The mean marks obtained by 50students in a test is 23, where a and b are two missing data .Find a
and b.
Marks 0-10 10-20 20-30 30-40 40-50
No. of students 4 a 20 b 4
Answers
The value of a and b is 6 and 16 respectively.
Given:
Mean = 23
Total number of students = 50
Marks 0-10 10-20 20-30 30-40 40-50
No. of 4 a 20 b 4
students
To Find:
We need to find the values of a and b
Solution:
Total number of students = 50
⇒ 4 + a + 20 + b + 4 = 50
a + b = 50 - 28
a + b = 22 ...(1)
Now, we can calculate the class marks as follows-
Marks 0-10 10-20 20-30 30-40 40-50
Frequency (f) 4 a 20 b 4
Class mark (x) 5 15 25 35 45
fx 20 15a 500 35b 180
Thus, mean will be-
mean = (20 + 15a + 500 + 35b + 180)/50
23 × 50 = 700 + 15a + 35b
1150 - 700 = 15a + 35b
450 = 15a + 35b
90 = 3a + 7b ...(2)
Now, multiplying (1) by 3 we get-
3a + 3b = 66 ...(3)
Subtracting (3) from (2)-
4b = 24
b = 6
⇒ a = 16
Thus, the value of a and b is 6 and 16 respectively.
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