# Computing mean and SD from percentiles in normal distribution

#### saratogacoach

##### New Member
Am somewhat of a novice. Been trying to figure out how to convert some percentile scores in a normal distribution to get the mean and SD. Think that it must involve a Z table, but so far have not figured out how to use this or a z calculator.

The results are:
score
23 15th percentile
26 30th percentile
29 50th percentile (is this the mean?)
32 70th percentile
35 85th percentile

Maybe the mean and SD cannot be calculated with only this data?

Any help appreciated.

#### Dason

They can. You already did the mean. Let's say you knew the standard deviation - how would you calculate what percentile a value falls at.

#### saratogacoach

##### New Member
They can. You already did the mean. Let's say you knew the standard deviation - how would you calculate what percentile a value falls at.
So, the mean is 29.
I looked up the 85th percentile in a Z table: 1.036. Not sure what formula to use to convert the 85th percentile value (35), or another score value, to a standard deviation?

#### Dason

If you had the standard deviation and wanted to know the percentile that corresponded to the value 32 what would you do

#### saratogacoach

##### New Member
If you had the standard deviation and wanted to know the percentile that corresponded to the value 32 what would you do
I'll do some more online searching, see if I can figure out the formula. Thank you for your help and suggestions.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
@Dason is trying to have you make the connection. Perhaps - another clue may help. What is the standard normal value for a standard deviation and respective area under the curve? So the mean is 50% area since it is in the middle of the bell curve and has a standard normal value of 0. You likely just need to open our your textbook and stare at the values in the standard normal table to understand what information is available.

#### saratogacoach

##### New Member
@Dason is trying to have you make the connection. Perhaps - another clue may help. What is the standard normal value for a standard deviation and respective area under the curve? So the mean is 50% area since it is in the middle of the bell curve and has a standard normal value of 0. You likely just need to open our your textbook and stare at the values in the standard normal table to understand what information is available.
Hi,

Thank you for your helpful suggestion. While I think that I may be able to figure out the SD, I am beginning to wonder if the results are actually a normal distribution. I will first need to further check this out in the research study (I saw these results in a summary of the research) before concluding that it is a normal distribution. I think that if not a normal distribution, the graphing that I was hoping to do, using mean and SD and Excel, won't work.

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