Question

9. From the following distribution of marks obtained by 50 students in statistics, calculate average
marks by short out method.
Marks
No. of Students
More than 0
50
More than 10
45
More than 20
38
More than 30
26
More than 40
10
More than 50
4​

Answer 1

Answer:

Let us first of all convert cumulative frequencies into simple frequencies .

(i) M = Size of (N2) th item

= Size of (502) th item = Size of 25th item

Median lies class 20-30.

M=l1+N2−c.f.f×i

=20+502−1020×10=20+25−1020×10

=20+1520×10=20+7.5=27.5

(ii) Since , 60% candidates are passed and 40% have failed , the minimum pass marks are given by P40 . In other words , we have to find the value of P40.

P40 = Size of 40(N100) th item

Size of 40(50100)th item

= Size of 20 th item

P40 lies in the class 20-30.

P40=l1+40(N100)−c.f.f×i=20+40(50100)−1020×10

=20+20−1020×10=20+1020×10

=20+5=25

Median = 27.5.

Minimum marks obtained by a pass candedate =25.