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.)
failed

Solution

failed
failed

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 [].

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
A nurse is preparing to administer medications to a client who is not wearing an identification bracelet. Which of the following actions should the nurse take before administering the medications? Verify the client's identity using their diagnosis. Use one identifier to confirm the client's identity. Use the client's room number to identify the client. Have the client confirm their name and date of birth.
failedAnswered
H−is known as hydrogen hydride helium fluoride
failedAnswered
The relationship between food and mood is unsubstantiated unidirectional simple complex
failedAnswered
Find all zeros. One zero has been given. 9) f(x)=3x^3+2x^2-19x+6; 2
failedAnswered
Question 19 Mark this question Use a Riemann sum with 4 rectangles of equal width to approximate the area between y=x^3+2 and the x-axis on the interval [-1,1]. Use the righthand endpoint of each subinterval. 4.5 units ^2 9 units ^2 8.0625 units ^2 3.5 units ^2