How to Identify an Outlier Using IQR and Z Score Methods
In a data collection, outliers are stragglers, which means they are extremely high or extremely low values. In simple words, it’s the data that lies outside other values in a set.
For example, we have a set of random numbers as follows,
2, 98, 101, 103, 106, 109, 112, 205
Here, 2 and 205 are the outliers.
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Most of the data points clustered along the straight line very closely, as you can see in the above chart. The outlier is far from other points.
Outlier Meaning
An outlier is an observation in which in a random sample of a population lies an abnormal distance from other values. In a way, this definition leaves it up to the analyst to determine what would be considered abnormal. It is important to classify normal observations before abnormal observations can be picked out.
Defining Outliers
Examination for important features, including symmetry and deviations from assumptions, of the overall shape of the graphed results.
Examination of the information for odd findings that are far away from the data collection. Such points are also classified as outliers.
Inliers
An Inlier, on the other hand, is an inaccurate data value that is simply within a statistical distribution, making it difficult to separate it from good data values. A simple example of an inlier might be a value recorded in the incorrect units in a record, say degrees Fahrenheit rather than degrees Celsius.
Extreme and Mild Outlier
Mild Outlier:
The data values below the first quartile or above the third quartile that lie between 1.5 times and 3.0 times the interquartile scale.
Extreme Outlier:
Any data values that lie more than 3.0 times the interquartile range below the first quartile or above the third quartile are extreme outliers.
How to Find Outliers?
Extreme Value Analysis: The statistical tails of the underlying data distribution are measured.
Probabilistic and Statistical models: From a probabilistic model of the data, evaluate unlikely instances.
Linear Models: Projection techniques that use linear correlations to model the data into lower dimensions. Outliers can be, for instance, main component analysis and data with significant residual errors.
Proximity-based Models: Data instances as determined by cluster, density or nearest neighbor analysis that is separated from the mass of the data.
Information-Theoretic Models: Outliers are detected as data instances that increase the complexity of the dataset (minimum code length).
High-Dimensional Outlier Detection: Methods that scan outlier subspaces provide a higher-dimensional breakdown of distance-based measures.
Causes of Inlier and Outlier
1. Human Mistakes: Errors in data entry.
2. Instrument Mistakes: Errors in the calculation.
3. Experimental Errors: Extraction of data or planning/executing errors for experiments.
4. Intentional: Dummy outliers for evaluating methods of detection.
5. Errors in Data Processing: Data manipulation or unwanted mutations in the data collection.
6. Errors in Sampling: Collecting or combining data from incorrect or different sources.
Uses of Outliers
Outliers help in Fraud detection, fraudulent loan applications, Intrusion detection in the networks, Activity monitoring, Network performance, Satellite image analysis, Detecting novelties in images, Detecting mislabelled data, and many more.
Fun Fact
Do you know that there is an outlier company which is actually a clothing entity? You can find different kinds of outlier jeans which are famous among the people especially the outlier chinos.
Conclusion
Outliers should be properly investigated. They also provide useful information about the procedure under review or the process of collecting and documenting data. One should try to understand why they occurred and whether similar values are likely to continue to occur before contemplating the potential removal of these points from the results. Outliers are considered bad data points most of the time.
FAQs on Outlier in Statistics Explained Clearly
1. What is an outlier in statistics?
An outlier is a data value that is significantly higher or lower than the rest of the values in a dataset. It does not follow the overall pattern of the data and may indicate variability, measurement error, or unusual behavior.
- Outliers can occur in small or large datasets.
- They can strongly affect the mean and standard deviation.
- They are commonly identified using graphs like box plots or formulas such as the IQR rule.
2. How do you identify an outlier using the IQR method?
An outlier using the Interquartile Range (IQR) method is any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR. Follow these steps:
- Find Q1 (first quartile) and Q3 (third quartile).
- Compute IQR = Q3 − Q1.
- Calculate lower limit: Q1 − 1.5×IQR.
- Calculate upper limit: Q3 + 1.5×IQR.
- Any value outside these limits is an outlier.
3. What is the formula for detecting outliers?
The most common formula for detecting outliers is based on the IQR rule: values less than Q1 − 1.5×IQR or greater than Q3 + 1.5×IQR are outliers. Another method uses the Z-score:
- Z = (x − μ) / σ
- If |Z| > 3, the value is often considered an outlier.
4. Can you give an example of finding an outlier?
An outlier can be found by applying the IQR rule to a dataset such as 2, 4, 5, 6, 8, 50.
- Q1 = 4, Q3 = 8
- IQR = 8 − 4 = 4
- Lower limit = 4 − 1.5×4 = −2
- Upper limit = 8 + 1.5×4 = 14
- Since 50 > 14, 50 is an outlier.
5. How do outliers affect the mean and median?
Outliers strongly affect the mean but usually have little effect on the median.
- The mean uses all values, so extreme numbers shift it significantly.
- The median depends only on position, so it remains more stable.
- Because of this, the median is preferred when outliers are present.
6. What is the difference between an outlier and extreme value?
An outlier is a value that lies outside the expected statistical range, while an extreme value is simply very high or low but may still follow the data pattern.
- Outliers are identified using formal rules like IQR or Z-scores.
- Extreme values are visually large or small but not always statistically unusual.
- All outliers are extreme, but not all extreme values are outliers.
7. Should outliers always be removed from data?
Outliers should not always be removed; they should only be removed if they are errors or irrelevant to the study.
- If caused by measurement error, removal is reasonable.
- If they represent real variation, they should be kept.
- Always analyze the context before deleting data.
8. How do you find outliers using a box plot?
A box plot shows outliers as individual points beyond the whiskers.
- The box represents Q1 to Q3.
- The line inside the box is the median.
- Whiskers extend to 1.5×IQR from Q1 and Q3.
- Points beyond the whiskers are outliers.
9. What is a Z-score outlier?
A Z-score outlier is a value whose Z-score is greater than 3 or less than −3. The formula is:
- Z = (x − μ) / σ
10. Why is it important to detect outliers?
Detecting outliers is important because they can distort statistical analysis and conclusions.
- They can change the mean and standard deviation.
- They may indicate experimental errors.
- They can reveal important unusual events or trends.
- Identifying outliers improves data accuracy and reliability.
