find the missing frequency?

Question

marks       frequency

20to30        5

30to40        9

40to50        13     

50to60       ?

60to70       20

70to80         15

80to90         8

90to100        9

 

Answer 1

Hi Kayal

 

If not additional information available, the best approach to this problem is to use local interpolation.

 

If you assign each value of the frequency to the mean value of each mark, we have:

 

Mean        Freq

 25              5
 35              9
 45            13

 55              X
 65            20
 75             15
 85               8
 95               9 

 

You can see that the behavior of the frequency is to increase from 5 to 20, and later decrease. Because you are only interested to estimate the unknown frequency "X", it is located in the portion of the graph that is increasing until 20. Also, the frequency is linearly increasing from 5 to 13...then, it is not bad to assume that this linear trend is also valid for the missing frequency.

 

In this case, the local slope, M, between the pair of points (45,13) and (65,20) is given by:

 

     M = (20 - 13)/(65 - 45)

 

     M = 7/20

 

Now, keeping this slope valid for the unknown frequency X, we have:

   

             (X - 13)/(55 - 45)  = 7/20

 

              X - 13 = (7/20)*10

 

              X = 13 + 7/2  = 16.5

 

The missing frequency is 17, if you rounded.

  

Answer 2

Without additional information, it's not possible to answer this question.