Question

the numbers of runs scored by a softball team in 20 games are given. 3, 4, 8, 12, 7, 5, 4, 12, 3, 9, 11, 4, 14, 8, 2, 10, 3, 10, 9, 7. what is the interquartile range. iqr = 6 iqr = 7.5 iqr = 12 iqr = 10

Explanation:

Step1: Sort the data

$3,3,3,4,4,4,5,7,7,8,9,9,10,10,11,12,12,14,14,20$

Step2: Find the median (Q2)

Since $n = 20$ (even), $Q2=\frac{8 + 9}{2}=8.5$

Step3: Find Q1

The lower - half data is $3,3,3,4,4,4,5,7,7,8$. Since $n = 10$ (even), $Q1=\frac{4+4}{2}=4$

Step4: Find Q3

The upper - half data is $9,9,10,10,11,12,12,14,14,20$. Since $n = 10$ (even), $Q3=\frac{11 + 12}{2}=11.5$

Step5: Calculate IQR

$IQR=Q3 - Q1=11.5−4 = 7.5$

Answer:

IQR = 7.5