Question

Consider the following data set showing the number of days with hail in six randomly chosen years in Denver:

D = {2,3,6,14,21,X}

The number X is not legible, but we do know that X > 21.

The following questions involve numbers from the 5-number summary for this data set.

a) what is the third quartile, Q₃?

b) what is the interquartile range?

c)use the 1.5 IQR criterion to determine the value C such that if X ≤ C , then X would not be an outlier and if X > C , then X would be an outlier.

Answer 1

(a)

Arranging numbers in ascending order, we get:

2,3,6,14,21,X

Upper half is:

14,21,X

Middle of these numbers = 21.

So,

the third quartile, Q3 = 21

So,

Answer is:

21

(b)

Bottom Half is:

2,3,6

Middle of these numbers = 3

So,

Q1 = 3

So,

the interquartile range = IQR = Q3 - Q1 = 31 - 3 = 18

So,

Answer is:

18

(c)

Lower Fence = Q1 - (1.5 X IQR) = 3 - (1.5 X 18) = 3 - 27 = - 24

Upper Fence = Q3 + (1.5 X IQR) = 31 + (1.5 X 18) = 3 + 27 = 30

The value of C= 30 If X ≤ C , then X would not be an outlier and if X > C , then X would be an outlier.

So,

Answer is:

30