question about 'extreme values'...

[ilovesuck]

from VCAA exam 2 2004
Core, question 1 e iii

my answer was the mean, as no outliers are present; however, the exam report says that the median is correct due to the presence of extreme values.  while i understand how these 'extreme values' can affect the mean, i was never taught that because of them, the mean would be incorrect to use.

furthermore, how are we supposed to identify these 'extreme values'? 

outliers can be recognised using the formulas for upper and lower boundaries, however extreme values seem to be subjective, which makes the answer, to me, seem stupid.

can someone clarify?

i hope something as ambiguous as this does not show up this year...

[jsimmo]

yeah, the answer is the median because if you look at the boxplot for males you can see that it is heavily SKEWED and hence, the mean would not be the best option because it would be affected by the 'skewness' in the data. If the boxplot showed a symmetrical distrbution then it would be acceptable to use the mean because the data is even and hence the mean would not be affected by the extreme values.

just remember:

if the data is positively or negatively skewed = use the median
if the data is symmetrical = you can use both the median or mean (but the mean is preferred)

ALSO.. to "Explain your answer." you would just say that because the data is negatively skewed it is heavily affected by outliers/extreme values and hence the median would be the best option to use.

[*Roxxii*]

They mention extreme values because when a point/s is significantly higher or lower than the majority of the data, but are not high or low enough to be defined by the term 'outlier', they still cause the mean to be a less reliable measure of the centre, just like outliers and skewed distributions.