What measure of central tendency and variation best describes this data

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Leah.J
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If the data is skewed, which measures would best describe the data ? Mean or median or mode ? Standard deviation,variance, IQR or range?
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NotNotBatman
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Any thoughts?
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Leah.J
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(Original post by NotNotBatman)
Any thoughts?
I don't think range should be used in any case. between mean median and mode I'm thinking median but I don't know. The mean would be affected by the skewness but isn't that a good thing ? Wouldn't that show that our data is skewed. mode same thing.
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NotNotBatman
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(Original post by Leah.J)
I don't think range should be used in any case. between mean median and mode I'm thinking median but I don't know. The mean would be affected by the skewness but isn't that a good thing ? Wouldn't that show that our data is skewed. mode same thing.
If we are given the data in some format and can already see that it is skewed, we aren't showing that it is skewed again, but deciding a measure for central tendency, that is what is the better measure for the centre?
The mean is sensitive to extreme values. If you were deciding on a measure of centre for say household income, then the mean would take into account the billionaires and those earning a few thousand, now think about it; adding on a billionaires is going to affect the mean considerably more than the median. It is better to find the median, as it shows the value which 50% of the population are above and 50% of the population are below. So in the example, billionaires are only assigned a numerical placement rather than artificially increasing the centre.

Now in practice this isn't necessarily always the case, actually the advantages fail in many cases, but in introductory material this is how it is presented.

Given this, think about what the best measure for spread is.
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Leah.J
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(Original post by NotNotBatman)
If we are given the data in some format and can already see that it is skewed, we aren't showing that it is skewed again, but deciding a measure for central tendency, that is what is the better measure for the centre?
The mean is sensitive to extreme values. If you were deciding on a measure of centre for say household income, then the mean would take into account the billionaires and those earning a few thousand, now think about it; adding on a billionaires is going to affect the mean considerably more than the median. It is better to find the median, as it shows the value which 50% of the population are above and 50% of the population are below. So in the example, billionaires are only assigned a numerical placement rather than artificially increasing the centre.

Now in practice this isn't necessarily always the case, actually the advantages fail in many cases, but in introductory material this is how it is presented.

Given this, think about what the best measure for spread is.
Oh that makes sense, so .. IQR
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