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I was recently asked to choose from the basic set of descriptive statistics which ones are sufficient.

Mean Median Mode Standard deviation E. Variance Range IQR (or IR) Skewness Kurtosis

This was a test question, and I guess I have the wrong idea about sufficiency because I was under the impression that it was on a per-distribution basis.

Can someone explain to me how to generally classify statistics as sufficient or not, and why? I'll also add that I am very new to statistics, and the only explination of sufficiency offered is that a stat uses all available data.

Thanks!

zachd1_618
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  • Please see my answer below; if you have additional questions on this topic, please let me know! – 324 Dec 10 '19 at 02:09

1 Answers1

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Mean is good when the data lacks major outliers. For example, if you had several outliers on the lower end of your data, it would push the mean down, so a more robust descriptive statistic in this case would be the median. The median is more robust to extreme outliers.

Likewise, standard deviation and variance are helpful when the mean is used for the same reason. Outliers would increase the spread, and therefore, increase these statistics. A more robust descriptive statistic would be the IQR which can illustrate the spread without being too spread out. Like the median, the IQR is robust to extreme outliers.

Hope this helps!

324
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