Explain why the median might be considered a more reliable measure of central tendency than the mean for a data set that is thought to contain an outlier.

The mean is affected by data size - an outlier can skew the mean away from where the majority of the data lies.

The median is not dependent on the size of data, it is dependent on the number of data-points and so a relatively small number of outliers will not significantly impact on its value.

Lets consider a set of numbers, say,

1,1,2,2,3,3,4,4,5

In this case, the median is 3 while the mean is 2.77.

If one of the data is replaced by an extreme number, say 5 becomes 100, the set of number will become:

1,1,2,2,3,3,4,4,100

The median is still 3! However, the mean will become 13.3. That’s why we say that the mean is easily influenced a lot by outliers (extreme values in a set of numbers). And we would say the median is more reliable to measure the central tendency in such cases.

Both can show the central tendency of a data set. However, in this case, an outlier can be either the lowest or the highest value in a dataset, which can significantly bias the mean value with the outlier included than excluded. While the median of a dataset is more fixed in this case and thus more reliable.

The mean is the most frequently used measure of central tendency because it uses all values in the data set to give you an average.

However, calculating the mean of a data set that contains an outlier (an extremely large or small number that is too far away from the rest of the data points) would produce a misleading answer.

For data with outliers, the median is better than the mean because extremely large values don’t influence it.

Because the outlier will not be a typical member of the group. If it is on the positive side, it will distort the measure of central tendency upwards whereas on the negative side it would be downwards. A good example of this is salaries in a company where the MD is paid an enormous salary and the majority of the staff are on the national minimum wage.