What does it tell you when the mean is a lot higher than the median and the mode?

When the mean is significantly higher than the median and the mode, it suggests that the data is skewed to the right, also known as positive skewness. This is because the mean is influenced by the values at the extreme end of the distribution.

Here are the steps to understand this:

1. In a perfectly symmetrical distribution, the mean, median, and mode are all the same.

2. When the mean is higher than the median and mode, it indicates that there are values on the higher end of the distribution that are pulling the mean upwards.

3. These higher values are known as outliers and they cause the distribution to be skewed to the right.

4. Therefore, the presence of outliers on the higher end of the distribution is what causes the mean to be significantly higher than the median and mode.

5. This is a common occurrence in distributions where the lower end has a limit (such as zero) but the higher end does not have a limit, resulting in a long tail on the right side of the distribution.

6. Examples of such distributions include income, house prices, or population age in a country with a high life expectancy.