Question

identify any outlier(s) of the data set. 5. 8,10,13,13,14,16,27 ______ use your calculator to find q1,q3 5) q1=_ q3=__ iqr=_ 6) q1=_ q3=__ iqr=___ outlier?

Explanation:

Step1: Arrange data in ascending order for dataset 5

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

Step2: Find position of Q1 and Q3 for dataset 5

There are $n = 7$ data - points. Position of $Q1=\frac{n + 1}{4}=\frac{7+1}{4}=2$. Position of $Q3=\frac{3(n + 1)}{4}=\frac{3\times(7 + 1)}{4}=6$. So, $Q1 = 10$, $Q3=16$.

Step3: Calculate IQR for dataset 5

$IQR=Q3 - Q1=16 - 10 = 6$.

Step4: Determine out - lier bounds for dataset 5

Lower bound $=Q1-1.5\times IQR=10-1.5\times6=10 - 9 = 1$. Upper bound $=Q3 + 1.5\times IQR=16+1.5\times6=16 + 9 = 25$. Since $27>25$, 27 is an outlier.

Step5: Arrange data in ascending order for dataset 6

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

Step6: Find position of Q1 and Q3 for dataset 6

There are $n = 8$ data - points. Position of $Q1=\frac{n+1}{4}=\frac{8 + 1}{4}=2.25$. So, $Q1=22+(22 - 22)\times0.25 = 22$. Position of $Q3=\frac{3(n + 1)}{4}=\frac{3\times(8 + 1)}{4}=6.75$. So, $Q3=32+(34 - 32)\times0.75=32 + 1.5 = 33.5$.

Step7: Calculate IQR for dataset 6

$IQR=Q3 - Q1=33.5 - 22 = 11.5$.

Step8: Determine out - lier bounds for dataset 6

Lower bound $=Q1-1.5\times IQR=22-1.5\times11.5=22-17.25 = 4.75$. Upper bound $=Q3+1.5\times IQR=33.5+1.5\times11.5=33.5 + 17.25 = 50.75$. Since all data points are within the bounds, there are no outliers.

Answer:

1. $Q1 = 10$, $Q3 = 16$, $IQR = 6$, Outlier: 27
2. $Q1 = 22$, $Q3 = 33.5$, $IQR = 11.5$, Outlier: None