Question

can mode be calculated for grouped data with unequal class sizes

Answer 1

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

Answer 2

YES.

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.