How to find if there are outliers, given mean, median, etc

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In summary, the conversation discusses how to solve a statistics question without a histogram. It suggests using a boxplot and defines an outlier as any data point beyond 1.5 times the interquartile range. The conversation also provides an example of finding outliers using this method.
  • #1
chriskeller1
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Hi guys, I'm getting ready for a stats exam and one of the questions looks like this
View attachment 3406
If I'm not given a histogram, how can this be solved?
 

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  • #2
I think a boxplot can be useful here. Have you tried to draw the boxplot?
 
  • #3
chriskeller1 said:
Hi guys, I'm getting ready for a stats exam and one of the questions looks like this
https://www.physicsforums.com/attachments/3406
If I'm not given a histogram, how can this be solved?

You do not need to do a box plot but you can adopt the conventional definition of outlier that corresponds to the whiskers of a box and whiskers plot. Then your definition of an outlier is any datum that lies beyond 1.5 times IQR of the 1st or 3rd quartiles.

Now the IQR=16.7-10.8=5.9, any datum that is less than 10.8-1.5 IQR= 1.95 or larger than 16.7 + 1.5 IQR = 25.55 is an outlier. Since the maximum is 25.8 there must be (mild) upper outliers.

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1. How do I calculate the interquartile range (IQR)?

The interquartile range is calculated by finding the difference between the third quartile (Q3) and the first quartile (Q1). This can be represented by the formula IQR = Q3 - Q1.

2. What is considered an outlier?

An outlier is a data point that falls significantly outside the expected range of values for a dataset, often defined as being more than 1.5 times the interquartile range above the third quartile or below the first quartile.

3. How do I determine if a data point is an outlier?

A data point can be considered an outlier if it falls more than 1.5 times the interquartile range above the third quartile or below the first quartile. This can be determined by calculating the z-score of the data point and comparing it to a threshold of 3. If the z-score is greater than 3, the data point is considered an outlier.

4. Can I use mean and median to identify outliers?

Yes, the mean and median are measures of central tendency that can be used to identify outliers. A data point that is significantly higher or lower than the mean or median may be considered an outlier.

5. How do I handle outliers in my data?

There is no one definitive answer for how to handle outliers in data. It ultimately depends on the specific dataset and the goals of the analysis. Some options for handling outliers include removing them from the dataset, transforming the data, or using robust statistical methods that are less affected by outliers.

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