Question

Consider the following ordered data.6 9 9 10 11 11 12 13 14(a) Find the low, Q1, median, Q3, and high.(b) Find the interquartile range.

Answer 1

6 ; 9 ; 11 ; 12.5; 14

B.) 3.5

Explanation:

Given the data:

6 9 9 10 11 11 12 13 14

a.) The low = 6 (lowest value in the dataset)

b.) Q1 = Lower quartile

Q1 = 1/4(n + 1)th term

n = sample size = 9

Q1 = 1/4(9 + 1) ; 1/4(10) = 2.5th term

Q1 = (2nd + 3rd term) / 2 = (9 + 9) / 2 = 9

Median Q2:

Q2 = 1/2(9 + 1) ; 1/2(10) = 5th term = 11

Upper Quartile Q3:

Q3 = 3/4(9 + 1) ; 3/4(10) = 7.5th term

Q3 = (7th + 8th term) / 2 = (12 + 13) / 2 = 12.5

Interquartile range (Q3 - Q1)

(12.5 - 9) = 3.5

The high = 14 (highest value in the dataset)