# Tertile vs. Quartile — What's the Difference?

By Tayyaba Rehman — Updated on November 2, 2023
Tertiles divide data into three equal parts; quartiles divide data into four. Both are statistical measures of spread.

## Key Differences

Tertiles and quartiles are both measures that divide a data set into equal parts. Tertiles divide data into three parts, meaning that each part represents a third of the data set. Quartiles, on the other hand, divide data into four equal parts, with each quartile containing a quarter of the data points.
When using tertiles, you identify two points within the data set: the first tertile (or lower tertile) and the second tertile (or upper tertile). These points are values such that one-third of the data lies below the first tertile and two-thirds below the second tertile. Quartiles identify three points: the first quartile (Q1), the second quartile (Q2, which is also the median), and the third quartile (Q3), splitting the data into quarters.
Analysts use tertiles when they prefer a division into thirds for more general groupings. In contrast, quartiles are often used in box plot representations of data and for more detailed analysis, as they provide a median value and facilitate the calculation of the interquartile range (IQR), which measures the middle spread of the data.
Understanding tertiles can be useful in fields like economics to categorize income groups into lower, middle, and upper thirds. Quartiles are frequently employed in finance and research to identify outliers and understand the distribution of a data set, especially for data sets that are not normally distributed.
In practical terms, choosing between tertiles and quartiles depends on the specific needs of the analysis. Tertiles might be simpler and provide a broader overview, while quartiles offer more detail and are fundamental for various statistical methods.

## Comparison Chart

### Number of Divisions

Divides data into 3 equal parts.
Divides data into 4 equal parts.

### Points of Division

Has two dividing points.
Has three dividing points.

### Median Representation

Does not specifically represent median.
Second quartile represents the median.

### Common Use

More detailed, includes median and IQR.

### Statistical Complexity

Simpler, used for general groupings.
More complex, used in detailed analysis.

## Compare with Definitions

#### Tertile

Tertiles split data into three groups of equal size.
His income falls into the highest tertile of the dataset.

#### Quartile

Quartiles divide a dataset into four equal parts, indicating variability.
The first quartile showed that 25% of the class scored below 60.

#### Tertile

Tertiles are a form of quantile used less frequently than quartiles or percentiles.
We used tertiles to analyze the survey responses.

#### Quartile

Quartiles can be used to describe the spread and central tendency of data.
Quartiles are critical for understanding the distribution of housing prices.

#### Tertile

Tertiles are statistical thresholds below which a certain percentage of data falls.
The examination scores were categorized into tertiles.

#### Quartile

Quartiles offer a detailed division of data, useful in identifying outliers.
Any data point above the third quartile was considered an outlier.

#### Tertile

Tertiles serve as cut-off points dividing a population into three equal-sized groups.
The population was divided by weight into tertiles for the study.

#### Quartile

Quartiles are points that separate data into quarters, providing a median value.
The median, a second quartile, was 75 on the test scores.

#### Tertile

Tertiles help in dividing data into three broad categories or ranks.
Tertiles revealed a clear distinction in the income distribution.

#### Quartile

Quartiles are used to calculate the interquartile range in descriptive statistics.
The interquartile range is the difference between the first and third quartiles.

#### Tertile

(statistics) Either of the two points that divide an ordered distribution into three parts, each containing a third of the population.

#### Quartile

In statistics, a quartile is a type of quantile which divides the number of data points into four parts, or quarters, of more-or-less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic.

#### Tertile

(statistics) Any one of the three groups so divided.
The first tertile results include January through April's revenues.

#### Quartile

Each of four equal groups into which a population can be divided according to the distribution of values of a particular variable
In the highest quartile, the mean age was 72

#### Quartile

Any of the groups that result when a frequency distribution is divided into four groups of equal size.

#### Quartile

Any of the values that separate each of these groups.

#### Quartile

(statistics) Any of the three points that divide an ordered distribution into four parts, each containing a quarter of the population.

#### Quartile

(statistics) Any one of the four groups so divided.
This school is ranked in the first quartile.

#### Quartile

(statistics) any of three points that divide an ordered distribution into four parts each containing one quarter of the scores

## Common Curiosities

#### Why might one choose to use tertiles?

Tertiles are chosen for simplicity or when a tripartite division of data is particularly meaningful.

#### Are tertiles and percentiles the same?

No, percentiles divide data into 100 equal parts, while tertiles divide into three.

#### How do you calculate tertiles?

Tertiles are calculated by finding data points that split the data into three equally numbered groups.

#### What exactly is a tertile in statistics?

A tertile is one of two points that divide a set of ordered data into three equal-sized groups.

#### Can tertiles be used for any size data set?

Yes, as long as the data set can be divided into three parts with a meaningful number of data points in each.

#### What defines a quartile?

A quartile is one of three points that divide a set of ordered data into four equal-sized groups.

#### Are quartiles always equally spaced?

No, the spacing between quartiles depends on the data's distribution, not the number of data points.

#### How do quartiles help with outlier detection?

Outliers can be identified as data points that lie outside the range defined by the first and third quartiles.

#### Can quartiles be used for categorical data?

Quartiles are typically used for numerical data, not categorical data.

#### Is there a formula for finding quartiles?

Yes, quartiles can be calculated using formulas that find the median and then the medians of the two halves of the data set.

#### Why use quartiles in data analysis?

Quartiles provide a detailed breakdown of a data set, including the median and spread.

#### Do tertiles give any information about data distribution?

Tertiles can provide a basic understanding of distribution but less detail than quartiles.

#### Is there any similarity between tertiles and quartiles?

Both tertiles and quartiles are ways of dividing a data set into equal-sized groups to describe its distribution.

#### Can tertiles or quartiles be visualized?

Yes, both can be visualized using graphs, though quartiles are commonly depicted in box plots.

#### What is the second quartile also known as?

The second quartile is also known as the median.

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