Mathematics desk
< April 10	<< Mar \| April \| May >>	April 12 >

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

April 11

Calculating mean from stddev and deviation

Suppose that I know that a distribution is normal. I know the standard deviation is 16. I know that 88.1% percent of values is <140. I want to calculate the mean. Is there an easy way to do this or does it solving the population density for the mean after filling in X and standard deviation? 199.15.144.250 (talk) 18:09, 11 April 2016 (UTC)[reply]

You can find it from the Cumulative distribution function for the normal distribution. The diagram on the right is for where the standard deviation is 1. You can see the 0.88 probability is somewhere near standard deviation 1.3, multiplying your SD 16 by that gives about 21 so the mean is somewhere near 140-21 = 119. You'd have use a proper table to get it more accurately. Dmcq (talk) 18:26, 11 April 2016 (UTC)[reply]

That isn't getting me anywhere. I tried a different route. I looked up 0.88100 in a Z-to-P table and found that Z=1.1. Therefore, if I remember correctly, (140-mean)/16=1.1. Calculating for the mean, I get 122.4. I assume that is incorrect because 140-16 = 124. If 88.1% are <140, then I expect the mean to be >140-16. 122.4 is <124. 199.15.144.250 (talk) 19:02, 11 April 2016 (UTC)[reply]

A correction, I read the table wrong. For P=0.88100, Z=1.18. That gives me Mean = 140 - (1.18*16) = 121.12. That is still below 140, which tells me that I'm doing this wrong. 199.15.144.250 (talk) 19:15, 11 April 2016 (UTC)[reply]

Your calculation is correct, what made you think it's wrong? -- Meni Rosenfeld (talk) 20:05, 11 April 2016 (UTC)[reply]

(Also, this isn't a "different route", it's exactly what Dmcq was saying - which isn't a surprise, there's basically just one way to solve this). -- Meni Rosenfeld (talk) 09:25, 12 April 2016 (UTC)[reply]

In my mind, I felt that the answer should be greater than 124, not less than 124. I did read the article on Cumulative distribution function, but nowhere in it does it give a hint about using the Z score to do this calculation. So, I didn't get the idea to use the Z score from that article. I gave up on that topic all together and just thought I'd try to covert P to Z and then do the calculation. 209.149.113.15 (talk) 12:15, 12 April 2016 (UTC)[reply]

I think this reasoning of yours: "If 88.1% are <140, then I expect the mean to be >140-16" -- is not correct. Think of it this way: if I have a standard normal distribution then its cumulative distribution tells me that ~88% are <1.25, but that doesn't tell me much about the mean, which is zero. SemanticMantis (talk) 14:11, 12 April 2016 (UTC)[reply]