In comparing 2 groups of numbers, I have been asked to consider the following:

1) Center

2) Spread

3) Shape

4) Outliers

in determining whether it would be:

BENEFICIAL to first convert each group of numbers to z scores

NOT BENEFICIAL to first convert each group of numbers to z scores

NOT HAVE AN EFFECT ON THE COMPARISON to first convert each group of numbers to z scores

Any thoughts on this? I have looked at textbooks/ searched the internet but am having difficulties getting explanations of when/ when not to convert to z scores for purposes of comparison in relation to each of the above situations (center, spread, shape, outliers). Your input on any/ all of the above would be much appreciated. Thanks in advance.

NB. This question does not involve any specific data.