Question

in the data set below, what is the interquartile range? 80 33 19 27 43 47 46

Explanation:

Step1: Sort the data set

$$19,27,33,43,46,47,80$$

Step2: Find the median (Q2)

The median is the middle value. Since there are 7 values, the 4th value is the median.
$$Q2 = 43$$

Step3: Find Q1 (median of the lower half)

The lower half is \(19,27,33\). The median of this is \(27\), so \(Q1 = 27\)

Step4: Find Q3 (median of the upper half)

The upper half is \(46,47,80\). The median of this is \(47\), so \(Q3 = 47\)

Step5: Calculate the inter - quartile range (IQR)

$$IQR=Q3 - Q1$$
$$IQR = 47-27$$

Answer:

\(20\)