The absentee record of students in a given term is as follows. If the mean absentee for the term is 15.5, find the frequencies 'x' and 'y'.
Number of Days | 0-5 | 5-10 | 10-15 | 15-20 | 20-25 |
Total Number of Students | 15 | 16 | x | 8 | y |
Number of Days |
25-30 |
30-35 |
35-40 |
Total |
Total Number of Students |
8 |
6 |
4 |
70 |
Calculation:
Class-Interval | Frequency (fi) | MidPoint (x_{i}) | (fi) (xi) |
0-5 | 15 | 2.5 | 37.5 |
5-10 | 16 | 7.5 | 120 |
10-15 | x | 12.5 | 12.5x |
15-20 | 8 | 17.5 | 140 |
20-25 | y | 22.5 | 22.5y |
25-30 | 8 | 27.5 | 220 |
30-35 | 6 | 32.5 | 195 |
35-40 | 4 | 37.5 | 150 |
Total | 70 | 862.5 + 12.5x + 22.5y |
Mean = (Sum of fi xi)/fi
⇒ 15.5 = (862.5+ 12.5x + 22.5y)/70
⇒ 15.5 × 70 = 862.5+ 12.5x + 22.5y
⇒ 1085 - 862.5 = 12.5x + 22.5y
⇒ 222.5 = 12.5x + 22.5y
⇒ 89 = 5x + 9y ----(1)
Also sum of all students is 70
⇒ 15 + 16 + x + 8 + y + 8 + 6 + 4 = 70
⇒ x + y = 13 ----(2)
By solving (1) and (2) we'll get x = 7 and y = 6
∴ x = 7, y = 6
As sum of all students = 70
⇒ 15 + 16 + x + 8 + y + 8 + 6 + 4 = 70
⇒ x + y = 13
From the given options, sum of x and y is 13 in option 4 only
∴ x = 7, y = 6