Math Problem Solver

Question 1 (20)

(Covers concepts from summary statistics chapter, including mean, median, mode, and

standard deviation.)

1.1 Calculate the mean monthly revenue for Branch C and interpret the result. (3)

1.2 Determine the median revenue for Branch B over the six months and explain its

significance compared to the mean. (4)

1.3 The mode is often useful in understanding business trends. Identify if a mode exists for

Branch D’s revenue data. Justify your answer. (3)

1.4 Compute the range and standard deviation for Branch E’s revenue. Interpret what these

measures indicate about revenue fluctuations. (6)

1.5 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.)

2.1 Construct a bar chart to visually compare the monthly revenue trends of all five

branches. (5)

2.2 Draw a scatterplot showing the relationship between customer footfall and revenue.

Identify the type of correlation and interpret its meaning. (5)

2.3 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.)

3.1 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)

3.2 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.)

4.1 Using the data on customer footfall and revenue, explain how correlation analysis can

help XYZ Superstores understand sales patterns. (5)

4.2 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?