8. Consider the MINITAB output shown here. You do not have access to all the dat
ID: 3232681 • Letter: 8
Question
8. Consider the MINITAB output shown here. You do not have access to all the data, but you have been told that the largest five numbers are 70, 86, 86, 86, and 93. Which of the following statements are true?
I. The data are skewed to the right.
II. This data set has more than one outlier.
III. We are justified in using z-procedures here because we are given the mean and median.
Worksheet size: 3500 cells MTB > Describe C1.
N MEAN MEDIAN TRMEAN STDEV SEMEAN
C1 50 34.74 28.00 32.98 21.82 3.09
MIN MAX Q1 Q3
C1 3.00 93.00 18.75 45.50
Worksheet size: 3500 cells MTB > Describe C1.
N MEAN MEDIAN TRMEAN STDEV SEMEAN
C1 50 34.74 28.00 32.98 21.82 3.09
MIN MAX Q1 Q3
C1 3.00 93.00 18.75 45.50
Explanation / Answer
Answer
II. This data set has more than one outlier.
Hint:
Interquartile range, IQR = Q3 – Q1 = 45.50 – 18.75 = 26.75
IQR * 1.5 = 26.75 * 1.5 = 40.125
Q3 + 1.5(IQR) = 45.50 + 40.125 = 85.625
Let us check whether there is any numbers greater than 85.625 in the data.
Clearly 86, 86, 86, and 93 are outliers.
Hence we can conclude that this data set has more than one outlier.
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