Explain whether there are any outliers in these data or not. The 5-number summary for the run times in minutes of the 150 highest grossing movies of 2010 is provided.

Question
Explain whether there are any outliers in these data or not.
The 5-number summary for the run times in minutes of the 150 highest grossing movies of 2010 is provided.

Answers (1)

2020-10-21
Calculation:
Inter quartile range:
In contrast to the range, which measures only differences between the extremes, the inter quartile range (also called mid spread) is the difference between the third quartile and the first quartile. Thus, it measures the variation in the middle 50 percent of the data, and, unlike the range, is not affected by extreme values. \(IQR = Q_{3} - Q_{1}\),
From the given 5-number summary for the run times in minutes \(Q_{1} = 98\ and\ Q_{3} = 116\).
\(IQR = Q_{3} - Q_{1}\)
\(= 116-98=18\)
Thus, the interquartile range is 18.
Outlier Rule:
If any observation is greater than \(Q_{3} + 1.5\) IQR or less than \(Q_{1} — 1.5\) IQR then that observation is considered as high or low outlier.
\(Upper fence = Q_{3} + 1.5\) IQR
\(= 116 + 1.5(18)= 116+27= 143\)
Here the maximum value 160 which is greater than the upper fence 143. Hence 160 is considered as the higher outlier.
\(Lower fence = Q_{1} — 1.5/\)IQR
\(= 98 — 1.5(18)\)
\(= 98-27=71\)
Here the minimum value 43 which is below the lower fence 71. Hence, 43 is considered as the low outlier.
Thus, there is a high and a low outlier in these data.
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