Question

6. There are 20 boys and 20 girls in a class. The average percentage marks of the students in the class are more than 70, but less than 85 for a particular monthly test. The average percentage marks scored by the boys is more than 60, but less than 75. What is the range of the average percentage marks scored by the girls?

Answer 1

its a big class

Answer 2

Range for girls should be same number above the class average as the boys is below. Reason, because the number of boys and girls is equal.
10 above will make the range for the girls 80 to 95 .

Answer 3

Let the overall average percentage marks be the highest possible, namely 84.
Then the total overall percentage marks = 84 * 40 = 3360.
Let the average percentage boys marks be the lowest possible, namely 61.
Then the total boys percentage marks = 61 * 20 = 1220.
The total girls percentage marks = 3360 - 1220 = 2140.
The average percentage girls marks = 2140/20 = 107.

The above calculation gives the upper limit of the range of average percentage marks scored by the girls.
The lower limit of the range of average percentage marks scored by the girls is found by considering the lowest possible overall percentage marks (71) and the highest possible average percentage boys marks (74). Can you find this limit?

Answer 4

average of averages
\[\frac{ 1 }{ 2 }(50 + 75) = 67.5\]
range = 67.5 ± 7.5

\[\frac{ 1 }{ 2 }(70 + 85) = 77.5\]
range = 77.5 ± 7.5

\[\frac{ 1 }{ 2 }(x + y) = z\]
\[\frac{ 1 }{ 2 }(67.5+ z) = 77.5\]
z = 87.5
range = 87.5 ± 7.5
{80 < µ < 95}