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Third Quartile Calculator

Created by Anna Szczepanek, PhD
Reviewed by Steven Wooding
Last updated: Jan 18, 2024


Welcome to Omni's third quartile calculator! Whether you're an expert or a newbie in the world of descriptive statistics, we're sure you'll find this upper-quartile tool useful.

In the article below, we'll discuss what the third quartile is and how to find it, both by hand or with our calculator. We'll also explain where the third quartile is in a box plot. Let's go!

What is the third quartile?

The third quartile (also called upper quartile, most often denoted by Q3), is the value that marks three quarters (75%) of data points when they are sorted in increasing order. In other words, three-quarters of the data points are less than the upper quartile, and one-quarter are greater than the upper quartile. We can also say that the third quartile splits off the highest 25% of data points from the lowest 75% of data points.

🔎 If you're familiar with the notion of percentile, you may have noticed that Q3 coincides with the 75th percentile. Want to understand better? Go to the percentile calculator.

Where is the third quartile in a box plot?

The third quartile is the right side of the box (if horizontal) or the top side (if vertical). The left/bottom side corresponds to the first quartile. Hence, the box's width is exactly the interquartile range (IQR).

How do I find the third quartile?

To compute the third quartile:

  1. Sort your data in increasing order.

  2. Determine the upper half of your data:

    • Even number of observations: Split your data set in half and take the upper half.

    • Odd number of observations: Take all the numbers bigger than the number in the middle of your set.

  3. Compute the upper quartile as the median of the upper half:

    • Odd number of observations: Take the number right in the middle.

    • Even number of observations: Take the average of the two values in the middle.

As you can see, finding the upper quartile is easy in theory but may be hard in practice, especially if the sample is very large. Thankfully, Omni's third quartile calculator can do all this work for you!

🙋 To make your life even easier, Omni's third quartile calculator determines not only the upper quartile but also the two other quartiles: the lower quartile (25th percentile) and the median (the second quartile, 50th percentile) of the data set.

Other Omni quartile tools

Happy with the third quartile calculator? If you want to discover more about quartiles, you can visit the following Omni tools:

FAQ

How do I find the semi-interquartile range given quartiles?

Recall that the semi-interquartile is half the interquartile range. Hence, to compute the semi-interquartile given quartiles:

  1. Compute the difference between the upper quartile and the lower quartile: Q3 - Q1.
  2. You've got the interquartile range. Divide it by 2.
  3. You've found the semi-interquartile!

What is the third quartile of the standard normal distribution?

Q3 = 0.67448 in the standard normal distribution. In any normal distribution, Q3 = μ + 0.67448σ, where μ is the mean and σ is the standard deviation of the normal distribution in question.

Anna Szczepanek, PhD
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