Question

the five point summary is as follows: min = 58.2, q₁ = 61.4, median = 63, q₃ = 64.5, max = 69.7. the interquartile range is iqr = 3.1. give the outlier fences below. table with lower fence and upper fence columns, each with a blank box list any outliers below. if there is more than 1, separate them by commas. blank box

Explanation:

Step1: Calculate Lower Fence

The formula for the lower fence is \( \text{Lower Fence} = Q_1 - 1.5 \times \text{IQR} \). We know \( Q_1 = 61.4 \) and \( \text{IQR} = 3.1 \). So, \( 1.5\times3.1 = 4.65 \), then \( 61.4 - 4.65 = 56.75 \).

Step2: Calculate Upper Fence

The formula for the upper fence is \( \text{Upper Fence} = Q_3 + 1.5 \times \text{IQR} \). We know \( Q_3 = 64.5 \) and \( \text{IQR} = 3.1 \). So, \( 1.5\times3.1 = 4.65 \), then \( 64.5 + 4.65 = 69.15 \).

Step3: Check for Outliers

We check if the minimum (58.2) is less than the lower fence (56.75) or the maximum (69.7) is greater than the upper fence (69.15). The minimum 58.2 > 56.75, but the maximum 69.7 > 69.15, so 69.7 is an outlier.

Answer:

Lower Fence: \( 56.75 \)
Upper Fence: \( 69.15 \)
Outliers: \( 69.7 \)