From the following distribution, calculate the missing frequency if N = 100 and Median = 30.
|
Marks |
No. of Students |
|
0-10 10-20 20-30 30-40 40-50 50-60 |
10 ? 25 30 ? 10 |
In the question, two frequencies are missing f1 and f2. We will get one frequency from summation of frequencies and the other from median formula :
|
Marks |
f |
c.f. |
|
0-10 10-20 20-30 30-40 40-50 50-60 |
10 f1 25 30 f2 10 |
10 10 + f1 35 + f1 65 + f1 65 + f1 + f2 75 +f1 + f2 |
|
Σ f = 100 |
We two that the sum of frequencies is equal to the cumulative frequency of the last class interval. Hence
75 + f1 + f2 = 100
or f1 + f2 = 100-75 = 25 .... (i)
We have been given median (30) which must be in 30 - 40 class interval.
Hence class interval = 30-40
Median = 30 (given)
Substituting the value of f, in (i) equation we get,
15 + f2 = 25
Hence f2 = 25 - 15 = 10
