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A store sells 12 different kinds of bathtubs. These data represent the maximum number of liters of water that the bathtubs will hold.

240, 272, 280, 285, 295, 285, 300, 290, 310, 305, 285, 305

Identify all outliers of the data set. Use the values of the upper and lower fences to explain your answer.

Oct 3, 2019

#1
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240, 272, 280, 285, 295, 285, 300, 290, 310, 305, 285, 305

Order the data from low to high

240, 272, 280, 285, 285, 285, 290, 295, 300, 305, 305, 310

The median is [285 + 290 ] / 2  = 287.5

The first quartile, Q1, is  [ 280 + 285]/2  = 282.5

The third quartile, Q3, is  [ 300+305] /2  = 302.5

The interquartile range  is   Q3 - Q1  =  302.5 - 282.5  =  20

Inner fence

Lower bound  =  Q1 - 1.5 (Q3 - Q1) =  282.5 - 1.5 (20)  = 252.5

Upper  bound =  Q3 + 1.5 (Q3 - Q1)  = 302.5 + 1.5(20)  =  332.5

Any data point falling outside these bounds (inner fence) is a minor outlier

So.....240  would be a minor outlier

Outer Fence

Lower Bound  =  Q1 - 3 (Q3 - Q1)  = 282.5 - 3(20)  = 222.5

Upper Bound  =  Q3 + 3(Q3 -Q1)  = 302.5 + 3(20)  = 362.5

Any data point falling  outside these bounds (outer fence)  is a major outlier

Note that no value is a major outlier   Oct 3, 2019