### Statistics Knowledge Portal

A free online introduction to statistics

# Measures of Central Tendency and Variability

## What are measures of central tendency?

Measures of central tendency provide us with essential information about the central or average values in a dataset, helping us identify the "typical" value around which data points tend to cluster.

## What are measures of variability?

Measures of variability help us understand the extent to which data points deviate from the central tendency. The ability to quantify the spread of data points in a dataset is essential to deriving deeper insights about your data and making informed decisions.

## Understanding measures of central tendency

Measures of central tendency are used in a variety of ways to analyze and interpret data. They provide a single, representative value that can be helpful for quickly understanding the general characteristics of a dataset, helping analysts understand where the data tends to cluster and identify any unusual values. The key measures are:

### Mean, Median and Mode

• Mean: The arithmetic average of a dataset.
• Median: The middle value when data is arranged in order.
• Mode: The most frequently occurring value in a dataset.

Each measure of central tendency has its strengths and is appropriate in different situations. The choice of which measure to use depends on the characteristics of the data and the specific goals of the analysis. Learn more about how to use the mean, median and mode.

## Exploring variability

While central tendency focuses on the "typical" value, it is often at least as important to understand how spread out your data is. Analyzing the distribution of data points around the central tendency can help with things like assessing data quality, comparing variability across data sets and identifying outliers.

Listed below are key topics related to measuring variability. Click on the links to learn more:

• Normal distribution: Discover the theoretical foundation of data distribution, the bell-shaped curve that forms the basis for many statistical analyses.
• Standard deviation: Learn how to quantify the spread of data points around the mean, providing a comprehensive view of data distribution.
• Empirical rule: Explore the 68-95-99.7 rule, a guideline for understanding the percentage of data within specific standard deviation ranges in a normal distribution.
• Z-score: Understand how z-scores quantify a data point's position relative to the mean, facilitating standardized comparisons across datasets.