The IQR is a useful measure of how spread out the data points in your data set are from the mean. High values indicate that the data points spread out more than they cluster closely together around the mean, while low values suggest that they cluster more tightly.
To calculate the IQR, you need to divide your data into two equal parts. The first part is called the lower quartile (Q1) and the second is the upper quartile (Q3).
It’s a robust measure
The interquartile range (IQR) is a common measure of statistical dispersion. It is calculated by subtracting the third quartile from the first quartile, representing the middle half of your data set.
Because the IQR is affected by only the middle 50% of your data, it’s robust to outliers. In fact, it’s so robust that some statisticians use a combination of the IQR and a central tendency to get a fuller picture of your data’s distribution.
IQR is one of the most common measures of variability, and it is particularly useful for outliers and skewness. However, it’s not suitable for all normally-shaped distributions, as it doesn’t work well when the underlying data is contaminated with a mixture of two normal distributions.
It’s a measure of central tendency
A measure of central tendency is used when the data in a set tends to cluster around a single mean. This is usually the case for ordinal and interval/ratio variables.
For symmetric numerical data, the mode, median and mean report the most common values in the distribution. For skewed data, they are often replaced with the interquartile range or other percentile-based measures.
To Calculate IQR, divide your data into four even parts, or quarters, called quartiles. Each quartile contains a specific number of data points.
The interquartile range is the difference between the upper and lower quartiles. It is also known as the interquartile spread, middle 50%, fourth spread and H-spread.
The IQR is used to build box plots, simple graphical representations of probability distributions. It’s also a good way to identify outliers.
It’s a measure of skewed distributions
The interquartile range is an excellent measure of skewed distributions because it doesn’t rely on extreme values. This means it doesn’t suffer from the same kinds of errors as the more common mean and standard deviation.
IQR is also a good way to find outliers in data. Outliers are observations that fall below Q1-1.5 IQR or above Q3+1.5 IQR.
In box plots, the highest and lowest occurring values are indicated by a series of whiskers that stretch across the box. Any data point that falls outside the whiskers is an outlier.
The IQR can be calculated by taking a figure from the third quartile and subtracting it from the first quartile. It is useful to compare with other measures of central tendency, like the median, for a complete picture of your distribution.
It’s a measure of outliers
Outliers are data points that don’t quite “fit” into a pattern on your dataset. They may indicate an experimental error, measurement variability, or anomaly that needs further investigation.
Outlying data can have a detrimental impact on the mean and standard deviation of your data set, and should be eliminated from your dataset. You can identify outliers using z-scores, which convert extreme data points into a number that shows how far they deviate from the mean.
IQR, which stands for interquartile range, is another measure of outliers. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).
Using IQR, you can create box plots that display your distributional characteristics, including your outliers. It also allows you to detect outliers before they cause any problems with your data analysis.