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.
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