How does central tendency relate to normal distribution?
1 Answer
Any normal distribution has a graph that is perfectly symmetric about a vertical line through its peak. Therefore, all measures of central tendency (most commonly, the mean, median, and mode) give the same answer: the
Explanation:
A normal distribution with mean
The graph of this function is the classical "bell-shaped curve". The standard normal distribution with
graph{(1/sqrt(2pi))*e^(-x^2/2) [-2.5, 2.5, -1.25, 1.25]}
The mean of a general normal distribution is equal to the improper integral
This integral is not too hard to do when
The median is the value of
The mode is the
All the measures of central tendency therefore give the same answer: the