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…

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?

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?

Answer

Answer:

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

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.