Well how is an average calculated from a frequency?
Hi,
I am new here, please discuss this given below.
“Why an average computed from a frequency distribution is not exactly the same as computed from the raw data? Give the reason”
Well how is an average calculated from a frequency?
Stop cowardice, ban guns!
You can compute all three without bias, assuming the frequency distribution is really the frequency distribution and not the frequency distribution of a binned version of the original data. So the underlying assumption behind the original question seems to be false or you are not telling us everything we need to know.
I agree with Maartenbius. I was thinking if you did not have raw data and used weights from frequency dist, then bins could slightly err the Cal ulation.
Stop cowardice, ban guns!
Either your instructor is just wrong, or this question is part of a larger exercise which gives the relevant information that you are not telling us. Context is important!!!!!
If this is an isolated question, then I would just give a counter-example, for example:
Code:. // open some example data: . sysuse auto (1978 Automobile Data) . . // compute mean and median using raw data . sum rep78, detail Repair Record 1978 ------------------------------------------------------------- Percentiles Smallest 1% 1 1 5% 2 1 10% 2 2 Obs 69 25% 3 2 Sum of Wgt. 69 50% 3 Mean 3.405797 Largest Std. Dev. .9899323 75% 4 5 90% 5 5 Variance .9799659 95% 5 5 Skewness -.0570331 99% 5 5 Kurtosis 2.678086 . . // using the frequency distribution . tab rep78 Repair | Record 1978 | Freq. Percent Cum. ------------+----------------------------------- 1 | 2 2.90 2.90 2 | 8 11.59 14.49 3 | 30 43.48 57.97 4 | 18 26.09 84.06 5 | 11 15.94 100.00 ------------+----------------------------------- Total | 69 100.00 . . // the cumulative percentage passes 50 at . // rep78=3, so the median is 3 . . // the mean is: . di (2*1+8*2+30*3+18*4+11*5)/69 3.4057971
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