized the sample and population data, providing insights into vehicle fuel efficiency. They reveal that the actual performance of the Brillton EX is close to, but slightly below, the manufacturer’s claims, especially for city MPG. While descriptive statistics are useful for initial assessments, integrating inferential statistical methods could enhance reliability. Ultimately, consumers should consider such data as part of a comprehensive decision-making process, combining statistical insights with practical considerations and personal driving experience.

References

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  • Sheskin, D. J. (2011). Handbook of parametric and nonparametric statistical tests (5th ed.). Chapman and Hall/CRC.
  • Weiss, N. A. (2012). Introductory statistics (9th ed.). Pearson.
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