Question

Three girls and nine boys sat a Physics examination.

The three girls' marks were 92%, 80% and 71%.
The mean of all 12 marks was 84%.
The standard deviation of all 12 marks was 5%.
Calculate the standard deviation of the boys' marks.

Answer 1

To calculate the standard deviation of the boys' marks, subtract the contribution of the girls' marks from the overall standard deviation. The standard deviation of the boys' marks is 1%.

Step-by-step explanation:

To calculate the standard deviation of the boys' marks, we need to subtract the contribution of the girls' marks from the overall standard deviation. This can be done by using the fact that the standard deviation is a measure of how spread out the data is from the mean. We can calculate the standard deviation of the boys' marks as follows:

1. Calculate the mean of the girls' marks: (92% + 80% + 71%) / 3 = 81%

2. Calculate the mean of the boys' marks: (84% * 12 - 81% * 3) / 9 = 83%

3. Calculate the standard deviation of the boys' marks:

a) Calculate the sum of the squares of the differences between each boy's mark and the mean: (84% - 83%)^2 + (84% - 83%)^2 + ... + (84% - 83%)^2 = 9 * (84% - 83%)^2

b) Divide the sum by the number of boys: (9 * (84% - 83%)^2) / 9 = (84% - 83%)^2

c) Take the square root to find the standard deviation: sqrt((84% - 83%)^2) = 1%

Therefore, the standard deviation of the boys' marks is 1%.