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Part 4 of 5 Find \( Q_{1}, Q_{3} \), and IQR. (Round your answers to one decimal place as needed.) \[ \begin{array}{r}Q_{1} \\ Q_{3}\end{array}=\square \] IQR \( =\square \)

Ask by Pope Cruz. in the United States
Mar 08,2025

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Answer

To find \( Q_1 \), \( Q_3 \), and the IQR, follow these steps: 1. **Sort the Data:** Arrange all numbers in order from smallest to largest. 2. **Find the Median:** Identify the middle number. If there's an odd number of data points, it's the middle one; if even, it's the average of the two middle numbers. 3. **Determine Halves:** Split the data into the lower half for \( Q_1 \) and the upper half for \( Q_3 \). 4. **Compute Quartiles:** Find the median of each half to get \( Q_1 \) and \( Q_3 \). 5. **Calculate IQR:** Subtract \( Q_1 \) from \( Q_3 \) to get the interquartile range. 6. **Round:** Round all values to one decimal place. Since the specific data isn't provided, you'll need to apply these steps to your dataset to find the exact values for \( Q_1 \), \( Q_3 \), and the IQR.

Solution

We first note that to compute the quartiles and the interquartile range (IQR) we need the raw data (or a frequency distribution) to work with. Since the dataset was not provided in this part, here is a general step‐by‐step method for finding the first quartile \(Q_1\), the third quartile \(Q_3\), and the IQR: 1. **Sort the Data:** Arrange the data values in increasing order. 2. **Find the Median:** Identify the median (the middle value). If there is an odd number of data points, the median is the middle number; if even, it is the average of the two central numbers. 3. **Determine the Lower and Upper Halves:** - The lower half of the dataset (not including the median if the number of data points is odd) is used to compute \(Q_1\). - The upper half of the dataset is used to compute \(Q_3\). 4. **Compute \(Q_1\) and \(Q_3\):** - \(Q_1\) is the median of the lower half of the data. - \(Q_3\) is the median of the upper half of the data. 5. **Calculate the IQR:** \[ \text{IQR} = Q_3 - Q_1 \] 6. **Round your Answers:** Round \(Q_1\), \(Q_3\), and the IQR to one decimal place as needed. Without the numerical data provided, we cannot compute specific numeric values for \(Q_1\), \(Q_3\), and the IQR. Please provide the dataset or the necessary values so that we can carry out the computations and fill in the blanks: \[ \begin{array}{r} Q_{1} \\[6mm] Q_{3} \end{array}=\square \] \[ \text{IQR}=\square \] If you have the dataset available from earlier parts, please share it so we may proceed with the calculation.

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To determine \( Q_1 \), \( Q_3 \), and the interquartile range (IQR), you typically start with a sorted dataset. Let’s assume you have a dataset: 1. **Sorting the Data**: Arrange your dataset in ascending order. 2. **Calculating \( Q_1 \) and \( Q_3 \)**: - \( Q_1 \) is the median of the first half of the data. - \( Q_3 \) is the median of the second half of the data. 3. **Finding IQR**: The IQR is calculated as \( IQR = Q_3 - Q_1 \). After following these steps, you will find your answers to round to one decimal point as necessary. If you can provide the dataset, I can help you calculate \( Q_1 \), \( Q_3 \), and the IQR!

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