Math Problem Statement

The mean, median, and mode are all equal in a normal distribution. Determine if the statement is true or false.

Solution

The question asks whether the statement is true or false:

"The mean, median, and mode are all equal in a normal distribution."

This statement is true. In a perfectly normal distribution, the mean, median, and mode are all the same because the data is symmetrically distributed, with the peak at the center.

So the correct answer is C. The statement is true.

Would you like more details on this? Here are five related questions:

  1. How does the normal distribution differ from a skewed distribution?
  2. Can the mean, median, and mode ever be different in a normal distribution?
  3. Why is the normal distribution important in statistics?
  4. What is the empirical rule (68-95-99.7 rule) for normal distributions?
  5. How can the standard deviation impact the shape of a normal distribution?

Tip: In a positively or negatively skewed distribution, the mean, median, and mode will not be equal, as the data is not symmetrical.

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Math Problem Analysis

Mathematical Concepts

Statistics
Normal Distribution
Mean
Median
Mode

Formulas

-

Theorems

Normal Distribution Theorem

Suitable Grade Level

Grades 9-12