Descriptive statistics for business: mean, median, standard deviation and outliers

“The average order is 62.” It sounds like a useful fact, but on its own it can hide almost everything that matters. Are most orders near 62, or are most around 30 with a few huge ones pulling the figure up? Is next month’s 70 a real improvement or ordinary noise?

Descriptive statistics answer those questions. You need only a few: the mean, the median, a measure of spread such as standard deviation or interquartile range, and a way to spot outliers. This guide explains each in plain terms, shows the Excel function for each, and uses the NIST Engineering Statistics Handbook, a US government reference, as the main source.

Mean and median: two kinds of “typical”

The mean is what most people call the average: add the values and divide by how many there are. In Excel it is AVERAGE. The median is the middle value once the data is sorted, with half the values above and half below. With an even number of values, it is the average of the two middle ones. In Excel it is MEDIAN.

For a symmetrical set of numbers, the two are the same. Microsoft’s MEDIAN page makes this point: for a symmetrical distribution, the mean, median and mode coincide. Business data is often not symmetrical. Order values, salaries, deal sizes and time to resolve support tickets tend to have a long tail of large values.

NIST’s handbook on measures of location explains what happens then. In a skewed distribution, the mean is pulled towards the tail. A long right tail makes the mean bigger than the median. Extreme values distort the mean, while the median, based on rank order, is not distorted by them. NIST states that for data with extreme tail values, “the median provides a better estimate of location than does the mean.”

A practical rule follows: calculate both. If they are close, the data is roughly balanced and the mean is fine. If the mean is well above the median, a minority of large values is doing the work, and you should report the median, or both, with a sentence explaining the gap.

Spread: standard deviation and interquartile range

Two sets of numbers can share the same average and look completely different. Spread tells you how far values typically sit from the centre.

Standard deviation is the most common measure. NIST’s page on measures of scale defines it as the square root of the variance, where variance is the average squared distance from the mean, using n minus 1 in the denominator for a sample. Because the distances are squared, values far from the mean carry extra weight. In Excel, use STDEV.S when your data is a sample, which is most business data, and STDEV.P only when you truly have every value in the population. STDEV.S ignores text, logical values and empty cells in a range.

The interquartile range (IQR) is the gap between the 25th and 75th percentiles, so it describes the middle half of the data and ignores the tails. In Excel, QUARTILE.INC returns the first quartile with an argument of 1 and the third with 3, so =QUARTILE.INC(B2:B500,3)-QUARTILE.INC(B2:B500,1) gives the IQR.

NIST’s guidance on choosing between them is clear. Standard deviation is appropriate when the data is roughly normal, the familiar bell shape. With long tails, it can become very large and close to useless, and measures such as the IQR or the median absolute deviation are better. So pair them: mean with standard deviation for balanced data, median with IQR for skewed data.

Outliers: find them, then investigate

NIST defines an outlier as an observation that lies an abnormal distance from the other values, and leaves the definition of “abnormal” to the analyst. A widely used rule, the one behind box plots, uses the quartiles:

• Lower inner fence: Q1 minus 1.5 times the IQR. Upper inner fence: Q3 plus 1.5 times the IQR.
• Lower outer fence: Q1 minus 3 times the IQR. Upper outer fence: Q3 plus 3 times the IQR.
• A value beyond an inner fence is a mild outlier. A value beyond an outer fence is an extreme outlier.

Finding an outlier is the start, not the end. NIST says outliers should be investigated carefully, because they can reveal useful information about the process or about how data was collected and recorded. Before removing a point, understand why it appeared and whether similar values are likely to recur. Some outliers are typing errors. Others are your biggest customer.

A worked example (illustration only)

A small B2B software firm looks at the value of ten deals closed last quarter, in thousands: 4, 5, 5, 6, 6, 7, 7, 8, 9 and 63.

The upper inner fence is 7.75 plus 1.5 times 2.5, which is 11.5. The upper outer fence is 7.75 plus 3 times 2.5, which is 15.25. The 63 deal is beyond both, so it is an extreme outlier.

Reporting “average deal 12k” would mislead the sales team into planning around deals that nine out of ten customers do not sign. The honest summary is: “Typical deal about 6.5k (median), with most between roughly 5k and 8k. One enterprise deal of 63k.” The next step is to ask whether that deal was a one-off or the start of a new segment, which is a business question rather than a statistical one.

Common mistakes

• Reporting only the mean for skewed data such as order values or salaries.
• Quoting an average with no measure of spread, so nobody can tell a real change from noise.
• Using STDEV.P on a sample, which understates the spread slightly.
• Deleting outliers automatically because they spoil the chart.
• Comparing averages from groups of very different sizes without saying so.
• Including blanks entered as zeros, which drags both the mean and median down.

When these measures are enough, and when they are not

Mean, median, spread and an outlier check are enough for most management reporting: describing customers, orders, response times or costs. Plot a histogram alongside them, because NIST’s own advice on choosing a measure depends on seeing the shape of the data first.

They are not enough when you need to say whether a difference is real, such as an A/B test or a before-and-after comparison, or when you want to predict one variable from another. Those questions need inferential methods, like confidence intervals and regression, which build on the descriptive measures covered here.