Categorical data

[beginner]

Hi,

when you look at the bottom of this page you'll find a table which gives a general overview about statistics.

Can anyone explain me why Frequency . Contingency table is just asigned to Categorical data (equal to discrete data) and not to Continuous data?
And the same for Location, Dispersion and Moments which are just asigned to to Continuous data. I thought it is possible to calculate the mean, median etc. for discrete values as well?

Best regards,
beginner

[AtlasFrysmith]

You haven't posted the table you're referring to, but let me take a stab at it.

Categorical data is NOT equivalent to discrete data.

While you're right that measures like mean, variance, etc can be applied to discrete data, you need to be careful when dealing with categorical data, because the numbers assigned to each category don't necessarily have any numeric significance.

Think about a data set about the color of cars in the US. You might code white=1, red=2, blue=3, and so on. The numbers are just tags--a mean of 2.5wouldn't mean that the average car is purple. You can compute the mean, but it doesn't have any importance. If this isn't clear, just imagine switching the tags so that blue=1, white=2, red=3. You'll get a totally different mean if you compute it, even though the actual distribution of colors hasn't changed. That should be a big sign that you're not using a meaningful measure.

I hope this helps. Let me know if you have more questions.

[beginner]

hi AtlasFrysmith,

thank you very much for your clear answer!
Now I understand the difference between these three
kinds of data.

Now, it is also clear why only the term 'frequency' is assigned
to the categorical data and neither the mean nor other similar
measurements.

Assuming 200 cars having 5 different colors you may be able
to show the color distribution of these cars but however, as you have explained, it makes no sense to calculate the mean for this kind of data.

Many thanks,
beginner