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.
The mean % score after 8 exams is M, and the sum of the scores is 8 M. After 10 exams the sum of scores is 8M + 100 and the new mean is (8M +100)/10 = 0.8M + 10. Compare that with M. It is lower by (0.2M -10)
A similar approach can be used for the new standard deviation. The answer will depend upon the previous 8-test standard deviation and mean.
To find the mean and standard deviation of the data after 8 unit tests and after 10 unit tests, we can utilize the information given. Although we don't know the specific scores for the other tests, we can still calculate the mean and standard deviation based on the given data.
Let's break it down step by step:
1. Calculate the mean after 8 unit tests:
- Since 8 out of 10 unit tests were completed, we have 8 scores.
- Add up the 8 scores and divide the sum by 8 to find the mean.
2. Calculate the standard deviation after 8 unit tests:
- We can't directly calculate the standard deviation yet, as we don't know the specific scores for the other two tests.
- However, we can define a range of potential scores for the missing tests.
- Consider all possible scores between 0 and 100 for the missing tests.
- Calculate the mean and standard deviation for each potential combination of scores.
- This will result in multiple potential means and standard deviations.
- Take note of the range of values.
3. Calculate the mean after 10 unit tests:
- Add up the 8 known scores, the 0 score for the ninth test, and the score of 100 for the tenth test.
- Divide the sum by 10 to find the mean.
4. Calculate the standard deviation after 10 unit tests:
- Repeat the process used for step 2, but now consider all possible scores for the missing test.
- Calculate the mean and standard deviation for each potential combination of scores.
- Take note of the range of values.
By comparing the mean and standard deviation after 8 unit tests to the mean and standard deviation after 10 unit tests, you can determine how the inclusion of the missing scores affects the overall statistics of the dataset.