0
$\begingroup$

A psychology teacher has given an exam in which the highest score possible is 200 points. the mean score for the 30 students who took the exam was 156, and the standard deviation was 24. Because there was one question that every student answered incorrectly, the teacher decides to give each student 10 extra points and then divide each score by 2, so the total possible score is 100. What will the mean and the standard deviation of the scores be after this transformation?

I cannot figure out how to solve this question, I know it might seem easy and simple but I tried to figure out how to at least come up with the first step but failed to do so. I would appreciate if someone can elaborate or give me guidance on how to solve this question

Improve this question
$\endgroup$
11
  • 2
    $\begingroup$ 1. Every post here is seeking help with a stats question (otherwise it's off topic). As a result your title does nothing to help people figure out whether it's a question they want to try to help with. Please edit your title to reflect what the question is about. 2. Please read the help center on homework-style questions, which are treated differently. If you can't show any attempt you're going to need to ask something very specific about your difficulties. If you can't do that, you need to do some search and research (including ... ctd $\endgroup$
    – Glen_b
    Commented Sep 4, 2019 at 23:36
  • 2
    $\begingroup$ Yes, I read that already; as I explained you have two choices in that case; you either need to ask a very specific question that would allow you to start, or you need to do more search and research. A very general "how do I do this" on a homework style question makes it not quite suitable for our site, even if you're seeking guidance. A more specific question, addressing the first thing you don't understand may well be suitable, though it's probably more productive to do more research yourself and move the specific question further along the process. $\endgroup$
    – Glen_b
    Commented Sep 5, 2019 at 13:15
  • 1
    $\begingroup$ @Glen_b I am not sure what the best advice to the OP should be. The question is very elementary & it wouldn't take much research to find the properties that explain how a linear transformation affects the mean and standard deviation of a random with a finite mean and standard deviation. I would have thought that this question is appropriate if the self study tag is used. Almost any hint that could be given as an answer would make it very obvious how to get the solution. I think I gave the hint that would serve as an answer but I felt too embarrassed to do more than make a comment. $\endgroup$
    – Michael R. Chernick
    Commented Sep 5, 2019 at 18:10
  • 1
    $\begingroup$ @Michael Glen reopened it quickly. I just wanted to thank you for your generous help in the comments you have posted. $\endgroup$
    – whuber ♦
    Commented Sep 5, 2019 at 22:45
  • 1
    $\begingroup$ I have fixed the title and reopened but I would like the OP to undertake the other requested edits (i.e. to idenitfy a specific issue to ask about, something that will enable them to make some progress). $\endgroup$
    – Glen_b
    Commented Sep 5, 2019 at 22:47

1 Answer 1

Reset to default
1
$\begingroup$

Since this is self-study, some hints:

  1. You have the number of students, and the mean. So calculate the total from that
  2. Every student was given 10 extra points. Using this you can get the new total
  3. This was divided by 2. New total should be easy then!
  4. Having the new total the new mean should be easy.

The new standard deviation cannot be got from only the new total, but the same linear transformation was used on each students score. Adding the same number of points to each cannot change the standard deviation ... so the only relevant is the division by two. How does dividing each sample point with 2 change the standard deviation?

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.