Questions: Are there any outliers? Show your calculations. Q3. 21

Transcript text: Are there any outliers? Show your calculations. Q3. 21

Solution

Step 1: Identify the Five-Number Summary

The five-number summary provided is:

Step 2: Calculate the Interquartile Range (IQR)

The IQR is calculated as: \[ \text{IQR} = Q3 - Q1 \] \[ \text{IQR} = 36.5 - 7 = 29.5 \]

Step 3: Determine the Outlier Boundaries

Outliers are typically defined as values that are 1.5 times the IQR below Q1 or above Q3.

Lower boundary: \( Q1 - 1.5 \times \text{IQR} \) \[ 7 - 1.5 \times 29.5 = 7 - 44.25 = -37.25 \]
Upper boundary: \( Q3 + 1.5 \times \text{IQR} \) \[ 36.5 + 1.5 \times 29.5 = 36.5 + 44.25 = 80.75 \]

There are no outliers since all data points fall within the range \([-37.25, 80.75]\).

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