Combining mean and standard deviation: mean score on AP Biology exam was 3.10...

Janeelise

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On an AP Statistics quiz I got this question and I have no clue how to solve it because it was never taught. I looked online for help but nothing has gotten me to the correct answe

In 2016, the mean score on the AP Biology exam was 3.10, with a standard deviation of 1.05. The mean score on the AP US History exam was a 2.74, with a standard deviation of 1.42. What is the combined mean and standard deviation for these exams?”


 
On an AP Statistics quiz I got this question and I have no clue how to solve it because it was never taught. I looked online for help but nothing has gotten me to the correct answe

In 2016, the mean score on the AP Biology exam was 3.10, with a standard deviation of 1.05. The mean score on the AP US History exam was a 2.74, with a standard deviation of 1.42. What is the combined mean and standard deviation for these exams?”



You should have been shown, or somehow discovered along the way...

1) Means are additive. <== Seriously, just add them.
2) Variance is additive. <== What does this suggest concerning the combining of the Standard Deviations?
 
You should have been shown, or somehow discovered along the way...

1) Means are additive. <== Seriously, just add them.
2) Variance is additive. <== What does this suggest concerning the combining of the Standard Deviations?

Everything you said is true, and helpful hints for answering this question. I'm just wondering though: the question isn't asking for a sum of the two scores, with a variance for the sum. It's asking for a mean of the two scores, right? (Like, AP exam scores are out of 5). So doesn't that mean the OP needs to compute the mean of the means, and the error in that mean?
 
You should have been shown, or somehow discovered along the way...

1) Means are additive. <== Seriously, just add them.
2) Variance is additive. <== What does this suggest concerning the combining of the Standard Deviations?


I tried just adding them, and it said I got it wrong.
 
I tried just adding them, and it said I got it wrong.
What numbers did you add? What result did you obtain? What is the "it" that said your value was incorrect? What value did it provide?

Thank you! ;)
 
For the standard deviation you square each standard deviation given by the 2nd power. So it would look like 1.42^2 (I believe this is how it is written) which gives you 2.0164 do the same for the 1.05. 1.05^2= 1.1025. Now with both of these you add them which now give you 3.1189 and is rounded to 3.12. This would be the answer for standard deviation. Hope this helped! :)
Nice shot at the variance. How about the Standard Deviation?

Also, and maybe there is an answer to this, why are you so confident about the rounding procedure. Seems rather arbitrary. Willing to be wrong.
 
So for those who need help it already gives you the mean and standard deviation. The two means that are given to you just need to be added, which looks like: 3.10+ 2.74= 5.84 this is the final answer for the mean. Now we need to find the standard deviation. DO NOT just add them, you must raise them both by the second power: 1.42^2 (I believe this is how it is written) which gives us 2.0164 now do the same for 1.05. 1.05^2= 1.1025. We still aren’t finished, we must add the two numbers we got: 2.0164 +1.1025= 3.1189 (rounded it equals 3.12) FINAL STEP: don’t not forget to square root this number which will give you 1.766 (rounded will give you 1.77) this is your final number. Hope this helped! :)
 
Are we assuming the same number of students took each exam? Biology and History? Seems unlikely.
 
On an AP Statistics quiz I got this question and I have no clue how to solve it because it was never taught. I looked online for help but nothing has gotten me to the correct answe

In 2016, the mean score on the AP Biology exam was 3.10, with a standard deviation of 1.05. The mean score on the AP US History exam was a 2.74, with a standard deviation of 1.42. What is the combined mean and standard deviation for these exams?”
Stupid question. What is meant by combined?
 
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