Question

When is the mean a better statistic then the median? Give an example

When is the median a better statistic then the mean? Give an example

Answer 1

When the sample size is large and does not include outliers, the mean score usually provides a better measure of central tendency..The mean is usually the best measure of central tendency to use when your data distribution is continuous and symmetrical, such as when your data is normally distributed. However, it all depends on what you are trying to show from your data.

As for example consider we want the average height of students of Fifth standard of a school. we count heights of all student and find the mean.

Let’s say you run a customer satisfaction survey with a sample of 9 and rate their overall satisfaction scores on a scale of 1 to 10. You get an average of 5.22. You know that in general, you tend to retain customers with a score over 3, so you’re satisfied because this indicates that you’re still above where you want to be. But then, suddenly, you lose 6 of those 9 customers. You go back to look at your data, and you find these scores:

1, 3, 3, 3, 3, 5, 9, 10, 10

The median of this group is a 3, indicating that at least half of your customers or more were unhappy. The scores became lopsided because of the unexpected 10’s, and you missed out on an important part of your data – the midpoint that indicated that as many as half of your customers or more were dissatisfied with your company.

Median can play a major role in things like income level research as well, because a few millionaires may make it look like the socio-economic status of your sample is higher than it really is.

Whenever a graph falls on a normal distribution, using the mean is a good choice. But if your data has extreme scores (such as the difference between a millionaire and someone making 30,000 a year), you will need to look at median, because you’ll find a much more representative number for your sample.