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:

  1. What is the relationship between mean, median, and mode in a negatively skewed distribution?
  2. How does outlier data affect the mean compared to the median?
  3. Can the median ever be larger than the mean in a dataset? In what situation?
  4. What does the skewness of a distribution indicate about the data?
  5. 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