Descriptive Statistics for Managers: Mean, Median and Why They Differ
Descriptive statistics for managers in plain English: mean, median, mode, range, percentiles and standard deviation, and why the mean and median often differ.
· 4 min read · Summarix team
Descriptive statistics summarise a set of numbers: what is typical (mean, median, mode) and how spread out they are (range, percentiles, standard deviation). For managers, the most important lesson is that the mean and the median often tell different stories, especially with money. If your average order is R1,800 but your median order is R650, a few large orders are pulling the average up, and most customers look nothing like ‘average’.
Measures of the typical value
Mean (the average)
Add all the values and divide by how many there are. In Excel: =AVERAGE(range). The mean uses every value, which is its strength and its weakness: one extreme value moves it a lot.
Median (the middle value)
Sort the values and take the one in the middle (or the average of the two middle values). In Excel: =MEDIAN(range). Half the values are below it and half above. Extreme values barely affect it.
Mode (the most common value)
The value that appears most often. Useful for things like the most common basket size or the most popular price point, less useful for continuous amounts.
Why mean and median differ: a worked example
Say you have ten customer orders this week (illustrative numbers): R300, R350, R400, R450, R500, R550, R600, R650, R700 and R15,000.
- Mean: total R19,500 ÷ 10 = R1,950.
- Median: average of the 5th and 6th values, R500 and R550 = R525.
Nine out of ten orders were under R700, yet the ‘average order’ is almost R2,000. If you plan marketing or free-delivery thresholds around R1,950, you will misjudge almost every customer. The median describes the typical order; the mean tells you total revenue per order. Both are correct; they answer different questions.
| Use the mean when… | Use the median when… |
|---|---|
| You need totals to add up (revenue per order × orders = revenue) | You want to describe a typical customer, deal or employee |
| Data is roughly symmetric with no big outliers | Data is skewed or has outliers |
| You are forecasting totals | You are setting thresholds or comparing typical experience |
Measures of spread
Range
Maximum minus minimum. Quick, but determined entirely by the two most extreme values, so it is easily distorted. Still useful as a sense check: a delivery time range of 1 to 94 days suggests a data problem.
Percentiles and quartiles
The 90th percentile is the value below which 90% of observations fall. In Excel: =PERCENTILE.INC(range, 0.9). Percentiles are excellent for service levels: ‘90% of support tickets are resolved within 26 hours’ is more meaningful than an average resolution time that a few stuck tickets have inflated. The 25th and 75th percentiles (quartiles) are also the basis of the IQR method for spotting anomalies.
Standard deviation
Roughly, how far values typically sit from the mean. In Excel: =STDEV.S(range) for a sample. Two branches may both average R40,000 in daily sales, but if one has a standard deviation of R3,000 and the other R15,000, the second is far less predictable, which matters for staffing and stock.
A related measure is the coefficient of variation: standard deviation ÷ mean. It lets you compare variability between things of different sizes. A CV of 0.1 is steady; 0.5 or more is volatile.
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Common mistakes managers make with averages
- Averaging averages. If branch A averaged R500 across 1,000 orders and branch B R1,000 across 100 orders, the overall average is not R750. It is (R500,000 + R100,000) ÷ 1,100 ≈ R545.
- Ignoring the count. An average of 4.8 stars from 5 reviews means much less than 4.5 from 500.
- Letting blanks count as zero. Blank values treated as zero drag the mean down. See the data cleaning checklist.
- Reporting only the mean for skewed data. Report the median alongside it.
- Comparing periods of different lengths. Use per-day figures when months differ in trading days.
Reading a distribution without a chart
You can often picture the shape of your data from a few numbers. If the mean and median are close, the data is roughly symmetric. If the mean is well above the median, a long tail of big values exists. If the 90th percentile is five times the median, a small group of customers or deals is doing a lot of the work, which is worth knowing when you plan account management or credit limits. A histogram confirms the picture, but these quick comparisons will usually tell you whether you need one.
A simple summary to ask for
For any important number, ask for five figures: count, mean, median, 10th percentile and 90th percentile. Together they tell you how many, what is typical, whether it is skewed, and how wide the spread is. Summarix includes statistical profiles like this in its reports; see features. For choosing which numbers deserve this attention, see how to choose KPIs.
Frequently asked questions
What is the difference between mean and median?
The mean is the sum divided by the count; the median is the middle value when sorted. The mean is pulled by extreme values, while the median is not.
When should I use the median instead of the average?
Use the median for skewed data with a few very large or small values, such as order values, salaries or resolution times, when you want to describe the typical case.
What does standard deviation tell a manager?
It shows how much values vary around the average. A high standard deviation means results are less predictable, which affects planning, staffing and stock.
Why is my average higher than most of my values?
A few large values are pulling it up. This right skew is common in business data; check the median to see the typical value.