mean (arithmetic mean)

Also called: arithmetic mean

The sum of all values divided by their count; sensitive to outliers.

The arithmetic mean is what most dashboards simply label "average": add up every value and divide by how many values there are.

$\bar{x} = \frac{x_1 + x_2 + \dots + x_n}{n} = \frac{1}{n}\sum_{i=1}^{n} x_i$

In everyday speech "average" can mean any typical value, so in a report it pays to be precise: the mean is one specific calculation. Average order value (AOV), average revenue per user (ARPU) and average session length are all means.

The mean's big strength is that it is tied to the total: mean × count = total, always. That makes it the right measure for forecasts and budgets. If CatChow expects 400 orders next month at a mean of $45, that is $18,000 of revenue. Neither the median nor the mode can do this.

Its weakness is the flip side of the same property. Every value counts in full, so one extreme value can drag the mean far from where most of the data sits. Product data (order values, time to purchase, revenue per customer) usually has a long right tail, and the mean then lands above what a typical customer does. Always glance at the median next to it: if the two are close, the data is roughly balanced; if the mean is well above the median, a few large values are pulling it up. For a mean that resists a handful of extremes there is the trimmed mean, and for combining means of segments of different size, the weighted mean.

Example

Five CatChow orders arrive on a Tuesday morning: $24, $28, $30, $38 and $130 (a cat café stocking up for the week).

$\bar{x} = \frac{24 + 28 + 30 + 38 + 130}{5} = \frac{250}{5} = 50$

The mean order is $50, yet four of the five orders are below $40. Sorting the values gives a median of $30 (the 3rd of 5), so the mean is about 1.67 times the median: a clear sign that one order is doing the pulling.

Both numbers are correct; they answer different questions. For revenue planning you need the mean: 5 orders × $50 = $250, exactly what came in. For "what does a normal customer spend?" the honest answer is the median, $30. Without the café's order the mean would be $(24 + 28 + 30 + 38) / 4 = 120 / 4 = 30$ dollars.

Common mistakes

Saying "average" without saying which one. Most tools compute the mean by default. Write "mean" or "median" explicitly so nobody compares apples with oranges.
Treating the mean as the typical value on skewed data. With a long right tail most customers sit below the mean: in one CatChow week, 16 of 20 orders were below the $45 mean.
Averaging averages. The simple mean of 2% mobile and 5% desktop conversion is not the overall rate when mobile has four times the traffic. Use a weighted mean or go back to the raw totals.
Deleting big values to "fix" the mean. If the question is about revenue, those orders are real money. Report the mean with and without them instead.
Trusting a mean from a handful of observations. With 10 orders, one new order can swing the mean a lot. Check $n$ before celebrating a jump.

Learn it in the course

Mean, median and mode: the typical value · Mean, median, mode and trimmed mean on real-looking CatChow orders: what each one answers, why one bulk order can fool the average, and how not to average averages.
Outliers and skewed data: how to find them · Why product metrics have long tails, how to find outliers with the IQR rule, and what to do with them: fix errors, segment different customers, and never delete whales without thinking.
Measures of spread: range, SD and quartiles · Two couriers with the same average delivery time, and why only one keeps the promise: measures of spread from range and variance to standard deviation (calculated step by step), quartiles, IQR and the coefficient of variation.
Sample vs population and the normal distribution · Sample vs population: why we study samples to learn about all users, why the bell-shaped normal distribution shows up everywhere, and how the central limit theorem ties them together.
One-way ANOVA: comparing many groups · Testing three or more variants at once with a one-way ANOVA, without inflating false positives.