Question

calculating the interquartile range of a data set
what is the interquartile range for the data set?
december temperatures

Explanation:

Step1: Sort the data

Sort the temperatures: \(33, 34, 36, 36, 39, 39, 40, 42, 44\)

Step2: Find the median (Q2)

Since \(n = 9\) (odd), the median is the \(\frac{n + 1}{2}=\frac{9+1}{2}=5^{th}\) value. So \(Q2 = 39\)

Step3: Find Q1

The lower half is \(33, 34, 36, 36\). Since \(n = 4\) (even), \(Q1=\frac{34 + 36}{2}=35\)

Step4: Find Q3

The upper half is \(40, 42, 44\). Since \(n = 4\) (even), \(Q3=\frac{42+44}{2} = 43\)

Step5: Calculate the inter - quartile range (IQR)

\(IQR=Q3 - Q1\)
\(IQR=43-35\)

Answer:

\(8\)