the mean of a set of test scores is 64. a new student takes the same test and scores 80 marks. when his score is added to the other scores, the mean increases to 65. how many students sat for the test altogether?
Say there are n scores. If the mean is 64, then the total points is just 64n.
Now, we have one more score, and the mean rises to 65. So, we have n+1 scores with mean 65. And we have added 80 points to the total.
64n+80 = 65(n+1)
64n+80 = 65n+65
n = 15
To find the number of students who sat for the test altogether, we can use the concept of the mean (average) and the formula for calculating the mean.
Let's denote the number of students who sat for the test as "N". Here's how we can solve the problem step by step:
1. Given that the mean of the set of test scores is 64, we can use the formula for the mean to calculate the sum of all the test scores:
Total test scores = Mean * Number of students
Total test scores = 64 * N
2. After the new student's score (80) is added, the mean increases to 65. Now, we can update the formula for the mean and consider the new sum of test scores:
Total test scores + New student's score = New mean * Number of students
(64 * N) + 80 = 65 * (N + 1)
3. Simplify the equation:
64N + 80 = 65N + 65
4. Rearrange the equation by subtracting 64N from both sides:
80 = N + 65
5. Subtract 65 from both sides to isolate N:
80 - 65 = N
N = 15
Therefore, there were 15 students who sat for the test altogether.