HI

Cash compensation received by 12 employees put on redundancy by a
company are as follows:

2215   1888   1477   1059   977   956   947   924   899   856   856  
803

a.  Find mean and median
    my answer is 1154.75 for mean and 951.5 as median

b.  based on above result comment on skewness of the distribution of
employees    compensation.

   answer =  there is positive skewness

c.  Repeat part a ignoring the highest compensation

my answer for mean is 1058.36 and 9.47 as median


d.  with the reference to the results obtained in parts a, b, and c.
discuss the relative usefullness of the mean and the median as
measures of central location.

Pls verify if I have answered the above correctly.  If I haven't pls
explain where I have gone wrong.  Also part d.  I don't quite
understand.  Can I get some help with it please

Thanks for your help
Jabeda

Hi again jabeda!

Let'see each of your questions.

a. You got the right answer for the mean. The formula for the mean is
sum(X)/N, (N is the number of observations) so you had to sum all the
numbers in the data and then divide this result by 12. This gives
1154.75, you got the right answer. You can find more information on
the mean at

Mean (1 of 4)
http://davidmlane.com/hyperstat/A15885.html

You also got the right answer for the median. When there is an even
number of numbers (like in this case, where you have 12), the median
is the mean of the two middle numbers, in this case, it's the mean of
956 and 947. This effectively gives 95.1. More information on the
median can be found at

Median
http://davidmlane.com/hyperstat/A27533.html


b. Again, your answer is correct.

"For a positively skewed distribution, the mean will always be the
highest estimate of central tendency and the mode will always be the
lowest estimate of central tendency (assuming that the distribution
has only one mode) [...] In any skewed distribution (i.e., positive or
negative) the median will always fall in-between the mean and the
mode"

Measures of Central Tendency
http://simon.cs.vt.edu/SoSci/Site/MMM/mmm.html

Therefore, observing that the mean is higher than the median, one
concludes that the distribution is positively skewed. The intuition is
that a positively skewed distribution has a few high extreme values.
Since the mean is much more affected by this outliers in the
distribution than the median, a few very high values will result in a
mean higher than the median. You might want to check the following
page in order to learn more about skewness:

Skew (1 of 3)
http://davidmlane.com/hyperstat/A11284.html

The effect of skew on the mean and median
http://davidmlane.com/hyperstat/A92403.html


c. This one is calculated in the same way as exercise a, an you also
got the right answer, both for the mean and median. I assume that
where you put 9.47 you meant to put 947. The latter is the correct
answer, because now you have an even number of observations, and so
the median is the middle observation.


d. You can see from what happened to the mean and median after
removing the outlier 2215 that the mean is more sensitive to extreme
values than the median. The mean dropped considerably after removing
this extreme value, while the median was only slightly change. The
conclusion is then that the median is a more informative measure of
central tendency for skewed distributions. One example of a positively
skewed distribution is the distribution of income. Quote one of the
links above:

"One example is the distribution of income. Most people make under
$40,000 a year, but some make quite a bit more with a small number
making many millions of dollars per year. The positive tail therefore
extends out quite a long way whereas the negative tail stops at zero."

In these cases, if you look at the mean you will see that the mean
income is much higher than what most people earn. Therefore it's
better to use the median as a measure of central tendency.


Google search strategy
mean median
://www.google.com/search?sourceid=navclient&ie=UTF-8&oe=UTF-8&q=mean+median

skewness
://www.google.com/search?sourceid=navclient&ie=UTF-8&oe=UTF-8&q=skewness


Good job on questions a, b and c!  I hope this cleared things up for
you. If you still have any doubt regarding these questions, please
don't hesitate to request a clarification. Otherwise I await your
rating and final comments.


Best wishes!
elmarto

Thanks heaps once again for all your help

Regards
Jabeda