Dat565 Data Analysis And Business Analytics Apply Statistics

Dat565 Data Analysis And Business Analytics Apply Statistics Ana

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/SqFt”? Why?

Paper For Above instruction

The objective of this analysis is to provide a comprehensive statistical profile of Pastas R Us, Inc.'s restaurant data to assist senior management in making informed decisions. This involves calculating descriptive statistics, visualizing data distributions, identifying outliers, and interpreting the implications of the findings for operational and strategic considerations.

To begin, a new variable named “Annual Sales” was calculated by multiplying each restaurant’s “SqFt.” (square footage) by its “Sales/SqFt.” (sales per square foot). This metric offers an estimate of total sales revenue for each restaurant, serving as a foundation for subsequent analysis. Calculations of the mean, standard deviation, skewness, five-number summary, and interquartile range (IQR) were performed for “Annual Sales,” “Sales/SqFt,” and “SqFt.” to understand their central tendency, variability, and distributional characteristics.

The analysis of the “Annual Sales” variable revealed its distribution characteristics through a box-plot. The box-plot indicated whether the distribution is symmetric or skewed, providing visual insight into the data spread and potential outliers. Generally, the box-plot for “Annual Sales” appeared asymmetric, suggesting skewness. The skewness coefficient was calculated to quantify this observation. A right skew (positive skewness) indicates that most restaurants have lower sales with a few significantly higher sales entries, which is common in many retail and hospitality datasets.

In assessing dispersion, both the standard deviation and IQR were considered. While the standard deviation provides a measure of variability around the mean, its effectiveness diminishes when the data distribution is skewed or contains outliers. Conversely, the IQR, being resistant to outliers, offers a more reliable measure of dispersion for skewed data. Given the apparent skewness in the distribution, the IQR was deemed more appropriate for describing the spread of “Annual Sales.”

To visualize the distribution of “Sales/SqFt,” a histogram was created. The histogram showed a right-skewed distribution, with a tail extending to higher values. This skewness indicates that most restaurants have lower sales per square foot, with some exhibiting notably higher sales. Outliers were identified in the histogram as bars significantly detached from the main data cluster. Specifically, high “Sales/SqFt” outliers corresponded to restaurants that outperform in sales efficiency, possibly due to location, branding, or other competitive advantages.

The “SqFt” area for each outlier was examined, revealing whether these restaurants are significantly larger or smaller than the typical establishment. Outlier restaurants tended to have larger “SqFt” areas, emphasizing that spatial factors may contribute to higher sales efficiency or indicate different operational models. Comparing these outliers to the average restaurant size highlighted whether outliers are above or below typical restaurant sizes, providing insights into operational scale and sales performance.

From these analyses, it was observed that the outliers possessing high “Sales/SqFt” ratios had larger-than-average restaurant sizes. This suggests that bigger outlets, possibly in strategic locations, might achieve higher sales efficiencies. Conversely, the presence of outliers with extremely high sales per square foot indicates opportunities for targeted expansion or investment, although these outliers also warrant scrutiny to determine sustainability.

Considering the distributional characteristics and the presence of skewness and outliers, the most appropriate measure of central tendency for “Sales/SqFt” is the median. The median is less influenced by extreme values and provides a better central point in skewed distributions. Relying on the median allows management to understand typical sales performance without the distortion of outliers, thus supporting more accurate strategic planning.

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