Description

Business Statistics for Decision Making

Jun 2026 Examination

 

 

 

Q1. Benti Ltd., a mid-sized technology company, recently conducted an employee engagement survey and analyzed key productivity metrics across departments, including sales and engineering. The management calculated a Pearson correlation coefficient of 0.75, indicating a strong positive relationship between engagement and productivity. While the sales department, with high engagement, exceeded targets, engineering with lower engagement fell behind. The leadership is now seeking to implement new human resource initiatives, but wants to ensure these strategies are grounded in robust statistical analysis. Apply the concept of correlation analysis, specifically Pearson’s coefficient, to recommend how Benti Ltd. can use ongoing survey and productivity data to monitor and enhance the effectiveness of HR initiatives aimed at boosting engagement and productivity. How should the company integrate analytics into its decision-making process to drive sustainable improvements? (10 Marks)

Ans 1.

Introduction

Correlation analysis is a statistical technique that measures the strength and direction of the linear relationship between two quantitative variables. The Pearson correlation coefficient, denoted as r, ranges from negative one to positive one. A coefficient of 0.75, as computed at Benti Ltd. between employee engagement scores and departmental productivity metrics, indicates a strong positive relationship. This means that as engagement levels rise, productivity tends to increase in a predictable and measurable pattern. Such a finding provides the HR leadership with a statistically credible foundation for designing and justifying engagement-focused interventions, replacing anecdotal observation with quantitative evidence as the basis for people management decisions.

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Q2 (A). A retail company specializing in consumer electronics has recently completed a univariate analysis of their customer spending over the past year. The company observed a mean expenditure of $150 and a median of $120, with a positively skewed distribution as shown by their histogram. The management is now debating whether inventory management strategies should focus on the average (mean) spender or the more typical (median) customer profile. They must also consider the influence of a few high-value customers who significantly raise the mean. Critically evaluate whether the retail management team should prioritize the mean or median spending when devising their inventory and promotional strategies. Consider the implications of skewness in the data and justify which measure is more representative for operational decision-making in this scenario. (5 Marks)

Ans 2(A).

Introduction

In a positively skewed distribution, a small number of exceptionally high-spending customers pull the arithmetic mean upward, creating a visible gap between the mean and the median. For this consumer electronics retailer, the mean expenditure of $150 is inflated by a minority of premium buyers while the median of $120 more accurately represents the spending behaviour of the majority of the customer base. The $30 difference between these two measures is not a statistical curiosity. It is a commercially significant signal about where the bulk of actual customer demand is concentrated and how inventory and promotional

 

Q2 (B). A coaching institute groups students for extra practice sessions based only on their average test marks. However, teachers notice that some students in the same group perform very differently, some struggle to keep up, while others find the sessions too easy. To improve the grouping system, the academic team suggests using additional statistical measures such as standard deviation, quartile deviation, and skewness to better understand score variation. However, the management team is concerned that adding more statistical calculations may make the system complicated and slow down implementation. 1. Evaluate whether the institute should include measures of dispersion and skewness in the student grouping process. 2. Critically examine the trade-off between statistical accuracy and practical simplicity. 3. Justify whether the added statistical analysis is necessary for improving student performance and satisfaction. (5 Marks)

Ans 2(B).

Introduction

Grouping students based solely on average test marks assumes that identical means imply identical learning needs. This assumption fails when students with the same average exhibit very different score patterns across individual tests. One student may score consistently between 60 and 70 marks across all tests, while another with the same average may score 40 in some tests and 90 in others. Placing them in the same practice group and delivering sessions at the same pace and content level will fail both students. Measures of dispersion and