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.
Answered by UpStudy AI and reviewed by a Professional Tutor

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