Questions: In a normal distribution, which statement best describes the relationship between mean, median, and mode? The mode will always be the smallest value, while the mean and median will be the same. The mean will be in the center of the distribution and the mode and median may be higher or lower than the mean. The mean, median, and mode will all be in the middle of the distribution. The mode and median will fall in the center of the distribution and the mean will be larger than both.

In a normal distribution, which statement best describes the relationship between mean, median, and mode?
The mode will always be the smallest value, while the mean and median will be the same.
The mean will be in the center of the distribution and the mode and median may be higher or lower than the mean.
The mean, median, and mode will all be in the middle of the distribution.
The mode and median will fall in the center of the distribution and the mean will be larger than both.

Transcript text: In a normal distribution, which statement best describes the relationship between mean, median, and mode? The mode will always be the smallest value, while the mean and median will be the same. The mean will be in the center of the distribution and the mode and median may be higher or lower than the mean. The mean, median, and mode will all be in the middle of the distribution. The mode and median will fall in the center of the distribution and the mean will be larger than both.

Solution

Solution Steps

In a normal distribution, the mean, median, and mode are all equal and located at the center of the distribution. This is a fundamental property of the normal distribution.

Step 1: Understanding the Properties of a Normal Distribution

In a normal distribution, the mean (\(\mu\)), median, and mode are all equal. This is a key characteristic of the normal distribution, which is symmetric about its center.

Step 2: Identifying the Center of the Distribution

Since the mean, median, and mode are all equal in a normal distribution, they all lie at the center of the distribution. This central point is the peak of the bell curve.