6 For each of the following indicate whether it is resistant

6. For each of the following, indicate whether it is resistant to outliers or not. Do not bother to explain your answers, except for the last one.

a. Mean b. Standard deviation

c. Median

d. (Lower quartile + upper quartile)/2

e. (Maximum + minimum)/2

f. Mean absolute deviation (Explain your answer.)

Solution

a. Mean : Mean is not reistant to outlier. The outlier (extreme values) affects the mean and dragged to either side

b. Standard deviation : It is not resistent to outlier. Since the deviations taken from mean, so sum of the squares of the deviations also large. so it is not resistent.

c. Median : it is resistent. since this was based on the middle one or two observation. so it was not affected by outliers.

d. (Lower quartile + upper quartile)/2 = Lower and upper quartiles are resistent( unless the no.of values ae very small) since these are positional values calculate based on middle one or two of the lower and upper half of the data set. so this is resistent

e. (Maximum + minimum)/2 : This is not resistent .

f. Mean absolute deviation (Explain your answer.) This is not resistent. The actual absolute deviations is effected by the extreme observations. Therefore the mean absolute deviation is also affected