Math Problem Statement

Use the shape of the distribution to compare the mean and median. Are the mean and median equal? If not, which is greater?

Solution

The histogram you provided shows the height distribution of students. Based on the shape of the distribution, we can observe that it is left-skewed (there is a longer tail on the left side of the distribution). In such cases, the mean is typically less than the median because the lower values pull the mean towards the left, while the median, being the middle value, remains unaffected by extreme values.

Therefore, the correct answer is:

  • C: The median is greater.

Do you want more details or have any further questions?

Here are five related questions to expand your understanding:

  1. How is the mean affected in a right-skewed distribution?
  2. What would the mean and median look like in a perfectly symmetric distribution?
  3. Can you explain why the mean is more sensitive to extreme values than the median?
  4. How can outliers affect the mean in different types of distributions?
  5. How could you estimate the mean and median from a grouped frequency table?

Tip: In a skewed distribution, always check the direction of the skew to determine the relationship between the mean and median.

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Math Problem Analysis

Mathematical Concepts

Statistics
Mean
Median
Skewed Distributions

Formulas

-

Theorems

Properties of Skewed Distributions

Suitable Grade Level

Grades 9-12