Preparation For Writing Your Report To Senior Management

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?

Paper For Above instruction

The analysis of restaurant data through descriptive statistics provides valuable insights into the characteristics and variability within the dataset. The key variables in this context include “SqFt,” “Sales/SqFt,” and “Annual Sales,” which collectively help in understanding the operational scale, revenue generation, and outliers within the restaurant industry. Conducting comprehensive statistical analyses, such as calculating means, standard deviations, skewness, five-number summaries, and interquartile ranges (IQR), offers a nuanced view of the data distribution, spread, and potential anomalies.

Initially, creating a new column for “Annual Sales” by multiplying each restaurant’s “SqFt” by “Sales/SqFt” establishes a foundational metric for evaluating overall business performance. This calculation provides a direct measure of total revenue generated by each restaurant, integrating both size and sales efficiency. Once the “Annual Sales” data is computed, graphical representations such as box-plots are instrumental in visualizing distribution symmetry and identifying outliers. A box-plot reveals the median, quartiles, and potential outliers; if the plot appears symmetric, it suggests a normal distribution, whereas asymmetry indicates skewness. Understanding whether to utilize the interquartile range (IQR) or standard deviation for dispersion measurement depends on the distribution shape; typically, IQR is preferred for skewed data as it is robust against outliers.

For the variable “Sales/SqFt,” constructing a histogram displays the frequency distribution of sales per square foot across restaurants. Analyzing the histogram’s shape reveals whether the distribution is symmetric—suggesting a normal distribution—or skewed. In cases of skewness, the direction of skew indicates whether the tail is on the right (positive skew) or the left (negative skew). Outliers, evident as isolated bars or points distant from the central bulk, warrant further investigation of their “SqFt” values and how they compare to average restaurant sizes. Outliers with significantly larger “SqFt” may represent exceptionally large establishments, whereas smaller outliers could indicate compact or specialized eateries.

Evaluating outliers is essential because it influences the choice of measures of central tendency. For instance, in skewed distributions with extreme outliers, the median remains a more reliable indicator than the mean, which can be disproportionately affected by outliers. This is particularly relevant for “Sales/SqFt,” where a skewed distribution might suggest that reporting the median provides a more typical measure of sales efficiency across restaurants. Understanding the distribution shape and outliers informs strategic decisions, such as market segmentation, targeted marketing efforts, and resource allocation.

In summary, the descriptive statistics and visualizations of “Annual Sales” and “Sales/SqFt” reveal critical insights into the operational characteristics within the restaurant dataset. Recognizing skewness and outliers helps in selecting appropriate summary measures, with the median often being preferable for skewed and outlier-prone data. These analyses support data-driven decision-making and strategic planning to optimize restaurant performance.

References

• Andrew, A. (2019). Statistics for Business and Economics. Pearson.
• Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
• Montgomery, D. C., & Runger, G. C. (2014). Applied Statistics and Probability for Engineers. Wiley.
• Newbold, P., Carlson, W. L., & Thorne, B. (2013). Statistics for Business and Economics. Pearson.
• Ott, R. L., & Longnecker, M. (2015). An Introduction to Statistical Methods and Data Analysis. Brooks/Cole.
• Rumsey, D. J. (2016). Statistics for Dummies. John Wiley & Sons.
• Wasserman, L. (2013). All of Statistics: A Concise Course in Statistical Inference. Springer.
• Everitt, B. (2012). The Cambridge Dictionary of Statistics. Cambridge University Press.
• McClave, J. T., & Sincich, T. (2018). Statistics. Pearson.
• Conover, W. J. (1999). Practical Nonparametric Statistics. Wiley.