Question

It is known that the three largest values of a data set are 6.9, 7.8, and...

It is known that the three largest values of a data set are 6.9, 7.8, and 8.7; and the three smallest values of the same data set are 2.8, 2.7, and 2.4. If the quartiles are Q1 = 4.5, Me = 5.4 ands Q3 = 6.0, calculate the length of the upper and lower whiskers of a box plot.

A.

length of the lower whisker = 2.1   and length of the upper whisker = 1.8

B.

length of the lower whisker = 1.25   and   length of the upper whisker = 1.25

C.

None of the other three answers.

D.

length of the lower whisker = 1.7   and   length of the upper whisker = 1.5

Homework Answers

Answer #1

Given that , three largest values of a data set are 6.9, 7.8, and 8.7; and the three smallest values of the same data set are 2.8, 2.7, and 2.4. The quartiles are Q1 = 4.5, Median(Q2)= 5.4 and Q3 = 6.0

Since, we know

Lower whisker = smallest value greater than Q1-1.5*IQR


Upper Whisker = greatest value smaller than Q3+1.5*IQR

Where, IQR = Q3 - Q1

Here, IQR = 6.0 - 4.5 = 1.5

Lower whisker = 6.9 - 1.5(1.5) = 4.65

Upper Whisker = 2.8 + 1.5(1.5) = 5.05

Hence we get,

Upper Whisker = 5.05 and Lower whisker = 4.65

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