Question

the five point summary is as follows: min = 74.1, q₁ = 78.8, median = 81, q₃ = 81.8, max = 83.3. the interquartile range is iqr = 3.
give the outlier fences below.

lower fence	upper fence

list any outliers below. if there is more than 1, separate them by commas.
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Explanation:

Step1: Calculate Lower Fence

The formula for the lower fence is \( Q_1 - 1.5 \times \text{IQR} \). Given \( Q_1 = 78.8 \) and \( \text{IQR} = 3 \), we substitute these values:
\( 78.8 - 1.5 \times 3 = 78.8 - 4.5 = 74.3 \)

Step2: Calculate Upper Fence

The formula for the upper fence is \( Q_3 + 1.5 \times \text{IQR} \). Given \( Q_3 = 81.8 \) and \( \text{IQR} = 3 \), we substitute these values:
\( 81.8 + 1.5 \times 3 = 81.8 + 4.5 = 86.3 \)

Step3: Identify Outliers

We check if any data points (min, max) are outside the fences. The min is 74.1, which is less than the lower fence 74.3. The max is 83.3, which is less than the upper fence 86.3. So only 74.1 is an outlier.

Answer:

Lower Fence: \( 74.3 \)
Upper Fence: \( 86.3 \)
Outliers: \( 74.1 \)