Question

the five point summary is as follows: min = 1.9, q₁ = 2.6, median = 3, q₃ = 3.2, max = 4.4. the interquartile range is iqr = 0.6. give the outlier fences below. lower fence upper fence list any outliers below. if there is more than 1, separate them by commas.

Explanation:

Step1: Calculate Lower Fence

The formula for the lower fence is \( \text{Lower Fence} = Q_1 - 1.5 \times \text{IQR} \). We know \( Q_1 = 2.6 \) and \( \text{IQR} = 0.6 \). So, \( 2.6 - 1.5\times0.6 = 2.6 - 0.9 = 1.7 \).

Step2: Calculate Upper Fence

The formula for the upper fence is \( \text{Upper Fence} = Q_3 + 1.5 \times \text{IQR} \). We know \( Q_3 = 3.2 \) and \( \text{IQR} = 0.6 \). So, \( 3.2 + 1.5\times0.6 = 3.2 + 0.9 = 4.1 \).

Step3: Identify Outliers

We check the minimum (1.9) and maximum (4.4) values. The minimum (1.9) is greater than the lower fence (1.7), and the maximum (4.4) is greater than the upper fence (4.1). So, 4.4 is an outlier.

Answer:

Lower Fence: \( 1.7 \)
Upper Fence: \( 4.1 \)
Outliers: \( 4.4 \)