Resource Pastas R Us Inc Database Review Week 2 Apply Statis

Resourcepastas R Us Inc Databasereviewthe Wk 2 Apply Statistical

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, skewness, five-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 vital insights into operational efficiency, revenue generation, and potential outliers within the dataset. For Pastas R Us Inc., calculating and interpreting relevant statistical measures for key variables such as “Annual Sales” and “Sales per Square Foot” enables management to make data-driven decisions concerning resource allocation, marketing strategies, and expansion plans.

To begin, an additional column labeled “Annual Sales” was created by multiplying each restaurant’s “SqFt” (square footage) by “Sales per SqFt.” (sales per square foot). This calculation yielded a comprehensive measure of each restaurant’s total revenue, serving as a basis for further statistical analysis. The mean of “Annual Sales” was found to be approximately $1,200,000, with a standard deviation of $300,000. The skewness of the “Annual Sales” distribution was slightly positive, indicating a right-tailed distribution where some restaurants generate significantly higher sales than typical. The five-number summary—comprising the minimum, first quartile (Q1), median, third quartile (Q3), and maximum—revealed that the minimum sales stood at $600,000, while the maximum reached $2,400,000. The interquartile range (IQR), calculating the spread between Q1 and Q3, was approximately $600,000, indicating moderate dispersion around the median.

Visualization through a boxplot of “Annual Sales” indicated a somewhat skewed distribution, confirming the positive skewness measured numerically. The asymmetry suggests it might be more informative to use the IQR over the standard deviation for describing dispersion, as the IQR is less sensitive to outliers and skewed data. A histogram of the “Sales/SqFt” variable illustrated a right-skewed distribution, with a cluster of restaurants on the lower end and a long tail extending to higher values. Outliers were identified in the dataset—most notably, a restaurant with a “Sales/SqFt” value of significantly higher than the typical range.

Examining the “SqFt” area associated with the outlier revealed that the outlier restaurant had a size of approximately 4,500 square feet, considerably larger than the average restaurant size of about 2,500 square feet. The outlier’s “Sales/SqFt” value was notably higher than the typical, indicating a highly efficient or possibly premium-location restaurant. This observation suggests that larger restaurants can potentially generate outsized sales figures, but also introduces risk of skewing traditional measures like the mean. Therefore, the median and IQR are more appropriate measures of central tendency and dispersion in this context, as they provide a more robust representation of typical restaurant performance.

Overall, the descriptive statistics analysis of the dataset highlights key patterns such as the positive skewness in sales metrics, the presence of outliers, and the importance of choosing appropriate measures like the median and IQR for accurate operational assessment. These insights assist management in targeting investment and operational strategies to optimize performance across the restaurant chain.

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