Question

in the data set below, what is the interquartile range? 51 16 29 56 20 23 48

Explanation:

Step1: Sort the data set

$$16,20,23,29,48,51,56$$

Step2: Find the median (Q2)

The median is the middle value. Since there are 7 values, the 4th value is the median.
$$Q2 = 29$$

Step3: Find Q1 (median of the lower half)

The lower half is \(16,20,23\). The median of this is \(20\).
$$Q1 = 20$$

Step4: Find Q3 (median of the upper half)

The upper half is \(48,51,56\). The median of this is \(51\).
$$Q3 = 51$$

Step5: Calculate the inter - quartile range (IQR)

$$IQR=Q3 - Q1$$
$$IQR = 51-20$$

Answer:

\(31\)