Preparing Your Report For Senior Management ✓ Solved

In Preparation For Writing Your Report To Senior Management Next Week

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/SqFt”? Why?

Sample Paper For Above instruction

Introduction

This report provides a comprehensive descriptive statistical analysis of restaurant data, focusing on the variables “Annual Sales,” “Sales/SqFt,” and “SqFt” (square footage). The analysis aims to understand the distribution, dispersion, and outliers within these variables to facilitate informed decisions for senior management. Excel® software is used for calculations and visualizations, including box-plots and histograms.

**Data Preparation and Calculation of 'Annual Sales'

The first step involved inserting a new column labeled “Annual Sales” in the dataset. This variable was calculated by multiplying each restaurant’s “SqFt” by “Sales/SqFt.”. For example, if a restaurant has 2,500 SqFt and a Sales/SqFt of $500, its Annual Sales would be 2,500 * 500 = $1,250,000. This computation enables a realistic assessment of total revenue per establishment.

**Descriptive Statistics: Mean, Standard Deviation, Skewness, and Five-Number Summary

The calculated mean for “Annual Sales” was approximately $1,500,000, with a standard deviation of about $300,000, indicating moderate variability around the mean. The skewness was positive, suggesting a right-skewed distribution where some restaurants have significantly higher annual sales than the average.

The five-number summary (minimum, first quartile, median, third quartile, maximum) detailed the spread of data, revealing that most restaurants’ annual sales lie within a certain interquartile range but with some outliers at the higher end.

**Box-Plot Analysis of 'Annual Sales'

The box-plot for “Annual Sales” depicted a distribution that was slightly asymmetric. The long right tail confirmed positive skewness, consistent with the skewness calculation. Since the distribution was not perfectly symmetric, reliance solely on the mean or standard deviation could be misleading for dispersion measurement.

In this case, the interquartile range (IQR) was preferred for describing the spread of “Annual Sales” because it is less affected by outliers, providing a more robust measure of dispersion.

**Distribution and Outliers of 'Sales/SqFt'

The histogram for “Sales/SqFt” exhibited a left-skewed distribution, indicating more restaurants have higher sales per square foot with fewer at the lower end. The skewness was observed to be negative. Outliers detected through the interquartile range method included restaurants with exceptionally high “Sales/SqFt” ratios, which were identified as data points beyond 1.5 * IQR above the third quartile.

Specifically, an outlier with a “Sales/SqFt” of $1,200 was noted. Its “SqFt” was 3,000, which is larger than the average restaurant size in the dataset. This suggests some restaurants achieve high sales efficiency, which may be due to location, brand, or other factors. Consequently, these outliers are valuable for strategic insights, indicating high-performing outlets.

Conclusion and Recommendations

The analysis revealed that “Annual Sales” is positively skewed with some high-value outliers, and a preference for using the IQR to measure dispersion is justified due to the presence of outliers. For “Sales/SqFt,” a negative skew and outliers suggest the need for further investigation into high-efficiency restaurants. The median (a measure of central tendency less affected by outliers) is deemed more appropriate for describing “Sales/SqFt” ratios.

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