Data Analysis › Statistics

Descriptive Statistics

Summarising a dataset with counts, averages, spread and shape.

Also known as: summary statistics, descriptive stats, summary stats

Descriptive statistics are the numbers you compute to say what is in a dataset: how many rows there are, what a typical value looks like, how much the values vary, and what shape they form. They describe the data you have and make no claim about anything beyond it.

A first pass over a table usually covers the same four things:

SELECT COUNT(*)                AS row_count,
       COUNT(DISTINCT user_id) AS distinct_users,
       AVG(order_value)        AS mean_order,
       MIN(order_value), MAX(order_value)
FROM orders;

| What          | Common measures                | Why you need it                  |
|---------------|--------------------------------|----------------------------------|
| Count         | row count, distinct counts,    | "the average is 5" means little  |
|               | how many are missing           | without knowing how many rows    |
| Typical value | mean, median, mode             | see central tendency             |
| Spread        | range, standard deviation, IQR | two datasets can share a mean    |
|               |                                | and nothing else                 |
| Shape         | histogram, skew, number of     | tells you which of the above     |
|               | peaks                          | to trust                         |

The classic mistake is reporting the mean on its own. Two checkout flows can both average four minutes — one tight around four, one mostly one minute with a slow tail. Same average, completely different distribution shape, and a histogram settles it in seconds.

Two habits that keep summary numbers honest.

First, report the count next to the number. A percentage from twelve rows and a percentage from twelve thousand should not be quoted the same way.

Second, know what a blank means before you trust the row count. Most tools skip blanks inside AVERAGE but include them in a “count all” function, and spreadsheets and SQL disagree about text and blank handling. Check what your tool does rather than assuming — the spreadsheet is the usual place where this bites (spreadsheet formulas).

For a fuller first look at a table, see exploratory data analysis and data profiling.