Mean and Mean Absolute Deviation inferential statistics

Question

Consider the following data of runners in a race. The first data is from a certain year the second one is from the year after.

$Last\space year \space|\space Mean: 525s \space|\space MAD: 25s$

$This \space year \space|\space Mean: 613s \space|\space MAD: 21s$

The question asks to make inference from the measures of variability.

My answer:

The MAD this year is lower than last year, this means that more students were closer to the mean time taken to finish the race. Since the mean this year is greater than the mean last year, more students were slower this year.

I feel like this should be right, but I am not quite sure if it is the right inference from the data given.

Answer 1

It seems to be a self-study question so let me just give you some hints to figure it out by yourself.

• Mean is sensitive to outliers.
• MAD is an acronym generally used for median of deviations from median. MAD is a robust measure of variability, so it is insensitive to outliers (see also other questions tagged as mad). You may want to use it if you have clear outliers in your data.
• The MAD acronym is sometimes is also used for mean absolute deviation, you'd need to consult your materials for which one is it. If that is the case, if it is defined as an average absolute deviation from the mean, your reasoning is correct.