Question

in the data set below, what is the interquartile range? 53 53 53 54 57 58 58 60 62

Explanation:

Step1: Find the median

The data set has 9 values. The median (middle value) is the 5th value. So, the median is 57.

Step2: Split the data into lower and upper halves

Lower half: 53, 53, 53, 54. Upper half: 58, 58, 60, 62.

Step3: Find the first quartile ($Q_1$)

For the lower half (4 values), the first quartile is the average of the 2nd and 3rd values. $Q_1=\frac{53 + 53}{2}=53$.

Step4: Find the third quartile ($Q_3$)

For the upper half (4 values), the third quartile is the average of the 2nd and 3rd values. $Q_3=\frac{58+60}{2} = 59$.

Step5: Calculate the inter - quartile range (IQR)

The formula for IQR is $IQR=Q_3 - Q_1$. So, $IQR = 59-53=6$.

Answer:

6