in the data set below, what is the interquartile range? 1 2 2 4 5 7
in the data set below, what is the interquartile range? 1 2 2 4 5 7
Answer
Explanation:
Step1: Arrange data in order
The data set 1, 2, 2, 4, 5, 7 is already in ascending - order.
Step2: Find the median (Q2)
There are 6 data points. The median is the average of the 3rd and 4th ordered values. So, $Q2=\frac{2 + 4}{2}=3$.
Step3: Find the lower half and Q1
The lower half of the data is 1, 2, 2. The median of the lower half (Q1) is 2.
Step4: Find the upper half and Q3
The upper half of the data is 4, 5, 7. The median of the upper half (Q3) is 5.
Step5: Calculate the inter - quartile range (IQR)
$IQR = Q3−Q1$. Substitute Q1 = 2 and Q3 = 5, we get $IQR=5 - 2=3$.
Answer:
3