The options are skewed to the right or left or symmetric why?colser to mix?min?e
ID: 3207611 • Letter: T
Question
The options are
skewed to the right or left or symmetric
why?colser to mix?min?exactly halfway?
During a recent semester at a large national university, students having accounts on a mainframe computer had hard drive use (in kilobytes) described by the five-number summary, minimum = 647, Q1 = 653, median = 747, Q3 = 1028, and maximum = 170,000. Complete parts a and b below. Would you expect this distribution to be symmetric, skewed to the right, or skewed to the left? Explain. Fill in the blanks to complete the statement below. The distribution is, because the median is Use the 1.5 times IQR criterion to determine all potential outliers that are present. Choose the correct answer below. Since the maximum value is not within 1.5 times IQR of Q3, there is at least one outlier. Since the minimum value is not within 1.5 times IQR of Q1, there is at least one outlier. Since the minimum value is not within 1.5 times IQR of Q1 and the maximum value is not within 1.5 times IQR of Q3, there are at least two outliers. Since the minimum value is within 1.5 times IQR of Q1 and the maximum value is within 1.5 times IQR of Q3, there are no potential outliers.Explanation / Answer
It is given that for a set of data,
minimum=X=647,
Q1=653,
Q2=747,
Q3=1028,
and maximum=Y=170,000
a)
Q3-Q2=1028-747=281
Q2-Q1=747-653=94
As Q3-Q2>Q2-Q1, the distribution is skewed to the right (Bowley’s Criteria).
Therefore,
The distribution is skewed to the right, because the median is closer to Q1 than Q3.
b)
The 1.5*IQR criterion says that an observation is an outlier if it is greater than Q3+ [1.5*IQR] or less than Q1-[1.5*IQR]
IQR=Interquartile Range=Q3-Q1=1028-653=375
Hence Q3+ [1.5*IQR] =1028+ [1.5*375] =1590.5
And Q1-[1.5*IQR] =653-[1.5*375] =90.5
Out of the given data points X, Q1, Q2, Q3 and Y, only Y satisfies the above criterion.
We can conclude that there is at least one outlier in the data, since we do not know any other data points (Observations).
Therefore option “a” is the correct one.
a.Since the maximum value is not within 1.5*IQR of Q3, there is at least one outlier.