Question

in the data set below, what is the interquartile range? 1 1 1 1 1 1 3 3 4 6 6 6

Explanation:

Step1: Find the median of the data set

The data set has 12 numbers. The median is the average of the 6th and 7th numbers. The 6th number is 1 and the 7th number is 3. So the median \(Q_2=\frac{1 + 3}{2}=2\).

Step2: Find \(Q_1\) (lower - quartile)

The lower half of the data set is \(1,1,1,1,1,1\). The median of the lower half (since there are 6 numbers, the median is the average of the 3rd and 4th numbers). The 3rd and 4th numbers are both 1, so \(Q_1 = 1\).

Step3: Find \(Q_3\) (upper - quartile)

The upper half of the data set is \(3,4,6,6,6,6\). The median of the upper half (average of the 3rd and 4th numbers of the upper half). The 3rd number is 6 and the 4th number is 6, so \(Q_3=6\).

Step4: Calculate the inter - quartile range (IQR)

The formula for the inter - quartile range is \(IQR=Q_3 - Q_1\). Substitute \(Q_1 = 1\) and \(Q_3=6\) into the formula, we get \(IQR=6 - 1=5\).

Answer:

5