Descriptive Statistics

Descriptive statistics summarize a dataset with a handful of numbers — where its center is, and how spread out it is — but each one can mislead you if you don't know what it's actually sensitive to.

Mean, median, and mode

The mean (the everyday "average") adds everything up and divides by the count. The median is the middle value once everything is sorted. The mode is whichever value appears most often. For a nicely symmetric dataset, all three land close together — but they can diverge sharply the moment a dataset is skewed by a few extreme values.

incomes = [45000, 52000, 48000, 51000, 2400000]
sorted_incomes = sorted(incomes)
mid = len(sorted_incomes) // 2

mean = sum(incomes) / len(incomes)
median = sorted_incomes[mid]

print(f"Mean:   {mean:,.0f}")
print(f"Median: {median:,}")

Mean:   519,200
Median: 51,000

One household making $2.4M drags the mean up to over $519,000 — a number that doesn't describe a single actual household on this street. The median, $51,000, is a far more honest picture of what a "typical" household there earns. This is exactly why household income is usually reported as a median in the news, not a mean.

Variance and standard deviation

The mean or median tells you where the center is; variance and standard deviation tell you how spread out the data is around that center. A low standard deviation means most values sit close to the mean; a high one means they're scattered widely. Standard deviation is just the square root of variance, and it's the one usually reported because it's in the same units as the original data (dollars, not dollars-squared).

Reading these numbers together

None of these numbers means much in isolation. "Average order value: $85" tells you almost nothing about whether that's $85 every time or an average of a lot of $20 orders and a few $500 ones — you need the spread, and ideally the shape of the whole distribution, to actually understand what's going on.