# Descriptive statistics

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**Descriptive statistics** is a branch of statistics that denotes any of the many techniques used to summarize a set of data. In a sense, we are using the data on members of a set to describe the set. The techniques are commonly classified as:

- Graphical description in which we use graphs to summarize data.
- Tabular description in which we use tables to summarize data.
- Summary statistics in which we calculate certain values to summarize data.

In general, statistical data can be described as a list of *subjects* or *units* and the data associated with each of them. Although most research uses many data types for each *unit*, we will limit ourselves to just one data item each for this simple introduction.

We have two objectives for our summary:

- We want to choose a statistic that shows how different
*units*seem similar. Statistical textbooks call the solution to this objective, a*measure of central tendency.* - We want to choose another statistic that shows how they differ. This kind of statistic is often called a
*measure of statistical variability*.

When we are summarizing a quantity like length or weight or age, it is common to answer the first question with the **arithmetic mean,** the **median,** or the **mode.** Sometimes, we choose specific values from the cumulative distribution function called quantiles.

The most common measures of variability for quantitative data are the variance; its square root, the standard deviation; the range; interquartile range; and the absolute deviation.

## Steps in descriptive statistics

- Collect data
- Classify data
- Summarize data
- Present data
- Proceed to inferential statistics if there is enough data to draw a conclusion.

## See also

- statistical regularity
- planning statistical research
- statistical inference
- summary statistics
- data mining

## Key texts

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