Smarter Payroll Planning: A Case Study in Salary Dispersion for Small Businesses
- Nova Data Analytics
- Oct 1
- 5 min read
Running a small business often feels like walking a tightrope. You want to keep your best employees motivated and fairly compensated, but the budget is always under pressure. Many small and medium-sized enterprise (SME) owners know the sting of losing a talented cashier or supervisor to a competitor because they couldn’t adjust salaries quickly enough. It’s not just about numbers; it’s about people, livelihoods, and the future of your business.
In our previous blog, we looked at measures of central tendency and their importance in informing us of “typical” trends in the sales data from the retail store. This week, we will explore measures of variability, also known as measures of dispersion, to show how one small retail store used them to uncover salary imbalances, support financial planning and address employee equity concerns.
Setting the Stage: Understanding Salary Spread
Before diving into dispersion, it is important to consider other descriptive statistics that will help us interpret how the data is spread. These include:
Minimum & Maximum: These identified extreme values within the dataset. They showed what entry-level staff earn, and the maximum showed executive-level pay.
Percentiles: Revealed the percentage of values that fall below a certain value. For example, the 50% percentile is the salary below which half of the employees fall.
Quartiles: Divided the salaries into four equal parts (25%, 50%, 75%). This allowed us to group salaries into lower-paid workers, mid-level employees and top earners.
With these in place, we moved to dispersion measures that provide deeper insight.
Salary Dataset
Staff Role | Monthly Salary (R) |
Cashier | 5,000 |
Cashier | 5,200 |
Cashier | 5,500 |
Cashier | 6,000 |
Cashier | 6,200 |
Cashier | 6,500 |
Cashier | 7,000 |
Cashier | 7,500 |
Supervisor | 12,000 |
Supervisor | 13,000 |
Supervisor | 14,000 |
Supervisor | 15,000 |
Supervisor | 16,000 |
Supervisor | 17,000 |
Supervisor | 18,000 |
Department Head | 24,000 |
Department Head | 25,000 |
Department Head | 26,000 |
Department Head | 28,000 |
Department Head | 30,000 |
Department Head | 32,000 |
Store Manager | 38,000 |
Store Manager | 40,000 |
Store Manager | 42,000 |
Store Manager | 45,000 |
Store Director | 80,000 |
Store Director | 85,000 |
Store Director | 90,000 |
Store Director | 95,000 |
Store Director | 100,000 |
Linking descriptive stats to measures of dispersion.
We laid the groundwork for our analysis and then calculated measures of dispersion. Here is how they connect:
Range (Max - Min)
Directly uses the maximum and minimum values.
A salary range of R90,000 showed the gap between the lowest-paid cashier and the highest-paid director.
Salary ranges were not only useful across roles but were also determined within job titles.
Example: Among the cashiers, the range is R2,500 (R5,000 – R7,500).
This helps businesses to assess whether employees in the same role are paid fairly. A wide range would signal equity concerns, unless it reflects tenure, skills, or performance.
For the supervisors, the range was R6,000 (R12,000 – R18,000). This shows career progression potential within the role and can assist HR in structuring increments and promotions realistically.
Interquartile Range (IQR = Q3 – Q1)
Our data was skewed; the range is sensitive to outliers/extreme values, but the IQR is not.
It informed us of the middle 50% of the salaries. It showed us how spread out the typical salaries are for the bulk of the employees.
Variance and Standard Deviation
Percentiles and quartiles have cut-off points. Whereas the variance and standard deviation extend by looking at how far each salary is from the average.
Variance and SD work well for normally distributed data. However, our data are positively skewed, which is a common trend in salary data. Let’s say the data were normally distributed, we would state that a high SD would mean that the salaries are very unequal. A low SD would mean that salaries are close to the mean.
SD is the square root of the variance. Check out the PDF attached to the blog that shows all the equations included in the case study.
Median Absolute Deviation (MAD) - This was a more robust measure of variability that measures the “typical” spread around the median instead of the mean. This measure is useful when data is skewed without being distorted by a few high salaries.
The skewed distribution meant that IQR, Percentiles, and the MAD were better measures of spread since they are not influenced by extreme values.
Summary Results for Salary Data
Statistic | Value (R) |
Minimum | 5,000 |
Maximum | 100,000 |
Range | 95,000 |
25th Percentile | 7,000 |
Median (50th) | 18,000 |
75th Percentile | 40,000 |
90th Percentile | 90,000 |
Interquartile Range (IQR) | 33,000 |
Variance | 726,298,696 |
Std Deviation | 26,947 |
Interpretation and Recommendations for Business Decisions
Range (R95,000): Shows a very wide salary gap between the lowest and highest roles. Finance should budget knowing that the payroll is top-heavy and not evenly spread.
Quartiles: 25% of staff earn below R7,000 (mostly Cashiers), 50% earn below R18,000 (cashiers + supervisors). The HR department can then establish if employees feel undervalued compared to management. Transparency around how tenure, qualifications, and other factors influence salary structure became essential.
75th percentile (R40,000): This marks the point where only the managers and directors remain. This shows middle-tier salary opportunities.
90th percentile (R90, 000): Shows what the top executives earn. Benchmarking this against competitors helps to keep top talent.
IQR (R33,000): Gives a clear picture of inequality within the bulk of salaries, unaffected by the directors’ extreme salaries. This is a better guide for payroll planning compared to the variance and SD values.
High Variance & SD: These confirm inequality but are inflated by the directors’ salaries. SME’s can treat these as warning signs of inequality but not precise measures for financial planning.
Lessons for SMEs
Don’t rely on averages alone: They hide inequalities.
Check your IQR: It often gives a clearer picture of fairness across most employees than variance or SD. Generally, salary distributions are positively skewed.
Benchmark regularly: Compare percentiles with industry standards to stay competitive.
Communicate: Be open with staff about salary bands and what influences growth.
Conclusion:
For SMEs, salary decisions aren’t just about spreadsheets; they’re about people, trust, and the sustainability of your business. By looking beyond averages and using measures of dispersion, small businesses can make smarter, fairer financial decisions.
Further Reading
If you’d like to dive deeper into the methods and principles behind this case study, here are some recommended resources:
Business Analytics: Data Analysis & Decision Making – Albright, Winston & Zappe
Business Analytics: Communicating with Numbers – Koen Pauwels & Bart Baesens
Harvard Business Review – Analytics Articles
Investopedia – Descriptive Statistics Guide
Disclaimer: The dataset and salaries presented in this case study are fictitious and created solely for illustrative and educational purposes. They do not reflect the actual payroll structures of any company.
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