Question about property of symmetrical distribution

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ysheen

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In Notes 1, it says:

In a symmetrical distribution, mean, median and mode are equal.

However, I think, for below simple distribution, mean and median are equal, but mode are 1 and 3. What is the problem with my understanding? Thanks

1, 1, 2, 3, 3
 
I am sorry, Andys. I don't get your point.
 
What I meant was your data sample is not enough to discribe the characteristics of the data. Symmetrical distribution can have two modes, one on each side of the median, which is in case of your sample data. So you can say the data below mean and above mean is equally distributed.
Experts please recheck my concepts.
 
I think it is because the example you have given isn't a "normal distribution". A normal distribution has a mode = mean = mode, and with share valuation this is normally the case (I think) ie: you'll have the highest frequency in and around your mean.

A normal distribution should read something like:

0.5 - 1.00 - 1.25 - 1.49 - 1.50 - 1.50 - 1.51 - 1.75 - 2.00 - 2.50

Havent calculated it all, but it should give you a normal distribution ie: mean = mode = median. If you think of the shape of a normally distributed curve, the mode must be central because it has the highest frequency.

Kerry.
 
So we can conclude that description of property of symmetrical distribution is not always right. It should also state that this is only for case of unimodal distribution.
 
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