# Can mode be calculated for grouped data with unequal class sizes

2
by sum2

2015-09-21T13:40:42+05:30
Make the class sizes equal then we can find the mode.
the original data probably is not available.. so it may not be possible to make the class intervals equal.
2015-09-21T14:32:17+05:30

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Yes we can..  We need to do more computations and use an appropriate formula for that.

we calculate height of the class interval by dividing the frequency by that class width.  That class which has the maximum height will be the modal class, containing the mode.

Class        frequency              height
10 - 15          5                      5/5= 1
15  - 18          9                      9/3 = 3        call this H1
18 -  25         35                      35/7= 5
25 - 29          16                      16/4 = 4      Call this H2
30 - 32            4                        4/2 = 2

Now,  class 18 - 25      contains mode.
L = lower limit of the class 18.
w = width of the class.
height differences between classes on either side of  modal class:
h1 = 5 - 3 = 2
h2 = 5 - 4   = 1

Mode =  L +   h1 * w / (h1 + h2)  = 18 + 2 * 7 /(2+1)  = 68/3
= 22.6667
Also mode can be expressed as =  L + H2 * w / (H1 + H2) = 18 + 4*7/(3+4)
= 22.0

click on thanks button above pleas