# I have an issue summarising highly skewed data in a table

I have a numerical ordinal dataset (eg. 1-10) that's very highly skewed, with >90% of the values at 10. How can I best summarise this in a table? The median/IQR gives '10 (10, 10)' (which doesn't seem particularly useful).

I'm considering using minimum and maximum, or is there another descriptive statistic I could use to best display this?

Any help would be greatly appreciated, Thanks

• Have you tried a histogram? Commented Feb 15, 2023 at 12:17

Since the variable in question is discrete and with a limited range, I suggest considering a frequency table instead of focusing on single summaries. That is, attach to every value from 1 to 10, the number of occurrences. In addition, I would also divide each frequency by the sample size to get the relative frequency. Indeed, in case you want to compare this distribution with another, perhaps coming from another study, you must necessarily switch to relative frequencies unless the two samples have equal sizes.

You can do this in R very easily.

set.seed(12)
x <- sample(1:10, 1000, replace=T)
table(x)
x
1   2   3   4   5   6   7   8   9  10
95  97  99 104  98  93 116 102 100  96


Lastly, but I'd say more importantly, as a famous quotation says

A picture is worth a thousand words

consider picturing your data by means of a suitable graph. In this case, a barplot or pie plot fills the bill.

• Pie charts are ineffective visualizations and can be difficult to read correctly. Eg The issue with pie charts Commented Feb 15, 2023 at 13:33
• @dipetkov thank you for the remark. Yes, piecharts have limitations, but sometimes they do a good job, so I wouldn't rule them out a priori. Commented Feb 15, 2023 at 13:45