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March 29, 2024, 11:34:59 pm

Author Topic: Coefficent of variation  (Read 2092 times)  Share 

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Michelle94

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Coefficent of variation
« on: August 20, 2013, 11:57:27 am »
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if i have 2 data sets one has a coefficient of variation of 4.63% and one is 3.93% what does this tell me about the dispersion of the data???.
does the larger percentage indicate more spread of data ???

Zealous

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Re: Coefficent of variation
« Reply #1 on: August 20, 2013, 04:42:16 pm »
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To be more exact, it is called the coefficient of determination which is calculated by squaring r (correlation coefficient). You can then convert it to a percentage by multiplying the number by 100, which is the format you've presented.

The coefficient of determination allows you to state how much percent of variation in one variable (the dependent variable, on the y axis) is due to variation in another variable (the independent variable, x axis).

For example, for the 4.63%:
"4.63% of variation in the dependent variable can be explained by variation in the independent variable."

So the higher the coefficient of determination, the stronger the correlation between two variables, so the data sets will have a stronger positive/negative linear relationship.
« Last Edit: August 20, 2013, 04:44:43 pm by sushi. »
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Michelle94

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Re: Coefficent of variation
« Reply #2 on: August 20, 2013, 04:44:58 pm »
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okay i think im talking about a different thing,
this is for uni (business statistics) not further i just thought we learnt it in further but maybe not,

does the coefficient of determination have anything to do with the dispersion of data?

Zealous

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Re: Coefficent of variation
« Reply #3 on: August 20, 2013, 04:49:25 pm »
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okay i think im talking about a different thing,
this is for uni (business statistics) not further i just thought we learnt it in further but maybe not,

does the coefficient of determination have anything to do with the dispersion of data?

I would say (although not certain), that for higher values of the coefficient of determination (as the percentage increases) that there would be less spread in the data, as the data gets closer to resembling a straight line (in the case of a linear regression).
Note, that this is spread around the line, so residuals in this case. As the percentage increases, the residuals slowly get closer to 0 until every point lies on the regression equation line.
« Last Edit: August 20, 2013, 04:52:57 pm by sushi. »
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TrueTears

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Re: Coefficent of variation
« Reply #4 on: August 20, 2013, 04:53:10 pm »
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The coefficient of variation is defined by where is the mean of the probability distribution and is its standard deviation. It measures how dispersed the probability distribution is RELATIVE to its mean.

The (biased) sample estimate of the CoV is given by where is the (unbiased) sample standard deviation and is the sample mean.
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Michelle94

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Re: Coefficent of variation
« Reply #5 on: August 20, 2013, 05:59:27 pm »
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yes TT that is the one i was talking about.!!

so if one data set has a higher % than the other does it mean the larger one has a greater spread of data?????

Zealous

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Re: Coefficent of variation
« Reply #6 on: August 20, 2013, 06:09:31 pm »
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yes TT that is the one i was talking about.!!

so if one data set has a higher % than the other does it mean the larger one has a greater spread of data?????
Hahah ok, so what I was talking about was the coefficient of determination, which is what sounded closest to what you were talking about (we're in the Further Maths board haha)
=)
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Michelle94

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Re: Coefficent of variation
« Reply #7 on: August 20, 2013, 06:14:48 pm »
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Hahah ok, so what I was talking about was the coefficient of determination, which is what sounded closest to what you were talking about (we're in the Further Maths board haha)
=)

yeah im sorry i got confused with the 2 anyway hence why i posted on this board, so clarification was good.

TrueTears

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Re: Coefficent of variation
« Reply #8 on: August 20, 2013, 06:17:23 pm »
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yes TT that is the one i was talking about.!!

so if one data set has a higher % than the other does it mean the larger one has a greater spread of data?????
Relative to the mean - yes.
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