The mean and standard deviation of a set of data are two measurments that describe the data. A certain student has written 8 out of 10 unit exams, which are equally weighted. The student misses the ninth exam and receives a score of 0. However, for the last exam, the student studied and scored a 100%. Compare the mean and standard deviation after 8 unit tests and after 10 unit tests. My question is how do I find the mean and standard deviation when all I know is the mark on the 9th test is 0 and the tenth 100%. How do I do this question when I don't know any other marks. Please help I've never had a question with such limited information. I was told it really is possible to solve it with the information given.
Sorry to tell you, I don't know either.
To find the mean and standard deviation after 8 unit tests and after 10 unit tests, you will need to make some assumptions.
Assuming that the scores on the 8 unit tests the student has taken are known and given, you can find the mean and standard deviation using those scores. Let's say the scores on the 8 unit tests are as follows:
Test 1: x1
Test 2: x2
Test 3: x3
Test 4: x4
Test 5: x5
Test 6: x6
Test 7: x7
Test 8: x8
To find the mean after 8 unit tests, you sum up all the scores and divide by the number of tests (which is 8 in this case):
Mean = (x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8) / 8
To find the standard deviation after 8 unit tests, you can use the formula:
Standard Deviation = sqrt(((x1-Mean)^2 + (x2-Mean)^2 + ... + (x8-Mean)^2) / 8)
Now, to find the mean and standard deviation after 10 unit tests, we will take into account the scores on the 9th and 10th tests.
Given that the 9th test score is 0 and the 10th test score is 100, we can add these scores to the previous ones:
Test 1: x1
Test 2: x2
Test 3: x3
Test 4: x4
Test 5: x5
Test 6: x6
Test 7: x7
Test 8: x8
Test 9: 0
Test 10: 100
To find the mean after 10 unit tests, you sum up all the scores and divide by the number of tests (which is now 10):
Mean = (x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + 0 + 100) / 10
To find the standard deviation after 10 unit tests, you can use the same formula as before:
Standard Deviation = sqrt(((x1-Mean)^2 + (x2-Mean)^2 + ... + (x8-Mean)^2 + (0-Mean)^2 + (100-Mean)^2) / 10)
By plugging in the known values of the scores and using these formulas, you can calculate the mean and standard deviation after 8 unit tests and after 10 unit tests.