Background:
A retail company, XYZ Superstores, is analyzing its monthly sales performance across five branches over the past six months. The management is particularly interested in understanding sales trends, central tendencies, relationships between variables, and predictive modeling using statistics. The dataset includes monthly revenue (in R’000), customer footfall, and number of promotions offered per month for each branch.

Table: Monthly Revenue (in R’000) for Five Branches

Table: Customer Footfall and Promotions

XYZ Superstores wants to extract meaningful insights from this data to guide their marketing strategies and operational decisions.

Question 1 (20)

(Covers concepts from summary statistics chapter, including mean, median, mode, and standard deviation.)

Calculate the mean monthly revenue for Branch C and interpret the result. (3)
Determine the median revenue for Branch B over the six months and explain its significance  compared    to  the mean.   (4)
The mode is often useful in understanding business trends. Identify if a mode exists for Branch D’s revenue data.   Justify your    answer. (3)
Compute the range and standard deviation for Branch E’s revenue. Interpret what these measures  indicate    about   revenue fluctuations.   (6)
Discuss one advantage and one limitation of using the mean as a measure of central tendency in business decision-making.    (4)

Question 2 (15)

(Tests visual representation of data, including tables, histograms, and scatterplots.)

Construct a bar chart to visually compare the monthly revenue trends of all five branches.  (5)
Draw a scatterplot showing the relationship between customer footfall and revenue. Identify the type    of  correlation and interpret   its meaning.    (5)
Explain how a histogram could be used to analyze the frequency of different revenue levels for Branch A.    (5)

Question 3 (20)

(Assesses probability, confidence intervals, and inferential statistics concepts.)

Assume that the revenue for Branch C follows a normal distribution with a mean of R535,000 and a standard deviation of R15,000.

• What percentage of months had revenue above R550,000 based on the empirical rule? (4 marks)
• If the probability of revenue exceeding R550,000 is 0.20, calculate the Z-score and interpret the result. (4 marks)

The company wants to predict future customer footfall based on previous trends.

• Calculate the probability that a randomly chosen month had footfall exceeding 36,000 customers, assuming a normal distribution (mean = 36,000, standard deviation = 2,000). (4)
• Why is sampling important when making predictions for future months? (3)
• Discuss how confidence intervals could help XYZ Superstores estimate next month’s expected footfall with 95% certainty. (5)

Question 4 (15)

(Evaluates linear correlation and regression applications.)

Using the data on customer footfall and revenue, explain how correlation analysis can help  XYZ Superstores understand  sales   patterns.   (5)
Suppose a linear regression model is developed to predict revenue based on the number of promotions.

• Write the general form of a simple linear regression equation and explain its components. (4)
• How would you interpret a regression coefficient of 5000 in this model? (3)
• What limitations should XYZ Superstores consider when using regression analysis for decision-making? (3)

Answers to Above Questions on Statistics

Expert Answer: 1: In order to calculate the main monthly revenue for branch C, we need to add up all the figures from January to June, and divide it by 6 as it is for 6 months. It is performed as follows:
Brach C: 520+530+540+535+545+550/6
=536.67
This implies that Branch C is able to generate an average monthly revenue of R536670 during the 6 months period and this implies a strong and consistent performance as compared to other branches.

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