Suppose that the mean score of an exam was 77 when taken 30 students took it on time with a standard deviation of 2. A makeup of the same exam is given to 6 students. The retakes averaged a score of 83 with a standard deviation of 2.9. What is the average of the test scores?
To find the average of the test scores, we need to calculate the combined mean score of both the initial exam and the makeup exam.
First, let's calculate the total sum of the individual scores for the initial exam. Since we know the mean score is 77 and there were 30 students, we can use the formula: sum = mean * number of students.
sum_initial_exam = 77 * 30 = 2310.
Next, let's calculate the total sum of the individual scores for the makeup exam. Since we know the average score is 83 and there were 6 students, we can use the same formula: sum = mean * number of students.
sum_makeup_exam = 83 * 6 = 498.
To find the combined mean score, we need to add the sum of the initial exam scores and the sum of the makeup exam scores, and then divide by the total number of students.
combined_mean_score = (sum_initial_exam + sum_makeup_exam) / (number of students in initial exam + number of students in makeup exam).
combined_mean_score = (2310 + 498) / (30 + 6).
combined_mean_score = 2808 / 36.
combined_mean_score = 78.
Therefore, the average of the test scores is 78.