Questions: Suppose the data represent the inches of rainfall in April for a certain city over the course of 20 years. Given the quartiles Q₁=1.765, Q₂=3.795, and Q₃=5.415, determine the lower and upper fences. Are there any outliers, according to this criterion? 0.31 1.91 4.02 5.57 0.57 2.33 4.45 5.77 0.86 2.65 4.59 6.02 1.34 3.14 5.09 6.17 1.62 3.57 5.26 6.41 The lower fence is (Round to three decimal places as needed.)

Suppose the data represent the inches of rainfall in April for a certain city over the course of 20 years. Given the quartiles Q₁=1.765, Q₂=3.795, and Q₃=5.415, determine the lower and upper fences. Are there any outliers, according to this criterion? 0.31 1.91 4.02 5.57 0.57 2.33 4.45 5.77 0.86 2.65 4.59 6.02 1.34 3.14 5.09 6.17 1.62 3.57 5.26 6.41 The lower fence is (Round to three decimal places as needed.)
Transcript text: Suppose the data represent the inches of rainfall in April for a certain city over the course of 20 years. Given the quartiles $Q_{1}=1.765, Q_{2}=3.795$, and $Q_{3}=5.415$, determine the lower and upper fences. Are there any outliers, according to this criterion? \begin{tabular}{llll} 0.31 & 1.91 & 4.02 & 5.57 \\ \hline 0.57 & 2.33 & 4.45 & 5.77 \\ \hline 0.86 & 2.65 & 4.59 & 6.02 \\ \hline 1.34 & 3.14 & 5.09 & 6.17 \\ \hline 1.62 & 3.57 & 5.26 & 6.41 \end{tabular} The lower fence is $\square$ (Round to three decimal places as needed.)
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Solution

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Solution Steps

Step 1: Calculate Quartiles

Given the sorted dataset, the quartiles are calculated as follows:

  • $Q_1$ (First Quartile): 1.765
  • $Q_2$ (Second Quartile or Median): 3.795
  • $Q_3$ (Third Quartile): 5.415
Step 2: Compute Interquartile Range (IQR)

The Interquartile Range (IQR) is calculated by subtracting $Q_1$ from $Q_3$: $IQR = Q_3 - Q_1 = 3.65$

Step 3: Determine Lower and Upper Fences

The lower fence is calculated as $Q_1 - 1.5 \times IQR = -3.71$, and the upper fence is calculated as $Q_3 + 1.5 \times IQR = 10.89$.

Step 4: Identify Outliers

Outliers are data points that fall below the lower fence or above the upper fence. In this dataset, the outliers are: []

Final Answer:

The quartiles are $Q_1 = 1.765$, $Q_2 = 3.795$, $Q_3 = 5.415$ with an IQR of 3.65. The lower and upper fences are -3.71 and 10.89, respectively, identifying the outliers as [].

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