find the interquartile range of the following data set.\n3, 9, 12, 4, 6, 40, 25, 14, 10\n\na. 5\nb. 10\nc…
find the interquartile range of the following data set.\n3, 9, 12, 4, 6, 40, 25, 14, 10\n\na. 5\nb. 10\nc. 19.5\nd. 14.5
Answer
Answer:
D. 14.5
Explanation:
Step1: Sort the data set
$3,4,6,9,10,12,14,25,40$
Step2: Find the median (Q2)
Since there are 9 data - points, the median is the 5th value. So, $Q2 = 10$.
Step3: Find the lower half and Q1
The lower half is $3,4,6,9$. The median of the lower half (Q1) is $\frac{4 + 6}{2}=5$.
Step4: Find the upper half and Q3
The upper half is $12,14,25,40$. The median of the upper half (Q3) is $\frac{14+25}{2}=19.5$.
Step5: Calculate the inter - quartile range (IQR)
$IQR=Q3 - Q1=19.5−5 = 14.5$