how to calculate median of grouped data if group size is variable

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Amit Kumar 2011-11-11

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评论： Obed Kisovi 2017-6-5

I learned in school that Median = L + (n/2-cf)*h/f where L = lower limit of median class n = no. of observations cf = cumulative frequency of class preceding the median class, f = frequency of median class, h = class size (assuming class size to be equal).

I used to use this formula for grouped data of fix width like marks ........ no. of student 0 - 10 .......... 5 10 - 20 ........... 3 20 - 30 ......... 4 and so on. here grouped data is of fixed width 10=10-0=20-10=30-10 ans so on

BUT how will I calculate median if width is not fixed like

population ........ no. of town 5 - 10 ................. 500 10 - 20 ................. 100 20 - 50 .............. 50 50 - 100 ............. 30 100 - 200 ............. 20 200 - 500 ............... 10 500 - 1000 .................. 3 1000 and above ................. 2

how will I calculate median in this case

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Obed Kisovi 2017-6-5

Data set of grouped and has no equal width

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Answer 1

Image Analyst 2011-11-11

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As an approximation, can't you just re-bin your wide bins into the smallest bin so that you can use your formula for the approximate mean L? For example your smallest bin looks to be 5 which occurs for the range 5 < 10. So for your super wide bin at 500 - 1000, divide that up into 100 bins of 5. Though for a count of only 3 in that huge range you can't really get meaningful data. But if you had say, 100,000 count, you could have 100 bins of 1000 in each, if you re-binned it.