Question

find the range and interquartile range (iqr) of the data set:
21, 38, 42, 37, 40, 38, 24, 66, 40, 54, 28, 40

• press each hotspot.
• label the corresponding number below with the requested value.

range iqr

Explanation:

Step1: Sort the data set

First, sort the data set \(21,24,28,37,38,38,40,40,40,42,54,66\).

Step2: Calculate the range

The range is the difference between the maximum and minimum values.
\(\text{Range}=66 - 21=45\)

Step3: Find the median (Q2)

Since there are \(n = 12\) data points, the median is the average of the \(6^{th}\) and \(7^{th}\) values. \(Q2=\frac{38 + 40}{2}=39\)

Step4: Find Q1 and Q3

The lower half of the data is \(21,24,28,37,38,38\). The median of the lower half (\(Q1\)) is \(\frac{28+37}{2}=32.5\).
The upper half of the data is \(40,40,42,54,66\). The median of the upper half (\(Q3\)) is \(\frac{42 + 54}{2}=48\)

Step5: Calculate the IQR

\(\text{IQR}=Q3 - Q1=48-32.5 = 15.5\)

Answer:

1. \(45\)
2. \(15.5\)