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Gents,
I am doing a bit of coursework and i'm having a bit of an issue with a question.
I am doing a section on income equality ie. fraction of population vs fraction of income. I need to get some data points for an equally distributed population, ie. 50% of people earn 50% of income / 45 degree line.
I am told that the mean (hence the median given distribution) is £528/week and that the standard deviation is £281/week.
How can i go about plotting this line? I am assuming that I need to use Z=X-Mu/Standard Deviation (£281) to find a Z value in order to find X.
May be barking up the wrong tree - any professionals in the house? robowns at hotmail dot com if you are willing to school an idiot.
Many thanks,
Rob
On STW?
Everyone will earn well above the average, but will pretend not to...
Probably one for the chat forum.
Sorry I'm not following what you are asking. Do you want to calculated fractions from a distribution with mean 528 and standard deviation 281? A cumulative normal function can help with this.
What do you mean by "equally distributed" same CV (stdev/mean)? A Z-score is one tool to characterise how far from the mean one is.
Equally distributed meaning that 528 is exactly 50% of income/population. I need to show income in 5% increments. I need to show the solution so I assume dividing by 50 and times 45 is too simple.
I don't understand the 45 degree line.
It sounds to me like you have been set an even distribution problem. So plotting a graph with income as the x axis and % of pop as the y axis then you will get a symmetrical bell curve.
I'd tackle this my putting in the mean and sd in [b]named[/b] cells at the top of an excel workbook, then have a table below with deviation %, income, % of population as the column, deviation will be for -50%,-45%,...0%,...+50%, other two columns worked out by formula referencing the named cells, make a graph from columns 2 and 3.
In that case you want the normal distribution function. Create a column from zero to 1 in steps of 0.05 increments. Then n the column next to this use norminv(A_,528,281). Copy this down and it will give you the income for each percentile from 0 to 100 percent, centred on your distribution.
similar to TiRed but slightly different.
If you want to plot a normal distribution of the actual incomes (x)
in Excel,
column A: list numbers from 0 to say 1000, in steps of 10
column B: =NORMDIST(A1, 528, 281, False)
copy down, then plot as a line or XY scatter
For the cumulative plot:
column C: =NORMDIST(A1, 528, 281, True) and copy down.