# Median vs. Mean: What's the Difference?

Edited by Aimie Carlson || By Harlon Moss || Updated on October 16, 2023
Median is the middle value in a dataset; mean is its average.

## Key Differences

Median refers to the value that divides a set of data into two equal halves, meaning there are an equal number of data points above and below the median. Mean, on the other hand, is the sum of all data points divided by the total number of points.
When considering the median, one arranges the data points in ascending or descending order and identifies the middle point. The mean is a calculation that adds up every data point and then divides by the total count.
The median can often be a better representative in datasets with outliers, as it isn't swayed by extremely high or low values. Conversely, the mean is sensitive to these outliers, as every data point impacts its value.
For an odd set of numbers, the median is the exact middle number. For an even set, it's the average of the two middle numbers. The mean doesn't differentiate between odd or even sets; it always considers all values.
The use of median is prevalent in fields where data can be skewed, such as income studies, to get a clearer picture of central tendency. The mean, however, is used in many fields, from basic mathematics to advanced scientific studies, because of its comprehensive nature.

## Comparison Chart

### Definition

Middle value in an ordered dataset
Average of all values in a dataset

Not sensitive
Sensitive

### Calculation

Exact middle value or average of two middles
Sum of all values divided by count

### In Skewed Data

Often a better representative

### Usage

Fields with skewed data (e.g., income studies)

## Median and Mean Definitions

#### Median

The central point of a data set.
The median salary was \$50,000.

#### Mean

A measure of central location of data.
The mean temperature is consistent this year.

#### Median

The middle number in an ordered sequence.
Seven is the median in the sequence 3, 5, 7, 9, 11.

#### Mean

The average of a set of numbers.
The mean score of the class was 85.

#### Median

A measure of central tendency in statistics.
The median provides a clearer picture of the data distribution.

#### Mean

The sum of numbers divided by the count.
The mean height of students is increasing.

#### Median

The value separating higher and lower half of data.
The median score was higher this year.

#### Mean

An arithmetic average in statistics.
The mean is sensitive to extreme values in the data.

#### Median

The point at which half the values are above and half are below.
The median age of the group is 30.

#### Mean

A representative value for a data set.
The mean sales figure is a useful metric.

#### Median

Relating to, located in, or extending toward the middle.

#### Mean

To be used to convey; denote
"'The question is,' said Alice, 'whether you can make words mean so many different things'" (Lewis Carroll).

#### Median

(Anatomy) Of, relating to, or situated in or near the plane that divides a bilaterally symmetrical animal into right and left halves; mesial.

#### Mean

To act as a symbol of; signify or represent
In this poem, the budding flower means youth.

## FAQs

#### How is mean calculated?

Mean is calculated by adding all values and dividing by the total count.

#### How does mean react to outliers?

Mean is sensitive to outliers, as every data point affects its value.

#### Is median affected by outliers?

No, the median isn't swayed by extremely high or low values.

#### Can the mean be a number not present in the dataset?

Yes, the mean can be a value not specifically in the dataset.

#### How is median represented in a frequency distribution?

It's the value where half of the frequencies lie above and below.

#### Which is a better representation in income studies?

Often, the median.

#### When is the median especially useful?

The median is useful in datasets with skewed data or outliers.

#### Is the median always a number in the dataset?

For odd datasets, yes. For even datasets, it's the average of the two middle numbers.

#### How is the median of an even set of numbers found?

It's the average of the two middle numbers.

The mean.

#### When are both median and mean the same?

In symmetrical distributions without outliers.

#### What's an example of when mean might be misleading?

When a single very high or very low value skews the average.

#### In what type of distribution is the median to the left of the mean?

Right-skewed distribution.

#### Where are median and mean located in a left-skewed distribution?

The mean is typically less than the median.

#### What do both median and mean represent?

Both are measures of central tendency in a dataset.

#### What is the median?

The median is the middle value in an ordered data set.

#### How are mean and median related in a skewed distribution?

In a right-skewed distribution, the mean is typically greater than the median.

#### Can median and mean have the same value in a data set?

Yes, especially in symmetric distributions.

#### How do outliers affect the mean?

Outliers can significantly raise or lower the mean.

#### Why might someone use the mean?

The mean provides a comprehensive overview of the entire dataset.