Math Problem Statement

Use the skewed graph to determine which letter represents the mean, median, and mode.

Solution

From the image, we are given a skewed graph (which appears to be skewed to the right) with three labeled points, A, B, and C, and three questions regarding the mean, median, and mode.

a) Which letter represents the mean?

In a right-skewed distribution, the mean is pulled towards the tail (the right side), as it is sensitive to extreme values. Therefore, the mean is likely to be the farthest to the right.

Answer: C

b) Which letter represents the median?

The median is the middle value of the distribution. In a right-skewed graph, the median lies between the mode and the mean.

Answer: B

c) Which letter represents the mode?

The mode is the peak or the highest point of the distribution, representing the most frequent value.

Answer: A


Do you want more details or have any other questions?

5 Relative Questions:

  1. How does the skewness of a graph affect the positions of mean, median, and mode?
  2. What is the difference between left-skewed and right-skewed distributions?
  3. Can the mean, median, and mode ever be the same in a distribution?
  4. Why is the mean more affected by extreme values than the median?
  5. How would the graph change if it were left-skewed instead of right-skewed?

Tip: In a symmetric distribution (like a normal distribution), the mean, median, and mode coincide at the center.

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Math Problem Analysis

Mathematical Concepts

Descriptive Statistics
Skewness
Measures of Central Tendency

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12