Assignment Content Resource Pastas R Us Inc Database Review ✓ Solved

Assignment Contentresourcepastas R Us Inc Databasereviewthe Wk 2

Resource: Pastas R Us, Inc. Database 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?

Sample Paper For Above instruction

Introduction

This report provides a comprehensive statistical analysis of data from Pastas R Us, Inc., focusing on restaurant size and sales performance. Descriptive statistics like mean, standard deviation, skewness, and the interquartile range are utilized to understand the distribution and dispersion of key variables such as Square Footage (SqFt.), Sales per Square Foot (Sales/SqFt), and Annual Sales. Through graphical representations including box plots and histograms, the analysis aims to assess symmetry, identify outliers, and determine appropriate measures of central tendency for these variables, ultimately supporting managerial decision-making.

Data Preparation and Calculation of Annual Sales

To initiate the analysis, a new column named "Annual Sales" was inserted into the database, calculated by multiplying each restaurant's SqFt. by its Sales/SqFt. This metric provides an estimation of total annual revenue per restaurant, serving as a key indicator of financial performance. The formula used is:

Annual Sales = SqFt. x Sales/SqFt

This calculated variable forms the basis for subsequent descriptive statistical analysis, offering insights into the overall sales distribution across the restaurant chain.

Descriptive Statistics Analysis

1. Measures of Central Tendency and Dispersion for Each Variable

For each variable (SqFt, Sales/SqFt, and Annual Sales), the mean, standard deviation, skewness, and five-number summary (minimum, first quartile, median, third quartile, maximum) were computed using Excel. The interquartile range (IQR) was also calculated as Q3 - Q1 to assess data dispersion without the influence of outliers.

2. Box Plot for Annual Sales

A box plot was constructed to visualize the distribution of Annual Sales, highlighting median, quartiles, and potential outliers. The box plot indicates whether the distribution appears symmetric or skewed and helps identify outliers—data points that fall outside 1.5 times the IQR from the quartiles.

3. Analysis of Symmetry and Dispersion

The box plot for Annual Sales revealed a slight right skewness, indicating the tail extends more toward higher sales figures. The comparison of the standard deviation and IQR showed that IQR may be preferable for dispersion measurement if outliers are present, as it minimizes their impact.

4. Histogram of Sales per Square Foot

The histogram for Sales/SqFt demonstrated a left-skewed distribution, suggesting that most restaurants perform around a central value with a tail extending toward lower sales per square foot. There was at least one apparent outlier on the lower end of the distribution.

5. Outliers and Their Characteristics

Outliers were identified as data points lying outside 1.5 times the IQR. The outlier with the lowest Sales/SqFt had a Square Footage (SqFt) larger than the mean SqFt of the database, indicating a large restaurant with unusually low sales efficiency. This outlier's SqFt was significantly higher than the average restaurant's size, suggesting potential operational inefficiencies or unique circumstances such as catering or banquet facilities.

6. Central Tendency and Conclusion

Given the skewness observed, the median is a more appropriate measure of central tendency than the mean for Sales/SqFt, as it better represents the typical value unaffected by outliers. For Annual Sales, considering potential outliers and skewness, median and IQR are preferable measures when describing typical performance and variability.

Conclusion

The statistical analysis of the database highlights the importance of selecting appropriate measures for understanding restaurant performance. The presence of outliers, skewed distributions, and varying dispersion measures underscore the need for careful interpretation of sales data. Applying the median and IQR provides robust insights, aiding managerial decision-making regarding operational efficiency and resource allocation.

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