Preparation Review: The Week 2 Summative Assessment Pastas R ✓ Solved

Preparationreview The Wk 2 Summative Assessment Pastas R Us Statistic

Review the Wk 2 Summative Assessment: Pastas R Us Statistical Report assessment. Download the Pastas R Us data file. Complete the following on the Data tab of the Pastas R Us data file: Calculate “Annual Sales” for each restaurant. Annual Sales is the result of multiplying a restaurant’s “SqFt.” by “Sales/SqFt.” The first value has been provided for you. Calculate the mean, standard deviation, skew, 5-number summary, and interquartile range (IQR) for each of the variables.

The formulas and the first results have been provided for you. Create a boxplot (sometimes referred to as a box and whisker chart) for the “Annual Sales” variable. Create a histogram for the “Sales/SqFt” variable. Respond to the following questions on the Questions tab of the Pastas R Us data file: Does the annual sales boxplot look symmetric? Would you prefer the IQR instead of the standard deviation to describe the dispersion of the annual sales variable?

If so, why? Does the histogram show that the sales per square foot distribution is symmetric? If the sales per square foot distribution is not symmetric, what is the skew? If there are any outliers, which one(s)? What is the “SqFt” area of the outlier(s)? Is the outlier(s) smaller or larger than the average restaurant in the data? What can you conclude from this observation? What measure of central tendency may be more appropriate to describe “Sales/SqFt”? Why?

Sample Paper For Above instruction

The Pastas R Us dataset provides valuable insights into the financial and operational structure of various restaurant locations. Analyzing this data through descriptive statistics and visualizations allows us to better understand the distribution, variability, and potential outliers within the dataset.

Calculation of Annual Sales

The first step involves calculating the “Annual Sales” for each restaurant. This metric is derived by multiplying the restaurant's “Square Footage (SqFt.)” by its “Sales per Square Foot (Sales/SqFt).” This simple calculation ties the restaurant's physical size directly to its sales performance, offering an integrated metric for comparison. For instance, if a restaurant has a size of 2,000 square feet and generates $300 sales per square foot, its annual sales would amount to $600,000. The initial value has already been provided, ensuring consistency across calculations.

Descriptive Statistics

Once the “Annual Sales” are computed, the next step is to calculate essential descriptive statistics for all key variables including “SqFt,” “Sales/SqFt,” and “Annual Sales.” These include the mean, standard deviation, skewness, the five-number summary (minimum, first quartile, median, third quartile, maximum), and the interquartile range (IQR). These measures provide valuable insights into the central tendency, variability, and distribution shape of each variable.

Visual Data Analysis

Visualizations such as boxplots and histograms enhance our understanding of the data’s distribution. Creating a boxplot for “Annual Sales” helps assess its symmetry and identify any outliers. The boxplot’s shape—whether symmetric or skewed—can influence the choice of summary statistics, for example, favoring median and IQR over mean and standard deviation if skewness is present.

Similarly, creating a histogram for “Sales/SqFt” illuminates the distribution of sales efficiency across the restaurants. The shape of the histogram, whether symmetric or skewed, indicates the nature of variability among restaurants’ sales relative to their size. Outliers—indicated by isolated points beyond the whiskers—are particularly noteworthy. Examining their “SqFt” area provides context: are these outliers smaller or larger than the typical restaurant? This observation can reveal whether underperforming or overperforming establishments disproportionately affect the data analysis.

Interpretation and Conclusions

If the boxplot of annual sales appears skewed, using the interquartile range (IQR) might be preferable over the standard deviation to describe dispersion, since IQR is less affected by outliers. The histogram's shape also informs about symmetry; a right-skewed distribution suggests the presence of high outliers or overperformers, while a left-skew indicates underperformers.

Recognizing outliers is crucial for business analysis. Outliers with larger “SqFt” compared to the average might indicate new or expanding locations, whereas smaller outliers could be underperforming or smaller establishments.

In conclusion, in datasets with significant skewness and outliers, median and IQR often serve as more robust measures of central tendency and dispersion, respectively, than mean and standard deviation. These insights guide operational and strategic decisions—whether optimizing existing locations, planning new ventures, or targeted interventions.

References

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