Question

How does the mean, median, and mode location differ between a symmetric to skewed distribution?

Why are measure of location, commonly called measures of center, not sufficient in themselves to get a good picture of a data set?

Answer 1

For symmetric distribution

mean= median= mode

For left skewed(-vely skewed)

Mode>Median>Mean

For right skewed(+ve ly skewed)

Mode<Median<Mean

This is how the mean ,median and mode varies with the skewness of the data.

The measure of centres work good when there is no outlier. Due to oultiers we cant get the good picture of a dataset. So we use Q1,Q3 and Inter quartile range to remove the outlier and then calculate the measures of centre to get a good picture.