Question

The table shows the annual compensation of 40 randomly chosen CEOs (millions of dollars). 4.91 1.79 23.00 7.34 13.40 5.22 2.22 4.94 193.74 16.26 24.98 8.68 10.19 16.34 2.59 3.62 86.09 13.11 27.77 6.61 8.96 5.59 1.87 4.88 24.19 15.46 18.97 5.72 8.28 2.70 0.74 3.70 36.83 16.45 20.29 7.34 9.57 4.29 1.66 2.33

. (c) Identify any unusual values. (Round your answers to 2 decimal places.) There are two unusual values: million and million.

Answer 1

Data on quartile value and Inter-quartile range:

Q1 = Median of the lower half of the data = (10th + 11th observation)/2

= (3.7+4.29)/2

= 3.995

Q3 = Median of the upper half of the data = (30th + 31th observation)/2

= (16.34+16.45)/2

= 16.395

IQR = Q3-Q1

= 16.395-3.995

= 12.4

Lower boundary for outlier: Q1 - 3*IQR

= 3.995 - 3*12.4

= -33.205

Upper boundary for outlier: Q3 + 3*IQR

= 53.595

These both are hard outlier boundaries as we have taken a factor of 3*IQR to calculate the outlier boundary and not 1.5*IQR which produces boundaries for soft outliers.

As we can see there are no values which are lower than lower boundary for outliers while there are two values which are higher than the upper boundary of outliers. These are:

86.09 millions of dollars

193.74 millions of dollars

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