Published on September 25, 2020 by Pritha Bhandari. Revised on November 11, 2022. In descriptive statistics, the interquartile range tells you the spread of
the middle half of your distribution. Quartiles segment any distribution that’s ordered from low to high into four equal parts. The interquartile range (IQR) contains the second and third quartiles, or the middle half of your data set. Whereas the range gives you the spread of the whole data set, the interquartile range gives you the range of the middle half of a data set. Calculate the interquartile rangeThe interquartile range is found by subtracting the Q1 value from the Q3 value:
Q1 is the value below which 25 percent of the distribution lies, while Q3 is the value below which 75 percent of the distribution lies. You can think of Q1 as the median of the first half and Q3 as the median of the second half of the distribution. Methods for finding the interquartile rangeAlthough there’s only one formula, there are various different methods for identifying the quartiles. You’ll get a different value for the interquartile range depending on the method you use. Here, we’ll discuss two of the most commonly used methods. These methods differ based on how they use the median. Exclusive method vs inclusive methodThe exclusive method excludes the median when identifying Q1 and Q3, while the inclusive method includes the median in identifying the quartiles. The procedure for finding the median is different depending on whether your data set is odd- or even-numbered.
While there is little consensus on the best method for finding the interquartile range, the exclusive interquartile range is always larger than the inclusive interquartile range. The exclusive interquartile range may be more appropriate for large samples, while for small samples, the inclusive interquartile range may be more representative because it’s a narrower range. Steps for the exclusive methodTo see how the exclusive method works by hand, we’ll use two examples: one with an even number of data points, and one with an odd number. Even-numbered data setWe’ll walk through four steps using a sample data set with 10 values.
Odd-numbered data setThis time we’ll use a data set with 11 values.
Steps for the inclusive methodAlmost all of the steps for the inclusive and exclusive method are identical. The difference is in how the data set is separated into two halves. The inclusive method is sometimes preferred for odd-numbered data sets because it doesn’t ignore the median, a real value in this type of data set.
We can see from these examples that using the inclusive method gives us a smaller IQR. With the same data set, the exclusive IQR is 24, and the inclusive IQR is 20. When is the interquartile range useful?The interquartile range is an especially useful measure of variability for skewed distributions. For these frequency distributions, the median is the best measure of central tendency because it’s the value exactly in the middle when all values are ordered from low to high. Along with the median, the IQR can give you an overview of where most of your values lie and how clustered they are. The IQR is also useful for datasets with outliers. Because it’s based on the middle half of the distribution, it’s less influenced by extreme values. Visualize the interquartile range in boxplotsA boxplot, or a box-and-whisker plot, summarizes a data set visually using a five-number summary. Every distribution can be organized using these five numbers:
The vertical lines in the box show Q1, the median, and Q3, while the whiskers at the ends show the highest and lowest values. In a boxplot, the width of the box shows you the interquartile range. A smaller width means you have less dispersion, while a larger width means you have more dispersion. An inclusive interquartile range will have a smaller width than an exclusive interquartile range. Boxplots are especially useful for showing the central tendency and dispersion of skewed distributions. The placement of the box tells you the direction of the skew. A box that’s much closer to the right side means you have a negatively skewed distribution, and a box closer to the left side tells you that you have a positively skewed distribution. Frequently asked questions about the interquartile rangeWhat are the two main methods for calculating interquartile range? The two most common methods for calculating interquartile range are the exclusive and inclusive methods. The exclusive method excludes the median when identifying Q1 and Q3, while the inclusive method includes the median as a value in the data set in identifying the quartiles. For each of these methods, you’ll need different procedures for finding the median, Q1 and Q3 depending on whether your sample size is even- or odd-numbered. The exclusive method works best for even-numbered sample sizes, while the inclusive method is often used with odd-numbered sample sizes. Cite this Scribbr articleIf you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.
Is this article helpful?You have already voted. Thanks :-) Your vote is saved :-) Processing your vote... What are the 5 functions in Excel?The most frequently used functions in Excel are:. AutoSum;. IF function;. LOOKUP function;. VLOOKUP function;. HLOOKUP function;. MATCH function;. CHOOSE function;. DATE function;. Why would you use now () in a formula quizlet?The NOW function is useful when you need to display the current date and time on a worksheet or calculate a value based on the current date and time, and have that value updated each time you open the worksheet.
What are formulas and functions in Excel?Formula is an expression that calculates values in a cell or in a range of cells. For example, =A2+A2+A3+A4 is a formula that adds up the values in cells A2 through A4. Function is a predefined formula already available in Excel.
Which function would you use if you wanted to count the number of values but ignore cells that have text or are empty?COUNTA doesn't count empty or blank cells. You need the COUNTBLANK function for that. More on COUNTBLANK below.
|