Which of the following statements is true for an outlier?It is a data point that is below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR.It is a data point that is below or above Q3 ± 1.5 x IQR.It is a data point that is below or above Q1 ± 1.5 x IQR. It is a data point that is between Q1 + 1.5 x IQR and Q3 - 1.5 x IQR.
Question
Which of the following statements is true for an outlier?It is a data point that is below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR.It is a data point that is below or above Q3 ± 1.5 x IQR.It is a data point that is below or above Q1 ± 1.5 x IQR. It is a data point that is between Q1 + 1.5 x IQR and Q3 - 1.5 x IQR.
Solution
The correct statement is: "It is a data point that is below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR."
Here's why:
In statistics, an outlier is an observation that lies an abnormal distance from other values in a random sample from a population. The interquartile range (IQR) is a measure of statistical dispersion, being equal to the difference between the upper and lower quartiles, Q3 and Q1, respectively.
The rule you're referring to is commonly known as the "1.5xIQR rule for outliers", and it states that a data point is considered an outlier if it is below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR.
The other statements are incorrect because they either include data points that are not considered outliers (like those between Q1 + 1.5 x IQR and Q3 - 1.5 x IQR) or they exclude data points that are considered outliers (like those below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR).
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