Identify any outlier(s) in the data. {52, 61, 42, 46, 50, 51, 49, 44, 40, 66, 53, 67, 45, 64, 60, 69}

An outlier in statistics is a data point that deviates considerably from other observations. An outlier can be caused by measurement variability or by experimental mistake; the latter is sometimes eliminated from the data set.

To find the outlier for the given data set follow the given steps.

Step one: The first step is to find the quartiles for the data set.

For this data set, the quartiles are:

Q1 = 45.5

Q3 = 62.5

Step Two: Find the Interquartile Range

The interquartile range is the difference between the first and third quartiles.

IQR = Q3 - Q1

IQR = 45.5 - 62.5

IQR = 17

Step Three:

The next step is to set up a fence beyond the first and third quartiles using the interquartile range.

Lower Fence = Q1 - (1.5 × IQR)

Lower Fence = 45.5 - (1.5 × 17)

Lower Fence = 20

Upper Fence = Q3 + (1.5 × IQR)

Upper Fence = 62.5 + (1.5 × 17)

Upper Fence = 88

Step Four: Find the Outliers

Any numbers in the data that are above or below the fences are outliers.

Since there are no numbers outside the two fences. Hence, it can be concluded that the given data set does not have, any outlier.

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