What it means
Any time you say "average order value was $86" or "half our customers order more than four times a year", you are using descriptive statistics. The family splits into two groups: measures of central tendency, which describe the typical value, and measures of dispersion, which describe how much variation sits around it.
Both are needed, because an average with no sense of spread hides more than it reveals. The measures of central tendency are the mean, the median and the mode.
The mean is the arithmetic average, the median is the middle value once the data is sorted, and the mode is the value that appears most often. The median is more useful whenever a few extreme figures would drag the mean somewhere misleading, which is why property prices and salaries are almost always quoted as medians.
Dispersion is measured with the range, the variance and the standard deviation. The range is simply the highest value minus the lowest; the standard deviation is a more careful measure of the typical distance of each observation from the mean.
A small standard deviation means the data clusters tightly, which usually indicates a predictable process. In a business setting these measures drive real decisions.
If average delivery time is four days with a standard deviation of half a day, you can promise five days safely, but if the standard deviation is three days the same promise will be broken constantly. Managers who look only at averages tend to be surprised by the tails.
The nuance worth carrying is the difference between descriptive and inferential statistics. Descriptive statistics make claims only about the data you have collected, while inferential statistics use a sample to estimate something about a larger population with a stated margin of error.
Calling a six-store average "the company average" when you have sixty stores is a quiet leap from one to the other.
In practice
Real-world examples.
Example
A recruitment agency reports that median time to hire is 32 days while the mean is 41 days. The gap tells the operations lead that a handful of very slow senior searches are distorting the average, so the team reports both figures to clients.
Example
An insurer analyses claim sizes and finds a mean claim of $2,400 with a standard deviation of $9,800. The enormous spread signals that pricing cannot be set from the average alone, and the actuarial team models the tail separately.
Example
A retailer compares basket sizes across two store formats. Both have a mean basket of $34, but the high street format has a standard deviation of $9 while the out-of-town format has $27, which changes how each store forecasts stock.
Formula
Calculation
Mean = Sum of values / Number of values. Sample variance = Sum of squared deviations from the mean / (Number of values - 1). Standard deviation = square root of the variance.
Weekly sales at six branches are $38,000, $42,000, $45,000, $47,000, $52,000 and $76,000. The total is $300,000, so the mean is $300,000 / 6 = $50,000. Sorting the values, the two middle figures are $45,000 and $47,000, so the median is $46,000. The range is $76,000 - $38,000 = $38,000.
For the spread, the deviations from the mean are -$12,000, -$8,000, -$5,000, -$3,000, $2,000 and $26,000. Squaring each gives 144,000,000 plus 64,000,000 plus 25,000,000 plus 9,000,000 plus 4,000,000 plus 676,000,000, which totals 922,000,000. Dividing by 5 gives a sample variance of 184,400,000, and the square root is a standard deviation of roughly $13,579. Notice that the mean of $50,000 sits above four of the six branches, because the $76,000 branch pulls it upward, which is exactly why the median of $46,000 is the more honest headline figure here.Case study
Seen in the real world.
Halden Freight is an illustrative, fictional courier company that promised customers a three-day delivery window based on its average transit time of 2.6 days. Complaints kept arriving even though the average never moved, and the operations director could not reconcile the two facts.
An analyst pulled the underlying data and calculated the full set of descriptive statistics rather than the mean alone. The median transit time was 2.2 days, but the standard deviation was 1.4 days, and the slowest 10% of shipments took more than five days. The average was accurate and the promise was still wrong, because customers experience individual deliveries, not the mean.
Halden changed its published window to four days for the two regions carrying almost all the variation and left three days everywhere else. Complaint volume fell by more than half within two months while the average transit time stayed exactly where it had been. This fictional case is a reminder that a measure of spread often matters more commercially than the measure of centre.
Watch out
Common mistakes.
- Quoting the mean on skewed data such as salaries or claim sizes, where the median describes the typical case far better.
- Reporting an average with no measure of spread, which hides the variation that customers and operations teams actually experience.
- Treating descriptive statistics from a small sample as facts about the whole population, which is the job of inferential statistics.
Questions
People also ask.
What is the difference between the mean and the median?
The mean is the arithmetic average of every value, while the median is the middle value when the data is sorted, and the median is less affected by extreme figures.
When should standard deviation be used instead of the range?
Use standard deviation whenever you want a stable measure of typical variation, because the range depends entirely on two observations and jumps around with any outlier.
Are descriptive statistics enough for decision making?
They are enough to describe what you observed, but any claim about a wider population, a cause or a future period needs inferential or predictive methods.
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