Yes, in a normal distribution, the mean and median are indeed the same.
To understand why, let’s first define what these terms mean:
- Mean: The mean is the average of all the values in a data set, calculated by summing all values and dividing by the number of values.
- Median: The median is the middle value of a data set when the values are arranged in ascending order. If there is an even number of values, it is the average of the two middle values.
A normal distribution, also known as a Gaussian distribution, is a symmetric bell-shaped curve where most of the observations cluster around the central peak and probabilities for values further away from the mean taper off equally in both directions.
In this symmetric distribution, the center of the curve represents both the mean and median, which is why they are equal. This property is crucial in statistics and helps to illustrate the characteristics of normally distributed data.
In summary, because of the symmetrical nature of a normal distribution, the mean and median will always match, providing a consistent central point in the data set.