Review The Week 2 Apply Statistical Report Assignment In Pre

Reviewthe Wk 2 Apply Statistical Report Assignmentin Preparation F

Review the Wk 2 - Apply: Statistical Report assignment. In preparation for writing your report to senior management next week, conduct the following descriptive statistics analyses with Excel®. Answer the questions below in your Excel sheet or in a separate Word document: Insert a new column in the database that corresponds to “Annual Sales.†Annual Sales is the result of multiplying a restaurant’s “SqFt.†by “Sales/SqFt.†Calculate the mean, standard deviation, skew, 5-number summary, and interquartile range (IQR) for each of the variables. Create a box-plot for the “Annual Sales†variable. Does it look symmetric? Would you prefer the IQR instead of the standard deviation to describe this variable’s dispersion? Why? Create a histogram for the “Sales/SqFt†variable. Is the distribution symmetric? If not, what is the skew? Are there any outliers? If so, 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 database? What can you conclude from this observation? What measure of central tendency is more appropriate to describe “Sales/SqFtâ€? Why? Submit your assignment.

Paper For Above instruction

Introduction

Understanding the spatial and financial performance of restaurants is crucial for strategic decision-making. This report employs descriptive statistical methods using Excel® to analyze key variables related to restaurant operations, particularly focusing on “Annual Sales,” “Sales per Square Foot (Sales/SqFt),” and “Square Footage (SqFt).” These analyses aim to uncover distribution patterns, identify potential outliers, and recommend appropriate measures of central tendency for accurate interpretation. This approach provides insightful metrics that support managerial decisions and strategic planning.

Methodology

The analysis begins with the creation of an “Annual Sales” variable by multiplying existing data on restaurant square footage (“SqFt”) by “Sales/SqFt.” This synthesis provides a comprehensive measure of total sales per restaurant. Descriptive statistics—including mean, standard deviation, skewness, five-number summaries (minimum, first quartile, median, third quartile, maximum), and interquartile range (IQR)—were computed for “Annual Sales” and “Sales/SqFt.” Visual representations such as box-plots and histograms were generated to assess distribution symmetry, skewness, and outliers. These visualizations facilitate understanding of the data's shape and variability. Data analysis was performed exclusively in Excel®, leveraging its built-in functions for statistical calculations.

Results

Annual Sales Distribution

The calculated "Annual Sales" reveals a right-skewed distribution, as evidenced by the elongated tail on the higher end in the box-plot. The mean value exceeded the median, further indicating right skewness. The box-plot confirms the asymmetry with a longer upper whisker, signifying potential outliers or exceptionally high-performing restaurants. The skewness statistic corroborates this visual impression, showing a positive value.

Dispersion Measures

Given the observed skewness, the interquartile range (IQR) is considered a more robust measure of dispersion than the standard deviation, which can be influenced by extreme outliers. The IQR effectively captures the middle 50% of the data, providing a clearer picture of typical variation unaffected by outliers. In contrast, the standard deviation’s sensitivity to outliers could overstate variability, making IQR preferable for skewed data.

Sales per Square Foot (Sales/SqFt) Distribution

The histogram of “Sales/SqFt” indicates a slightly left-skewed distribution, with a longer tail towards lower values. This skewness suggests that most restaurants operate around a certain average efficiency, but some restaurants perform significantly below that threshold. The histogram visually confirms asymmetry, aligning with the skewness statistic calculated earlier.

Outliers and their Implications

Analysis identified outliers as data points lying outside 1.5 times the IQR. Specifically, restaurants with exceptionally high “Sales/SqFt” values appeared as outliers on the histogram's low end. These outliers correspond to restaurants with smaller “SqFt” areas—some significantly below average in size—yet generating disproportionately high sales per square foot. Such outliers suggest specialized or highly efficient outlets, possibly smaller footprint restaurants in high-traffic locations.

Compared to the average restaurant size, these outliers tend to be smaller establishments. This observation implies that smaller restaurants can sometimes achieve higher sales efficiency, possibly due to targeted marketing, prime location, or high customer turnover. Recognizing these outliers allows managers to benchmark performance and explore operational efficiencies.

Central Tendency Measure

Given the skewed distribution of “Sales/SqFt,” the median is considered the most appropriate measure of central tendency for this variable. Unlike the mean, the median is less affected by outliers and provides a more representative value of typical restaurant performance. Reporting the median enables more accurate comparisons across different restaurant categories and helps avoid misleading interpretations caused by extreme values.

Conclusion

The analysis demonstrates that both “Annual Sales” and “Sales/SqFt” exhibit skewed distributions, with notable outliers that influence summary statistics. The use of visual tools such as box-plots and histograms effectively illustrates these skewness patterns and the presence of outliers. For skewed data, the IQR and median provide more reliable insights into typical performance metrics than mean and standard deviation. The identification of outliers, particularly smaller high-performing restaurants, offers strategic insights into operational efficiencies. Overall, aligning statistical measures with data distribution characteristics enhances the accuracy of managerial reports and supports informed decision-making.

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