Question

in the data set below, what is the interquartile range? 51 97 18 52 66 85 44 16 24 13 18 46

Explanation:

Step1: Sort the data set

$$13, 16, 18, 18, 24, 44, 46, 51, 52, 66, 85, 97$$

Step2: Find the median (Q2)

Since there are \(n = 12\) data points, the median is the average of the \(6^{th}\) and \(7^{th}\) values.
\(Q2=\frac{44 + 46}{2}=45\)

Step3: Find the lower half and Q1

The lower half is \(13, 16, 18, 18, 24, 44\). The median of the lower half (Q1) is the average of the \(3^{rd}\) and \(4^{th}\) values.
\(Q1=\frac{18+18}{2} = 18\)

Step4: Find the upper half and Q3

The upper half is \(51, 52, 66, 85, 97\). The median of the upper half (Q3) is the average of the \(3^{rd}\) and \(4^{th}\) values.
\(Q3=\frac{66 + 85}{2}=75.5\)

Step5: Calculate the inter - quartile range (IQR)

\(IQR=Q3 - Q1\)
\(IQR=75.5-18 = 57.5\)

Answer:

\(57.5\)