Question

State the three measures of dispersion discussed in this section. Are any of these measures resistant? Explain.

Answer 1

Now we are to discuss the resistant--

Resistant statistics don’t change (or change a tiny amount) when outliers are added to the mix. Resistance doesn’t mean it doesn’t move at all (that would be “immovable” instead). It means there might be a little movement in your results, but not much. When a statistic changes because of a “rogue” data point, your result can be far from the true value you’re trying to estimate. This bias can be avoided if you eliminate outliers or use weighting factors to minimize the damage they cause.

The arithmetic mean, the median is not at all influenced by the exact value of the largest objects and so provides a resistant measure of the central location. Likewise, a resistant measure of the scale can be obtained using the Inter-Quartile Range (IQR) given by the difference between the upper and lower quartiles .

The quartile deviation are divided some 1st,2nd 3rd quartiles. Here the inter quartile range is the resistant measure of dispersion.