Math Problem Statement
Select all of the number of hours larger than the median which would be an outlier, given the statistics: mean = 8.5 hours, MAD = 5.3 hours, median = 7 hours, Q1 = 5 hours, Q3 = 11 hours.
Solution
To determine which values are outliers larger than the median in this dataset, we follow these steps:
1. Outlier Boundaries
The formula for identifying outliers is:
Where:
Calculating the IQR:
Upper Bound:
Thus, any value greater than 20 is considered an outlier.
2. Checking Given Values
The options are:
- 20: This is not an outlier since it equals the upper bound.
- 21: This is an outlier since it is greater than 20.
- 25: This is an outlier since it is greater than 20.
- 15: This is not an outlier since it is less than the upper bound.
3. Correct Answers
The numbers larger than the median () and classified as outliers are:
- 21
- 25
Final Analysis
The correct selections should include 21 and 25 only.
Would you like more details on how I calculated the boundaries? Let me know!
Related Questions:
- How is the IQR (Interquartile Range) used to determine outliers?
- Why is the threshold used in statistics?
- What happens if the data has extreme outliers on both ends?
- How does the mean differ from the median in skewed datasets?
- How would you identify outliers in a box plot?
Tip:
Always verify both lower and upper outlier bounds when analyzing a dataset.
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Math Problem Analysis
Mathematical Concepts
Outliers
Interquartile Range (IQR)
Median
Upper Bound for Outliers
Formulas
Upper Bound = Q3 + 1.5 * IQR
IQR = Q3 - Q1
Theorems
Outlier Detection Rule based on IQR
Suitable Grade Level
Grades 8-10