First Quartile Calculator

With Omni's first quartile calculator, you'll never again struggle with calculating the first quartile or, in fact, any other quartile!

Quartiles, particularly the lower quartile, are one of the fundamental notions of descriptive statistics. If you're not yet very familiar with them, in the article below, we'll explain what the first quartile is and how to calculate it (both by hand and with the help of our calculator). We'll also tell you how to localize the first quartile in a box plot. Ready? Scroll down!

The first quartile (a.k.a. the lower quartile) is a measurement of position in a data set. It is the value that marks one quarter (25%) of data points sorted in ascending order. That is, 25% of the data points are less than the first quartile, and 75% of data points are greater than the first quartile. In other words, the lower quartile is the 25th percentile. The lower quarter is most often denoted as Q₁.

To determine the first quartile:

1. Sort your data in ascending order.

2. Determine the lower half of your data:

   • Even number of points: split your set exactly in half and take the lower (left) half.

   • Odd number of points: take all numbers to the left of the number exactly in the middle.

3. Find the median of the lower half:

   • Even number of data points: take the average of the two values in the middle.

   • Odd number of data points: take the number right in the middle.

4. You've found the lower quartile!

As you can see, it is easy to understand how to calculate the first quartile. However, large samples may pose a problem. That's when Omni's first quartile calculator enters the stage to help you calculate the first quartile in no time!

The lower quartile is the bottom side of a vertical box plot and the left side of a horizontal box plot. The other (top/right) side corresponds to the upper (third) quartile. The line inside the box is the median (the second quartile).

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

• Quartile calculator;
• Median calculator; and
• Third quartile calculator.

The interquartile range is the distance between quartiles. You determine it as follows:

1. Write down the lower quartile Q₁ and the upper quartile Q₃.
2. Determine the difference between the upper and lower quartile: Q₃ - Q₁.
3. You've just found the interquartile range IQR!
4. IQR is a measure of spread about the median: the smaller the IQR, the more your data is clumped.

In any normal distribution, Q₁ = μ - 0.67448σ, where μ stands for the mean and σ for the standard deviation of the distribution in question.

In particular, for the standard normal distribution (i.e., μ=0, σ=1) we have Q₁ = -0.67448.