In broad strokes, there are three causes for outliers—data entry or measurement errors, sampling problems and unusual conditions, and natural variation.

An outlier is a number that is at least 2 standard deviations away from the mean. For example, in the set, 1,1,1,1,1,1,1,7, 7 would be the outlier.

Given mu and sigma, a simple way to identify outliers is to compute a z-score for every xi, which is defined as the number of standard deviations away xi is from the mean […] Data values that have a z-score sigma greater than a threshold, for example, of three, are declared to be outliers.

Outliers are often easy to spot in histograms. For example, the point on the far left in the above figure is an outlier. A convenient definition of an outlier is a point which falls more than 1.5 times the interquartile range above the third quartile or below the first quartile.

An outlier is a person who is detached from the main body of a system. An outlier lives a rather special life compared to the majority of people.

Removing the outlier decreases the number of data by one and therefore you must decrease the divisor. For instance, when you find the mean of 0, 10, 10, 12, 12, you must divide the sum by 5, but when you remove the outlier of 0, you must then divide by 4.

5 ways to deal with outliers in data

1. Set up a filter in your testing tool. Even though this has a little cost, filtering out outliers is worth it.
2. Remove or change outliers during post-test analysis.
3. Change the value of outliers.
4. Consider the underlying distribution.
5. Consider the value of mild outliers.

If you go by standard convention removing an outlier will cause the standard deviation to decrease. In general though, an outlier is a data point that is extreme for the distribution of the observed data.

Standard deviation is sensitive to outliers. A single outlier can raise the standard deviation and in turn, distort the picture of spread. For data with approximately the same mean, the greater the spread, the greater the standard deviation.

We also see that the outlier increases the standard deviation, which gives the impression of a wide variability in scores. This makes sense because the standard deviation measures the average deviation of the data from the mean.

Mean and Standard Deviation Method If a value is a certain number of standard deviations away from the mean, that data point is identified as an outlier. The more extreme the outlier, the more the standard deviation is affected.

Using Z-scores to Detect Outliers Z-scores are the number of standard deviations above and below the mean that each value falls. For example, a Z-score of 2 indicates that an observation is two standard deviations above the average while a Z-score of -2 signifies it is two standard deviations below the mean.

Outliers. One definition of outliers is data that are more than 1.5 times the inter-quartile range before Q1 or after Q3. Since the quartiles for the standard normal distribution are +/-. 67, the IQR = 1.34, hence 1.5 times 1.34 = 2.01, and outliers are less than -2.68 or greater than 2.68.

When working with box plots, the IQR is computed by subtracting the first quartile from the third quartile. In a standard normal distribution (with mean 0 and standard deviation 1), the first and third quartiles are located at -0.67448 and +0.67448 respectively. Thus the interquartile range (IQR) is 1.34896.

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population. In a sense, this definition leaves it up to the analyst (or a consensus process) to decide what will be considered abnormal.

The interquartile range (IQR) is the distance between the first and third quartile marks. The IQR is a measurement of the variability about the median. More specifically, the IQR tells us the range of the middle half of the data.

Why we use 1.5IQR: Compare this – heuristically – with a normal distributions where 68% are within ±σ, so in that case IQR would be slightly less than σ. Cutting at ±1.5IQR is therefore somewhat comparable to cutting slightly below ±3σ, which would declare about 1% of measurements outliers.

The IQR cannot be negative because you subtract the larger quartile from the smaller one, always resulting positive, even with negative numbers. It is a range, so it has to be positive.

As a “rule of thumb”, an extreme value is considered to be an outlier if it is at least 1.5 interquartile ranges below the first quartile (Q1), or at least 1.5 interquartile ranges above the third quartile (Q3). …

– If our range has a natural restriction, (like it can’t possibly be negative), it’s okay for an outlier limit to be beyond that restriction. – If a value is more than Q3 + 3*IQR or less than Q1 – 3*IQR it is sometimes called an extreme outlier.