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Find \( Q_{1}, Q_{3} \), and IQR. (Round your answers to one decimal place as needed.) \[ Q_{1}=\square \] \( Q_{3}=\square \) List any outliers. Use the "Does not exist" button if there are none. \( \square \)

Ask by Zimmerman Barker. in the United States
Mar 08,2025

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Tutor-Verified Answer

Answer

There isn't enough information to find \( Q_1 \), \( Q_3 \), and the IQR. Please provide the data set or summary statistics to determine the quartiles and any outliers.

Solution

There isn’t enough information to solve the problem. In order to compute the quartiles \( Q_1 \) and \( Q_3 \) (and hence the interquartile range, \( \text{IQR}=Q_3-Q_1 \)) and determine any outliers, we need the data values (or a description such as a box plot with minimum, lower quartile, median, upper quartile, and maximum). Please provide the data set or the necessary summary statistics.

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Bonus Knowledge

To find \( Q_{1} \), \( Q_{3} \), and the Interquartile Range (IQR), you first need to arrange your data in ascending order. Once sorted, \( Q_{1} \) is the median of the lower half of the dataset, and \( Q_{3} \) is the median of the upper half. The IQR is computed as \( IQR = Q_{3} - Q_{1} \). Suppose your sorted dataset is: 2, 3, 5, 6, 7, 8, 12, 13, 14. 1. **Find \( Q_{1} \)**: The lower half is 2, 3, 5, 6. The median of this set is 4. 2. **Find \( Q_{3} \)**: The upper half is 8, 12, 13, 14. The median of this set is 12.5. 3. **Calculate IQR**: \( IQR = Q_{3} - Q_{1} = 12.5 - 4 = 8.5 \). Outliers can typically be determined by calculating \( 1.5 \times IQR \). Any value below \( Q_{1} - 1.5 \times IQR \) or above \( Q_{3} + 1.5 \times IQR \) may be considered an outlier. If any values in your dataset fall outside this range, those are your outliers. Otherwise, select "Does not exist."

Related Questions

Question 12(Mulliple Choice Warth 5 points) \[ (04.06 \mathrm{HC}) \] A researcher wants to test the claim that the proportion of juniors who watch television regularly is greater than the proportion of seniors who watch television regularly She finds that 56 of 70 randomly selected juniors and 47 of 85 randomly selected seniors report watching television regularly. Construct \( 95 \% \) confidence intervals for each population proportion. Which of the statemente gives the correct outcome of the research or's tert of the dalim? The \( 95 \% \) confidence interval for juniors is (706, 894), and the \( 95 \% \) confidence interval for seniors is ( 447,659 ). Since the intervals overlap, there is not enough evidence to say the proportion of juniors who watch television regularly may be higher than that of seniors. The \( 95 \% \) confidence interval for juniors is (721, 879), and the \( 95 \% \) confidence interval for seniors is (464, 642). Since the interval for juniors is higher than the interval for seniors, there is evidence to say the proportion of juniors who watch television regularly may be higher than that of seniors. The \( 95 \% \) confidence interval for juniors is ( 706,894 ), and the \( 95 \% \) confidence interval for seniors is ( 447,659 ). Since the interval for juniors is higher than the interval for seniors, there is evidence to say the proportion of juniors who watch television regularly may be higher than that of seniors. The \( 95 \% \) confidence interval for juniors is ( \( 721, .879 \) ), and the \( 95 \% \) confidence interval for seniors is (464, 642). Since the intervals overlap, there is not enough evidence to say the proportion of juniors who watch television regularly may be higher than that of seniors.

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