a teacher teaches two sections (A and B) of a class. Both sections have a mean score of 75. Section A only has 5 students and they all received a score of 75, while section B has 15 students with a mean score of 75 with a variance of 12. What is the standard deviation of the combined class (N=20, treat as the population).
a)9 b)6 c)4 d)3 e)2
So as a result section A has zero for the variance. I am having trouble figuring out the correct equation to solve this problem.
Variance = Σx^2/N, where x = X-μ. Since Σx^2 = 0 for the first group, it will contribute nothing to the Σx^2, so that term will remain the same for the combined class, but the N will increase from 15 to 20.
For the second group, since Variance = Σx^2/N,
Σx^2 = Variance * N = 12 * 15 = 180
Thus for the second group, variance = 180/20 = 9
However, the standard deviation is the square root of the variance. You should be able to calculate that.
I hope this helps. Thanks for asking.
To solve this problem, you can use the formula for the standard deviation of a population, which is the square root of the variance. The combined class has 20 students, with 5 in section A and 15 in section B.
First, let's calculate the variance for section B. We know that the mean score for section B is 75 and the variance is 12. The variance formula is:
Variance = sum((x - mean)^2) / n
Where 'x' represents each student's score, 'mean' is the mean score of section B, and 'n' is the number of students.
Since we are treating this as a population, we divide by the total number of students in section B:
Variance for section B = sum((x - 75)^2) / 15
Next, we can calculate the combined variance, taking into account both sections:
Combined Variance = [(Variance of section A * number of students in section A) + (Variance of section B * number of students in section B)] / (total number of students)
Since the variance for section A is zero (all students scored 75), the combined variance simplifies to:
Combined Variance = (Variance of section B * number of students in section B) / (total number of students)
Substituting the given values into the equation:
Combined Variance = (12 * 15) / 20 = 9
Finally, to find the standard deviation, we take the square root of the combined variance:
Standard Deviation = √(Combined Variance) = √(9) = 3
Therefore, the correct answer is d) 3.