A dataset consists of 20 distinct observations with a summation of 600. The firs

Question

A dataset consists of 20 distinct observations with a summation of 600. The first quartile, median, and third quartile of this dataset are calculated as 16.5, 22.5, and 38, respectively. Also, we know that the two highest observations in this dataset are 52.2 and 112. a. Are either of the two highest observations mild or extreme outliers? Explain. b. if we add 5 to each of the two highest observations, what is the new mean? c. Note that 112 is the maximum value in this dataset. If we decrease this observation by 50, what is the new median?

Explanation / Answer

Given Q1=16.5, median=22.5, Q3=38

IQR= Q3-Q1 = 38-16.5 = 21.5

a) Extreme outlier limits are => Q1-3*IQR = 16.5-3*21.5=-48 TO Q3+3*IQR = 38+3*21.5 = 102.5

Mild outlier limits are => Q1-1.5*IQR = 16.5-1.5*21.5= -15.75 TO Q3+1.5*IQR = 38+1.5*21.5= 70.25

52.2 lies within the limits but 112 is more extreme than the extreme outlier limits

Hence 112 is an extreme outlier.

b) The sum of all observations is 600.

Since 5 is added to each of the two highest observations the new total is 610.

therefore new mean= 610/20 = 30.5

c) If we subtract 50 from 112 we get 62 which is still the highest observation.

So there is no change in the median.

Therefore the median is 22.5.

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