Answer:
(B) 25.65, 10.71
Explanation:
To calculate the new sample mean, we add 5 to each of the original marks and take the mean of the new set of marks:
New marks: 30, 31, 18, 28, 28, 30, 22, 27, 22, 24, 17, 31, 35, 35, 23, 19, 17, 31, 22, 23
New sample mean = (30 + 31 + 18 + ... + 22 + 23) / 20
= 25.65
To calculate the new sample standard deviation, we first need to calculate the sum of squares of the differences between each mark and the original sample mean:
(25-20.65)^2 + (26-20.65)^2 + (13-20.65)^2 + ... + (17-20.65)^2 + (18-20.65)^2
= 21.49 + 20.25 + 47.61 + ... + 12.96 + 8.41
= 570.41
Then, we divide this sum of squares by n-1 (where n is the sample size) to get the variance, and take the square root to get the standard deviation:
New sample standard deviation = sqrt(570.41 / 19)
= 10.71
Therefore, the answer is (B) 25.65, 10.71