Measures of central tendency
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 This topic has 5 replies, 5 voices, and was last updated 17 years, 4 months ago by spampurge.

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July 26, 2005 at 10:28 am #40130
FinkelsteinParticipant@Nathan Include @Nathan in your post and this person will
be notified via email.I have a skewed distibution so am using Q1 as my measure of central tendency. Is there a hypothesis test I can use to check whether there is a true difference between two values for Q1?
0July 26, 2005 at 1:40 pm #123632
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.Q1 is a measure of non central location which is not the same thing as a measure of central tendency. The three measures of central tendency are mean, median, and mode. There are variations on the theme with respect to the mean – geometric and harmonic mean – but those are the biggies. For a skewed distribution the median is probably your best bet and there are tests for differences in median values. One of the favorites – and one which may be of value to you – would be the Mood’s median test. It is robust against outliers and it does assume the two distributions have the same shape.
0July 26, 2005 at 1:50 pm #123633somebody told me that mean is always lower than median, median is always lower than mode. is it true.
Ellis0July 26, 2005 at 2:03 pm #123634Hi Ellis,
sorry to disappoint that ‘somebody’ but they are clearly wrong…..in a man sized way.
Think about it.
eg. a set of random (but ascending)data (for ease of example);
5,9,9,9,12,13,13,17,19,19,21,24,26
Median = 13
Mean = 15 (.076)
Mode = 9
my 2 penneth
Jaybee0July 26, 2005 at 3:18 pm #123645
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.Jaybee is correct – somebody is wrong big time.
If you think of a distribution as a physical object then the mean would be the point at which you could just balance the distribution on your finger like at seesaw. For median – think grassy strip between the lanes of a 4 lane highway – that is the 50% point the point at which exactly half of the data is below and half is above – half the traffic in one direction – half the other (rush hour excepted :) ) and mode is the most frequent term and it can be just about anywhere.
If the distribution is symmetric then all three measurements will be quite close to and may be in fact equal to one another. If the distribution is asymmetric then all bets are off.0August 4, 2005 at 6:40 pm #124306
spampurgeMember@spampurge Include @spampurge in your post and this person will
be notified via email.A simple rule of thumb is this: If your distribution is negatively skewed, then the mean will “typically” be “pulled” down towards the “clump” of negative scores and if your distribution is positively skewed, then the mean is “typically” “pulled” up, towards the clump of positive scores. The median however, will always be the “middle most” score, where 50% of the scores in your distribution lie below and the other 50% lie above. As you can probably see, the mean in some cases will actually be higher or lower, or in the case of a normal distribution, “almost” equal to the median.This is one main reason the median is often referred to as a “more robust” measure of central tendency.
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