What is the relationship between the mean, median, and mode in a normal distribution?

In a normal distribution, the mean, median, and mode are all equal. This is one of the defining characteristics of a normal distribution.

Here's a step-by-step explanation:

1. Mean: The mean is the average of all the numbers in the data set. It is calculated by adding up all the numbers and then dividing by the count of numbers.

2. Median: The median is the middle number in a sorted list of numbers. If the list has an even number of observations, the median is the average of the two middle numbers.

3. Mode: The mode is the number that appears most frequently in the data set.

4. In a normal distribution, the data is symmetrically distributed with the highest frequency occurring at the center of the distribution. This central point is where the mean, median, and mode all fall, making them equal in a normal distribution.

5. This relationship may not hold in a skewed distribution. In a positively skewed distribution, the mean is usually greater than the median, which is greater than the mode. In a negatively skewed distribution, the mode is usually greater than the median, which is greater than the mean.