Question

Determine the missing frequencies when median =33.5 and mode =34
Marks: 0-10  10-20  20-30  30-40   40-50   50-60   60-70
F         :   4           16       ?             ?           ?           6            4      
F=100

Answer 1

total F = 100.
Therefore F is even.
For even,
Median = ((n/2)th observation + (n/2+1)th observation)/2
   33.5  = ((100/2)th obs. + (100/2+1)th obs.)/2
   33.5  = (50th obs. + (50+1)th obs.)/2
   33.5  = (50th obs. + 51th obs.)/2
   33.5 * 2 = 50th obs. + 51st obs.
   67 = 50th obs. + 51st obs.
   now mode = 34 
therefore, maximum no. must lie in 30-40.
frequency = 100 - 64 = 36.