When to use median, IQR and when to use mean, standard deviation?

Question

You have provided the IT team a histogram summarising the centre and spread with median and IQR. Why did you use median and IQR and not mean and standard deviation?

 A: A high outlier or a low outlier will significantly skew the data but would not influence mean and standard deviation that much, and would therefore not be noticed by the IT team.

 B:  A high outlier or a low outlier will significantly skew the data but would not influence mean and standard deviation that much. The median and IQR are less resilient to outliers, giving a better indication of where they are.

 C: A high outlier or a low outlier will significantly skew the data and could also substantially inflate or deflate the standard deviation. The median and IQR are more resilient to outliers, giving a better indication of centre and spread.

 D:  A high outlier or a low outlier will significantly skew the data and could also substantially inflate or deflate the standard deviation. The median and IQR are less resilient to outliers, giving a better indication of where they are.

Answer 1

Outliers can pull or push the mean significantly but may not significantly influence the standard deviation (SD). Because the SD is a measure of deviation from the mean (the spread of the data), if the mean is displayed by outliers, the range of datavalues could be misleading. The interquartile range is better in showing where the majority of the data lies. Also the median (quartile 2) is the central datavalue, and is not much influenced by outliers because it's based on where most of the data accumulates, so I'd go for option C.

Comments

Hello Rod, thank you for your help as always.