in the data set below, what is the interquartile range? 17 29 37 50 60 70 76 82
in the data set below, what is the interquartile range? 17 29 37 50 60 70 76 82
Answer
Answer:
43
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.