How to show mean and standard deviation of list as normal distribution

Questions
1

Hi,

I am wondering how I would view the following list as a Gaussian Distribution, where I could identify the mean and 2 s.d. of the list on the PDF Plot?
I’ve tried EmpiricalDistribution, but this does not seem to be the right approach for the Gaussian Distribution.
Any Suggestions?

list1 = {19.90242780218157, 19.68010673392892, 19.644108173664726, 
     19.640161036048497, 19.71134294036299, 19.710843903682065, 
  19.348711494095, 
     19.87457341673222, 19.843149344572304, 19.366402930537546, 
     19.46582125513058, 20.179314461998622, 25.541862883930044, 
     19.642044011126266, 18.68815531383665, 19.476250955396374, 
     20.34490566085163, 19.92509346795489, 19.82482925700683, 
  18.9986333499863, 
     19.345141870484063, 22.16163276517112, 18.881987107758984, 
     24.67205800311023, 20.087426600019292, 24.837569542980948, 
     20.22654181669474, 19.815367646057503, 20.4993492485762, 
  18.770072837352416, 
     24.615113344370727, 22.591146458469773, 25.19963872417463, 
     19.21125512237683, 19.597100593046655, 25.405469850749444, 
     24.523725860256388, 19.32387337221414, 19.22207841240215, 
     22.337489671951015, 20.588791990739647, 20.24687604222495, 
     22.149000150282767, 19.123810932617655, 25.91119977401667, 
     19.69608340834502, 18.761227667322864, 25.08768063538005, 
     21.366439780106163, 22.252925220446418, 25.584530633451017, 
     19.85561856759682, 20.85995800444034, 20.146301887571305, 
  26.00479521720087, 
     20.048537465325865, 19.407796368833736, 25.45600836006285, 
     24.409771228581576, 20.743645580625817, 20.22641893334154, 
     19.055834156182968, 20.476827176226394, 18.725419320548355, 
     19.72943538745961, 20.20172062841312, 20.32195605021778, 
  18.900978039083597, 
     21.060392281672865, 19.41099418840363, 24.194807568136554, 
     22.201031971608934, 24.384382432882802, 18.99315611948879, 
     20.392146376675537, 20.14241527284407, 26.144065324696864, 
     19.63853520090626, 21.272512575566964, 19.862761317999325, 
     19.569302659068786, 24.965171815799252, 24.679432391660605, 
     19.008660235489227, 20.147952561189626, 20.002425446739668, 
     25.31512460547045, 25.779591150153724, 24.1348173716589, 
  24.97275960292143, 
     24.1635046301929, 22.90235461944323, 25.53460661722764, 
  25.340349705660778, 
     21.045792235569014, 20.55868670235156, 19.180626437510483, 
     19.064982151406053, 20.419812825750977, 25.94213224076066}
2

I’m not sure I fully understand. Can you be more specific about what you want done with the list of data?

If I understand correctly, you first want to estimate the parametetrs of a normal distribution that best fit the data:

estDist = EstimatedDistribution[list1, NormalDistribution[mean, var]]

You can make a Plot of the resulting Distribution:

estPdf = Plot[PDF[estDist, x], {x, 15, 30}]

You can also make a histogram of your data. Some care must be taken so that the heights are given in a way that sizes them as a PDF:

dataHistogram = Histogram[list1, Automatic, "PDF"]

And lastly you can overlap the histogram and the estimated PDF:

Show[dataHistogram, estPdf]
3

Yes,
Thank you for the reply, it has helped a lot. What I am actually trying to show is a plot of the pdf, that has the mean and standard deviations labeled. (Perhaps with lines drawn from the x-axis to those points on the curve.)

Thanks again!

4

It sounds like you are looking to create multiple graphics and combine them together. Making customized graphics programatically requires knowing a bit of graphics programming.

[

Combining Graphics—Wolfram Documentation](Combining Graphics—Wolfram Documentation)
http://reference.wolfram.com/mathematica/ref/Epilog.html

Basically you want to create a graphic with a Line and some Text in specific locations.