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Select the outlier in the data set. $33$ , $43$ , $49$ , $57$ , $62$ , $67$ , $81$ , $561$

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Identify an outlier

Full solution

Q. Select the outlier in the data set.

33

,

43

,

49

,

57

,

62

,

67

,

81

,

561

Calculate Median: Calculate the median of the data set. $\newline$ Median = $(57 + 62) / 2$ $\newline$ = $119 / 2$ $\newline$ = $59.5$
Find Q $1$ : Find Q $1$ , the median of the first half of the data set. $\newline$ $Q1 = \frac{43 + 49}{2}$ $\newline$ $= \frac{92}{2}$ $\newline$ $= 46$
Find Q $3$ : Find Q $3$ , the median of the second half of the data set. $\newline$ $Q3 = \frac{67 + 81}{2}$ $\newline$ $= \frac{148}{2}$ $\newline$ $= 74$
Calculate IQR: Calculate the Interquartile Range (IQR). $\newline$ $IQR = Q3 - Q1$ $\newline$ $= 74 - 46$ $\newline$ $= 28$
Determine Lower Bound: Determine the lower bound. $\newline$ Lower bound = $Q1 - 1.5 \times IQR$ $\newline$ = $46 - 1.5 \times 28$ $\newline$ = $46 - 42$ $\newline$ = $4$
Determine Upper Bound: Determine the upper bound. $\newline$ Upper bound = $Q3 + 1.5 \times IQR$ $\newline$ = $74 + 1.5 \times 28$ $\newline$ = $74 + 42$ $\newline$ = $116$
Identify Outlier: Identify the outlier. $\newline$ The number $561$ is greater than the upper bound of $116$ , so it's the outlier. $\newline$ Outlier: $561$

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