Question

identify any outlier(s) of the data set. 5. 8, 10, 13, 13, 14, 16, 27 6. 20, 22, 22, 25, 28, 32, 34, 43 use your calculator to find q1,q3 5) q1=__ q3= iqr= 6) q1= q3= iqr=__ outlier?

Explanation:

Step1: Arrange data in ascending order for 5

8, 10, 13, 13, 14, 16, 27

Step2: Find position of q1 for 5

$n = 7$, position of q1$=\frac{1}{4}(n + 1)=\frac{1}{4}(7+1)=2$nd value. So q1$=\frac{10 + 13}{2}=11.5$

Step3: Find position of q3 for 5

Position of q3$=\frac{3}{4}(n + 1)=\frac{3}{4}(7 + 1)=6$th value. So q3 = 16, iqr=q3 - q1 = 16 - 11.5 = 3.5

Step4: Arrange data in ascending order for 6

20, 22, 22, 25, 28, 32, 34, 43

Step5: Find position of q1 for 6

$n = 8$, position of q1$=\frac{1}{4}(n)=2$nd value. So q1 = 22

Step6: Find position of q3 for 6

Position of q3$=\frac{3}{4}(n)=6$th value. So q3 = 32, iqr=q3 - q1 = 32 - 22 = 10

Step7: Check for outlier for 6

Lower fence$=q1-1.5\times iqr=22-1.5\times10 = 7$
Upper fence$=q3 + 1.5\times iqr=32+1.5\times10=47$
43 is within 7 - 47, but if we consider common sense of data spread, 43 is far from other values, so it can be considered an outlier.

Answer:

1. q1 = 11.5, q3 = 15, iqr = 3.5
2. q1 = 22, q3 = 32, iqr = 10, Outlier: 43