Intro to Descriptive Statistics

I. Overview

Descriptive statistics involves summarizing and organizing data from a sample to reveal its key characteristics, without making broader inferences about a population. It doesn’t try to make predictions or reach conclusions about a larger population (that’s inferential statistics); it simply describes exactly what you have in front of you.

Main Types

1. Measures of Central Tendency
This tells you where the "middle" of the data sits.

• Mean: The mathematical average.
• Median: The middle value when the data is lined up in order.
• Mode: The most frequently occurring value.

2. Measures of Variability (Spread)
This tells you how "stretched out" or "clustered" your data is.

• Range: The distance between the highest and lowest values.
• Standard Deviation: How much the data points typically deviate from the mean.
• Variance: The squared version of standard deviation, representing the degree of spread

3. Frequency Distribution
This is often shown as a table or a graph (like a histogram) that shows how often each individual value occurs. It helps you see the "shape" of your data—whether it's a perfect bell curve or skewed to one side.

II. Graphs

Descriptive statistics often uses graphs as a tool that helps you learn about the shape or distribution of a sample or a population. A graph can be a more effective way of presenting data than a mass of numbers because we can see where data clusters and where there are only a few data values.

Some of the types of graphs that are used to summarize and organize data are:

• the dot plot
• the bar graph
• the histogram
• the stem-and-leaf plot
• the frequency polygon (a type of broken line graph)
• the pie chart
• the box plot.

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Lumen: Intro to Descriptive Statistics