Question

calculating the interquartile range of a data set
december temperatures
what is the interquartile range for the data set?
8
day
temperature (°f)
1
33
2
34
3
42
4
36
5
39
6
36
7
39
8
40
9
44

Explanation:

Step1: Sort the data

First, sort the temperature data: \(33,34,36,36,39,39,40,42,44\)

Step2: Find the median (Q2)

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

Step3: Find Q1

The lower half of the data is \(33,34,36,36\). The median of the lower half (Q1) is \(\frac{34 + 36}{2}=35\)

Step4: Find Q3

The upper half of the data is \(40,42,44\). The median of the upper half (Q3) is \(42\)

Step5: Calculate the inter - quartile range (IQR)

The formula for IQR is \(IQR=Q3 - Q1\). Substitute \(Q1 = 35\) and \(Q3=42\) into the formula: \(IQR=42-35 = 7\)

Answer:

\(7\)