Question

1. the following data set represents the cost of an order (rounded to the nearest dollar) in a fast - food drive thru. 10, 21, 34, 12, 6, 3, 14, 18, 22, 29, 9, 2, 15, 12, 18

q1:
q3:
iqr:

Explanation:

Step1: Sort the data set

First, sort the data set \(3,6,9,10,12,14,15,18,18,21,22,29\) in ascending - order. There are \(n = 12\) data points.

Step2: Find the first - quartile (Q1)

The position of Q1 is \(i=\frac{n + 1}{4}=\frac{12+1}{4}=3.25\). So, \(Q1=9+(0.25)\times(10 - 9)=9.25\).

Step3: Find the third - quartile (Q3)

The position of Q3 is \(i = \frac{3(n + 1)}{4}=\frac{3\times(12 + 1)}{4}=9.75\). So, \(Q3=18+(0.75)\times(21 - 18)=20.25\).

Step4: Calculate the inter - quartile range (IQR)

The inter - quartile range \(IQR=Q3 - Q1\). Substitute \(Q1 = 9.25\) and \(Q3=20.25\) into the formula: \(IQR=20.25−9.25 = 11\).

Answer:

Q1: \(9.25\)
Q3: \(20.25\)
IQR: \(11\)