For a symmetrical probability density function (PDF), which of the following statements is true?
Understand the Problem
The question is asking which statement is true for a symmetrical probability density function. A symmetrical PDF has the same shape on both sides of the mean. Therefore, the mean, median, and mode are all equal because the distribution is balanced around the center.
Answer
The mean and median are equal, and the coefficient of skewness is zero.
For a symmetrical probability density function (PDF), the mean and median are equal. Additionally, the coefficient of skewness is zero.
Answer for screen readers
For a symmetrical probability density function (PDF), the mean and median are equal. Additionally, the coefficient of skewness is zero.
More Information
A symmetrical PDF means that the distribution is balanced around its center. The mean represents the average value, and the median represents the middle value. In a symmetrical distribution, these two values coincide. Skewness measures the asymmetry of a distribution, so a symmetrical distribution has zero skewness.
Tips
A common mistake is assuming that all PDFs are symmetrical. Many distributions are skewed, meaning they are not symmetrical.
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