Question

car dealership | number of cars sold
gmc | 84
chevrolet | 81
nissan | 92
toyota | 92
ford | 95
honda | 94
hyundai | 80
acura | 72
what is the interquartile range of this set of data?
○ 5
○ 7.5
○ 12.5
○ 23

Explanation:

Step1: Sort the data

First, sort the number of cars sold in ascending order: \(72, 80, 81, 84, 92, 92, 94, 95\)

Step2: Find the median

Since there are \(n = 8\) data points (even number), the median is the average of the \(\frac{n}{2}\) - th and \((\frac{n}{2}+1)\) - th values. The median \(Q_2=\frac{84 + 92}{2}=88\)

Step3: Find \(Q_1\) and \(Q_3\)

The lower half of the data is \(72, 80, 81, 84\). The median of the lower half (\(Q_1\)) is \(\frac{80+81}{2}=80.5\)
The upper half of the data is \(92, 92, 94, 95\). The median of the upper half (\(Q_3\)) is \(\frac{92 + 94}{2}=93\)

Step4: Calculate the inter - quartile range (IQR)

The formula for IQR is \(IQR=Q_3 - Q_1\). Substitute \(Q_1 = 80.5\) and \(Q_3=93\) into the formula: \(IQR=93-80.5 = 12.5\)

Answer:

12.5