Business Statistics You Actually Use
Mean can be distorted by outliers; median shows the typical case. Report both for revenue per customer.
Standard deviation measures spread — two products with the same average can have very different risk.
Correlation is not causation. Sales rising with ad spend may both be driven by the season.
Small samples lie often. Ten customers loving a feature is a signal, not proof.
The lesson mentions standard deviation as a measure of spread or risk. Let's clarify. A *low* standard deviation means most of your data points (like sales per day or revenue per customer) are very close to the average. This indicates consistency and predictability. For a business, this is often desirable as it makes forecasting and operational planning easier.
A *high* standard deviation means the data points are widely spread out from the average. You might have some extremely high sales days and some extremely low ones, or some whale customers and many tiny ones. While the average might look good, this signals volatility and risk. If you have two products with the same average monthly sales, the one with the higher standard deviation has a more unpredictable revenue stream.
An A/B test compares two versions under comparable conditions. The control group uses the existing version, and the treatment group uses the new version. To test a sales script, randomly assign leads to comparable groups of agents using either the old script or the new script during the same time period. Random assignment means using chance rather than choosing which leads get each script. Keep other conditions similar and compare conversion rates—the share of calls that result in a sale—so differences in timing, lead quality or agent experience do not explain the result.
Positive feedback from ten loyal customers is a promising signal, not proof of broad demand. Loyal customers may have different needs and stronger enthusiasm than other users. Test the feature with a larger, more representative sample: a group that reflects the range of customers you intend to serve, including newer, occasional and less enthusiastic users. A larger sample helps reduce uncertainty, but size alone does not fix a biased selection.
An A/B test compares outcomes for users randomly assigned to an existing version and a changed version. A statistically significant result means the observed difference would be unlikely under a no-effect assumption, according to a chosen statistical threshold and the test's assumptions. It does not guarantee a valuable business outcome. Commercial significance means the benefit is large enough to matter financially. For a small sign-up increase, estimate the value of the additional sign-ups and compare it with a month of developer time, ongoing costs and the value of other work those developers could do.
You, before you commit to a major change in your business based on a recent spike in sales, pause and ask: what else was happening? Was it a holiday, a competitor's misstep, or just a random good week? Always hunt for the 'why' behind the 'what'.
Learning objective
Use descriptive statistics and comparison design without confusing association with causation.
Understand the mechanism
Mean summarizes total divided by count; median is the middle ordered observation. Both can be useful. A large customer affects total revenue even if the median better describes a typical customer. Spread, sample size and missing data determine how much confidence to place in the summary.
Correlation can arise from a common cause. Holiday demand may raise both ad spending and sales. To estimate an ad effect, compare like with like and, where feasible, randomly assign eligible customers to treatment and control.
Put it to work
Define the decision and metric before collecting data. Record sample size and uncertainty; segment only with a defensible reason. Searching many segments until one looks successful increases false discoveries.
For experiments, keep offer, timing and eligibility comparable. Statistical significance is not the same as commercial importance. A tiny lift may not repay implementation costs, and a small sample can hide a valuable effect.
Worked example
- 1
Five orders are $10, $10, $10, $10 and $110. Mean = $150 ÷ 5 = $30; median = $10.
- 2
A campaign gets 12 sales from 100 visitors versus 10 from 100 in a control group.
- 3
That is a 2 percentage-point observed difference, but this small comparison alone is not convincing evidence of a repeatable lift.
Report what the data shows, what it cannot show and the decision still facing you.
Your practice lab
Orders are $20, $20, $30, $30 and $200. Compute mean and median. Explain why both belong in a business review.
Personal scratchpad · not graded or saved
Case Study: The Seasonal Sales Trap
An online retail store, 'Cozy Home Goods', ran its first major social media ad campaign throughout October. At the end of the month, the owner was thrilled to see that sales had jumped 40% compared to September. Attributing the success entirely to the ads, he immediately planned to double the ad budget for November and December.
Before committing the funds, his business partner decided to look at the previous two years of sales data. She discovered a clear pattern: sales consistently jumped 35-45% every October as customers began their holiday and cold-weather shopping, long before they ever ran ad campaigns. The ad campaign had run concurrently with a predictable seasonal spike.
Instead of doubling down based on a likely misinterpretation, they decided to analyze the specific sales that came directly from ad clicks. They found the ads were profitable, but responsible for only a small fraction of the total sales lift. They adjusted the budget to a more reasonable level and planned an A/B test for a less volatile quarter (like Q2) to find the true impact of their ads.
A change that happens after an action isn't proof the action caused it. Always examine historical data and seasonality before attributing success to a single factor.
Illustrative example — names and figures are composites for teaching.
Identify one key metric for your business (e.g., revenue per customer, conversion rate). Describe how you would track its mean and median, and what a significant difference between the two might tell you about your business.
Example: Metric: Average project value for my design agency. I'll track it in a spreadsheet for all closed deals. The mean shows my total revenue picture, but the median reveals the 'typical' project size. If the mean is much higher than the median, it means a few huge projects are inflating the average, indicating a risk if I lose one of those clients.
Go deeper — outside resources
- Market Research & Competitive Analysis · U.S. Small Business Administration
- A Refresher on A/B Testing · Harvard Business Review
- Statistics and Probability · Khan Academy
Key ideas
- Median resists outliers
- Spread = risk
- Correlation ≠ causation
- Respect sample size
Try it: Find a claim in the news based on a correlation. What else could explain it?
Quick check
1. One whale customer inflates your average. Use…
2. A city finds that ice cream sales are highly correlated with the number of drownings. What is the most logical explanation for this relationship?
3. Product A and Product B both average $1,000 in daily sales. Product A has a high standard deviation, while Product B's is low. Which statement is most likely true?
4. To accurately test if a new sales script increases call conversions, the best method is to:
5. You get feedback from ten of your most loyal customers that they love a potential new feature. What is the most prudent conclusion?
6. A complex A/B test on your website shows a 0.2% increase in sign-ups, and the result is 'statistically significant'. Implementing the change requires a month of developer time. What should be your primary consideration?