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Lesson

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Notes

\(\text{A point is an Outlier if}\)

\(\text{it is below } Q1-1.5IQR\)

\(\text{ or it is above } Q3+1.5IQR\)

\(\text{Inner Quartile Range}\)

\(IQR=Q3-Q1\)

Practice Problems

Do the following data sets contain an outlier?

\(\textbf{1)}\) \( \{1,2,3,4,5,6,7,14\} \)

Is there an Outlier?

\(14 \text{ is an outlier.}\)

Show Work

\(\,\,\,\,\,\,Q1 = 2.5\)

\(\,\,\,\,\,\,Q3 = 6.5\)

\(\,\,\,\,\,\,IQR = Q3-Q1 = 6.5-2.5 = 4\)

\(\,\,\,\,\,\,1.5IQR = 1.5 \cdot 4 = 6\)

\(\,\,\,\,\,\,Q1-1.5IQR=2.5-6=-3.5\)

\(\,\,\,\,\,\,Q3+1.5IQR=6.5+6=12.5\)

\(\,\,\,\,\,\,\text{Are any points outside of } -3.5 \text{ and } 12.5\)?

\(\,\,\,\,\,\,14 \gt 12.5\)

\(\,\,\,\,\,\,14 \text{ is an outlier.}\)

\(\textbf{2)}\) \( \{7,3,9,17,4,6,2\} \)

Is there an Outlier?

\(\text{No, there is not an outlier.}\)

Show Work

\(\,\,\,\,\,\,Q1 = 3\)

\(\,\,\,\,\,\,Q3 = 9\)

\(\,\,\,\,\,\,IQR = Q3-Q1 = 9-3 = 6\)

\(\,\,\,\,\,\,1.5IQR = 1.5 \cdot 6 = 9\)

\(\,\,\,\,\,\,Q1-1.5IQR=3-9=-6\)

\(\,\,\,\,\,\,Q3+1.5IQR=9+9=18\)

\(\,\,\,\,\,\,\text{All data points are in between } -6 \text{ and } 18\).

\(\,\,\,\,\,\,\text{There is not an outlier.}\)

\(\textbf{3)}\) \( \{1,2,3,4,5,6\} \)

Is there an Outlier?

\(\text{No, there is not an outlier.}\)

Show Work

\(\,\,\,\,\,\,Q1 = 2\)

\(\,\,\,\,\,\,Q3 = 5\)

\(\,\,\,\,\,\,IQR = Q3-Q1 = 5-2 = 3\)

\(\,\,\,\,\,\,1.5IQR = 1.5 \cdot 3 = 4.5\)

\(\,\,\,\,\,\,Q1-1.5IQR=2-4.5=-2.5\)

\(\,\,\,\,\,\,Q3+1.5IQR=5+4.5=9.5\)

\(\,\,\,\,\,\,\text{All data points are in between } -2.5 \text{ and } 9.5\).

\(\,\,\,\,\,\,\text{There is not an outlier.}\)

\(\textbf{4)}\) \( \{4,2,6,7,1,16,8,8\} \)

Is there an Outlier?

\(16 \text{ is an outlier.}\)

Show Work

\(\,\,\,\,\,\,Q1 = 3\)

\(\,\,\,\,\,\,Q3 = 8\)

\(\,\,\,\,\,\,IQR = Q3-Q1 = 8-3 = 5\)

\(\,\,\,\,\,\,1.5IQR = 1.5 \cdot 5 = 7.5\)

\(\,\,\,\,\,\,Q1-1.5IQR=3-7.5=-4.5\)

\(\,\,\,\,\,\,Q3+1.5IQR=8+7.5=15.5\)

\(\,\,\,\,\,\,\text{Are any points outside of } -4.5 \text{ and } 15.5\)?

\(\,\,\,\,\,\,16 \gt 15.5\)

\(\,\,\,\,\,\,16 \text{ is an outlier.}\)

\(\textbf{5)}\) \( \{5,5,6,2,5,4\} \)

Is there an Outlier?

\(\text{No, there is not an outlier.}\)

Show Work

\(\,\,\,\,\,\,Q1 = 4\)

\(\,\,\,\,\,\,Q3 = 5\)

\(\,\,\,\,\,\,IQR = Q3-Q1 = 5-4 = 1\)

\(\,\,\,\,\,\,1.5IQR = 1.5 \cdot 1 = 1.5\)

\(\,\,\,\,\,\,Q1-1.5IQR=4-1.5=2.5\)

\(\,\,\,\,\,\,Q3+1.5IQR=5+1.5=6.5\)

\(\,\,\,\,\,\,\text{All data points are in between } 2.5 \text{ and } 6.5\).

\(\,\,\,\,\,\,\text{There is not an outlier.}\)

\(\textbf{6)}\) \( \{1,2,3,4,5,6,7\} \)

Is there an Outlier?

\(\text{No, there is not an outlier.}\)

Show Work

\(\,\,\,\,\,\,Q1 = 2\)

\(\,\,\,\,\,\,Q3 = 6\)

\(\,\,\,\,\,\,IQR = Q3-Q1 = 6-2 = 4\)

\(\,\,\,\,\,\,1.5IQR = 1.5 \cdot 4 = 6\)

\(\,\,\,\,\,\,Q1-1.5IQR=2-6=-4\)

\(\,\,\,\,\,\,Q3+1.5IQR=6+6=12\)

\(\,\,\,\,\,\,\text{All data points are in between } -4 \text{ and } 12\).

\(\,\,\,\,\,\,\text{There is not an outlier.}\)

See Related Pages\(\)

\(\bullet\text{ Mean, Median and Mode}\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4,2,6,7,1,10,8,8…\)

\(\bullet\text{ Quartiles and IQR}\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,IQR=Q3-Q1…\)

\(\bullet\text{ Box and Whisker Plot}\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\)

\(\bullet\text{ Stem and Leaf Plot}\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\)

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