Timothy M. answered • 09/05/15
Tutor
New to Wyzant
Ph.D. in neuroscience with specialty in statistical analysis
Hello,
This will depend on what type of distribution you're talking about. I'm going to assume a normal (or Gaussian) distribution (if that's not correct, feel free to respond and we can figure it out).
For a normal distribution, the center is point at which the distribution peaks and is the point around which most of the data tend to cluster. Mathematically, it is the mean (average), median and mode.
If two groups have different "centers" for their distributions, this means that, on average, one group is different from the other. Let's take height as an example. On average, men are taller than women. If we look at the distributions of height for men and women, the center of the distribution will be higher for men (because the center is the mean and on average the mean is larger). Your description is generally correct. If two means are different, then the data are clustered around a higher mean in one group than in the other.
Timothy M.
Statisticians use "average" in a very confusing way. "Average" is an umbrella term that can refer to any measure of central tendency (mean, median or mode). But you're right in that, most of the time when we say "average" we're referring to the mean. So this will depend on the type of distribution you're working with. If the variable is normally distributed then the mean, median and mode are all the same number - so we can say that, on average, on distribution is higher/lower than another. If the variable is not normally distributed, then it will depend on what type of distribution you're working with.
Report
09/06/15
Nicole T.
09/06/15