Since our data set has an even number of values, the median could be located by averaging the two central values, in this case 50 and 51. The value of the median is not as important as how it divides the data when considering IQR. We now have two data sets, 1 to 50 in the lower set and 51 to 100 in the higher set. If this formula gives an integer i, take the average of the ith and the next values in the sorted data set.

• An outlier is an observation that lies abnormally far away from other values in a dataset.
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• In a standard normal distribution, the random variable, x, is called a standard score, or a z-score.
• Find the outliers in a data set by entering the numbers in the calculator below.

Such an outlier should definitely be discarded from the dataset. Some outliers signify that data is significantly different from others. For example, it may indicate an anomaly like bank fraud or a rare disease. Our fences will be 6 points below Q1 and 6 points above Q3.

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Some of the software below uses different approaches to calculating quartiles than what we used in the examples above. The difference in the calculations won’t be enough to alter your results significantly. The data below shows the number of daily visitors to a museum. The data below shows a high school basketball player’s points per game in 10 consecutive games.

An outlier is any score that does not fall within the common range of the majority of the scores in a data set. Outliers are either way too high or way too low to be truly representative data. Finding outliers is an important part of ensuring fair statistical reviews of data. Outliers can skew statistical evaluations either What Is the Interquartile Range Rule? up or down causing unrepresentative conclusions. As previously mentioned, the IQR is always used in concert with the median, just as the standard deviation is always used in concert with the mean. We have also mentioned that the median and IQR are trimmed estimators, meaning that they are not affected by outliers.

How to Identify an Outlier in a Dataset

Above, we used the locator method for calculating the IQR, but here are a few other methods you may encounter. This article explains what subsets are in statistics and why they are important. You’ll learn about different types of subsets with formulas and examples for each.

• The empirical rule indicates that
  99.7% of observations are within 3 standard deviations of the mean.
• Any data point less than the Lower Bound or more than the Upper Bound is considered as an outlier.
• Before we can find the interquartile range, we must find the quartiles.
• To find the median, arrange your data in ascending order.
• So, let’s see what each of those does and break down how to find their values in both an odd and an even dataset.
• Bell-shaped (normal) distributions are studied further later
  (for example,
  Chap. 17).
• IQR is used to measure variability by dividing a data set into quartiles.

IQR is used to measure variability by dividing a data set into quartiles. The data is sorted in ascending order and split into 4 equal parts. Q1, Q2, Q3 called first, second and third quartiles are the values which separate the 4 equal parts. When scale is taken as 1.5, then according to IQR Method any data which lies beyond 2.7σ from the mean (μ), on either side, shall be considered as outlier. And this decision range is the closest to what Gaussian Distribution tells us, i.e., 3σ.

How does removing outliers affect the median?

This provides some insight as to when and why we may want to consider the IQR. If there are outliers in a data set, they can throw off both the mean and the standard deviation, causing us to have a less clear picture of our data. Since the median and quartiles are resistant to outliers, it is better to use them if we suspect there are outliers present. The IQR tells us the range of the middle 50% of a data set (where most of the values lie). The interquartile range is often used to find outliers in data.

The first step is to find the quartiles for the data set. Find the outliers in a data set by entering the numbers in the calculator below. Find the interquartile range of eruption duration in the data set faithful. More specifically, the data point needs to fall more than 1.5 times the Interquartile range above the third quartile to be considered a high outlier. This means that a data point needs to fall more than 1.5 times the Interquartile range below the first quartile to be considered a low outlier.

Step 2: Identify the First and Third Quartile

The empirical rule indicates that
99.7% of observations are within 3 standard deviations of the mean. That is,
almost all observations are within three standard deviations of the mean. Now we can answer the question, “What is interquartile range?” We have shown that the IQR is simply the difference in the values of the first and third quartiles, Q1 and Q3.