Correct Answer - Option 1 : 159.2
Given:
Total number of student = 88
The number of girls is 20% more than the number of boys.
The average height of the boys = 164 cm
The average height of girls is 4 cm less than the average height of all the boys and girls in the class.
Formula used:
Average = (Sum of total observations)/(total numbers of observation)
Calculation:
Let the number of boys be 'x'.
Again let the total average of the student be 'y'.
So, the average height of girls = y – 4
The number of girls = 20% more than the number of boys
⇒ The numbers of girls = x + 20% of x
⇒ x + (20x)/100
⇒ (6x/5)
According to the question,
Total numbers of student = 88
⇒ x + (6x/5) = 88
⇒ (11x/5) = 88
⇒ x = 40
So, the number of girls = 6x/5 = (6 × 40)/5 = 48
The number of boys = x = 40
(Sum of total observations) = Average × (total numbers of observation)
Sum of total height of student = y × 88 = 88y
Sum of total height of boys = 164 × 40 = 6560
Sum of total height of girls = (y – 4) × 48 = 48y – 192
Sum of total height of student = sum of total height of boys and girl
⇒ 88y = 6560 + 48y – 192
⇒ 40y = 6368
⇒ y = 159.2
∴ The average height of total student is 159.2.
