Question

If there is an outlier, what would it tend to affect more?

Group of answer choices

Mean

Median

Mode

All equally

None of the above.

Answer 1

Outliers are extreme values present in the data. Median corresponds to the middle most observation. It remains unaffected by the presence of extreme values or outliers. Even if the values at the ends are too large, the median is not hampered as it is robust against outliers. For example, let us consider the data on weight in kgs of 5 individuals: 56,61,65,69,70. Clearly the median is 65. However, instead of 70, if the last observation was measured as 170, in that case also, the median will be 65! Thus median is not much affected by outliers.

Mode corresponds to the most frequently occurring observation in a data. Thus even if outliers are present, mode will not be affected much. This is illustrated by the following example. Consider the following data: 1,4,3,2,4,2,2,6,2. The maximum occurring digit is 2. Hence 2 is the mode in this case. However if the data contained an outlier: 1,4,300,2,4,2,2,6,2 then also the mode remains unchanged.

However mean is greatly affected by the presence of outliers as it is based on all observations. Consider the data: 1,2,3,4,5. The mean is 3. If however there is an outlier in the data such as: 1,2,3,4,500 the mean would have been 102. Thus it is clearly seen that out of mean, median and mode, mean is mostly affected by outliers.