The five-number summary for a variable X is given below. Calculate values of X that are considered to be outliers. Min Q1 Median Q3 Max 10 50 80 90 100
Question
The five-number summary for a variable X is given below. Calculate values of X that are considered to be outliers. Min Q1 Median Q3 Max 10 50 80 90 100
Solution
To identify outliers, we can use the Interquartile Range (IQR) method. The IQR is the range between the first quartile (25 percentile) and the third quartile (75 percentile). Here are the steps:
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Calculate the IQR: Q3 - Q1 = 90 - 50 = 40.
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Calculate the lower bound for outliers: Q1 - 1.5IQR = 50 - 1.540 = -10.
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Calculate the upper bound for outliers: Q3 + 1.5IQR = 90 + 1.540 = 150.
So, any values of X that are less than -10 or greater than 150 would be considered outliers. However, in this dataset, the minimum value is 10 and the maximum value is 100, so there are no outliers.
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