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

  1. #1

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

    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


  2. #2
    Only Slightly Obsessive jemidiah's Avatar
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    Re: how to calculate median of grouped data if group size is variable

    Your formula remains valid for non-fixed-width classes. h just needs to be the size of the class containing the median.
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    Re: how to calculate median of grouped data if group size is variable

    Quote Originally Posted by jemidiah View Post
    Your formula remains valid for non-fixed-width classes. h just needs to be the size of the class containing the median.
    Can i solve this way ????
    We will start counting from both ends and find the place where both sums are as close to equal as possible. For example, in our second illustration, there are 500 in the first batch, which is more than all the others together, therefore the median is in the first batch.

    I think it may work ..............

  4. #4
    Only Slightly Obsessive jemidiah's Avatar
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    Re: how to calculate median of grouped data if group size is variable

    There's some ambiguity in your description. Perhaps the best way to figure out which group the median lies in is probably to first add the frequencies to compute n (which you'll need to do anyway). Starting from the first group, successively add the group frequencies until you exceed n/2. The group which made you exceed n/2 contains the median.

    Ex: given frequencies (in order) 5, 12, 3, 6, 9, 15, 25, we have n=75, so n/2 = 37.5. Successively adding frequencies from the left, we get 5, 5+12=17, 17+3=20, 20+6=26, 26+9=35, 35+15=50 > 37.5. Thus the median occurs in the second to last group, that of size 15.
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    Re: how to calculate median of grouped data if group size is variable

    Quote Originally Posted by jemidiah View Post
    There's some ambiguity in your description. Perhaps the best way to figure out which group the median lies in is probably to first add the frequencies to compute n (which you'll need to do anyway). Starting from the first group, successively add the group frequencies until you exceed n/2. The group which made you exceed n/2 contains the median.

    Ex: given frequencies (in order) 5, 12, 3, 6, 9, 15, 25, we have n=75, so n/2 = 37.5. Successively adding frequencies from the left, we get 5, 5+12=17, 17+3=20, 20+6=26, 26+9=35, 35+15=50 > 37.5. Thus the median occurs in the second to last group, that of size 15.
    Hello ,
    I am using all the techniques requires to solve this and also what you have guided nut still i am not able to solve it till final solution.

  6. #6
    Only Slightly Obsessive jemidiah's Avatar
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    Re: how to calculate median of grouped data if group size is variable

    Ok.... Well, it should be quite obvious that the median occurs in the first group (which also follows from my median finding algorithm above). Then simply apply the formula L + (n/2-cf)*h/f where...
    L = 5, n = 715, cf = 0, h = 5, f = 500
    which gives 8.575. As a sanity check, since there are 715 people in the sample and 500 in this group, the median should be to the right of halfway through this group, which would be 7.5. And it is.
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