Math Problem Statement
Comparing mean and median, it is discovered:
(A) mean > median
(B) mean < median
(C) mean = median
(D) mean = SD
(E) none of these
Solution
The correct answer is:
(A) mean > median
This situation generally occurs when the data is positively skewed. In positively skewed (or right-skewed) distributions, the mean is typically greater than the median because the mean is pulled in the direction of the skew by the larger values in the dataset.
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Here are 5 related questions for deeper understanding:
- What is the relationship between mean, median, and mode in a negatively skewed distribution?
- How does outlier data affect the mean compared to the median?
- Can the median ever be larger than the mean in a dataset? In what situation?
- What does the skewness of a distribution indicate about the data?
- How can one determine if a distribution is symmetric?
Tip: The mean is sensitive to extreme values, while the median is more robust and resistant to outliers.
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Math Problem Analysis
Mathematical Concepts
Descriptive Statistics
Measures of Central Tendency
Skewness
Formulas
Mean = (ΣX) / N
Median: Middle value in a sorted dataset
Skewness: Skewness = 3(Mean - Median) / SD
Theorems
Skewness Theorem
Suitable Grade Level
Grades 9-12
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