Question

in the data set below, what is the interquartile range? 17 29 37 50 60 70 76 82

Explanation:

Step1: Find the median

The data set has 8 values. The median is the average of the 4th and 5th - ordered values. $\frac{50 + 60}{2}=55$.

Step2: Split data into lower and upper halves

Lower half: 17, 29, 37, 50. Upper half: 60, 70, 76, 82.

Step3: Find Q1 and Q3

Q1 is the median of the lower - half. Since there are 4 values in the lower half, Q1=$\frac{29 + 37}{2}=33$. Q3 is the median of the upper - half. Since there are 4 values in the upper half, Q3=$\frac{70+76}{2}=73$.

Step4: Calculate inter - quartile range

IQR = Q3 - Q1. So, IQR = 73 - 33=43.

Answer:

43