Math Problem Statement

Given the box plot, will the mean or the median provide a better description of the center? (1 point)

 

The mean, because the data distribution is symmetrical

The mean, because the data distribution is pulled to the left

The median, because the data distribution is pulled to the left

The median, because the data distribution is pulled to the right

Solution

The correct answer is:

The median, because the data distribution is pulled to the left.

Explanation:

  • When a data distribution is pulled to the left (negatively skewed), the mean tends to be lower than the median because the smaller values drag it down. In such cases, the median provides a better description of the center since it is not influenced by extreme values as much as the mean is.

Would you like more details or have any other questions?

Related Questions:

  1. How does skewness affect the mean and median?
  2. What is the difference between a positively skewed and negatively skewed distribution?
  3. Can the mean ever be a better measure of central tendency than the median in skewed data?
  4. How does the interquartile range (IQR) reflect in a box plot for skewed data?
  5. How does the box plot visually indicate skewness?

Tip:

If a dataset is highly skewed, always check both the mean and median before deciding which better represents the central tendency.

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Math Problem Analysis

Mathematical Concepts

Descriptive Statistics
Measures of Central Tendency
Skewness
Box Plot

Formulas

Mean = (Sum of all data points) / (Number of data points)
Median = Middle value when data is ordered

Theorems

Skewness Theorem: When data is skewed, the mean is pulled in the direction of the skew while the median remains more central.

Suitable Grade Level

Grades 9-12