# Calculating 95% confidence interval from mean, SD and number of subjects

#### drhealy

##### New Member
Dear All
I have been asked to present some information from a series of published articles according to Mean (+/- 95% Confidence Interval).

The statistical summaries are generally presented as:
Number of subjects (n)
Mean (X)
Standard deviation of the mean (sd)

How do I calculate the 95% confidence intervals from just this information? Do I need the actual raw data??
Thanks, best wishes
David

#### Dason

[TEX]\bar{x}\pm 1.96\frac{s}{\sqrt{n}}[/TEX]

where:
s = standard deviation of sample
[TEX]\bar{x}[/TEX]= mean of sample
n = sample size

Links on confidence interval of mean and standard error
Note that this is technically if you knew the population standard deviation. Since it sounds like this is being computed from the data you should probably use whatever the corresponding t-quantile is instead of 1.96. But if your sample size is large enough it will be close enough to essentially not matter.

#### drhealy

##### New Member
To clarify; I am compiling a data chart summarizing a lot of very small studies (eg. n of 30).
eg. study A of 30 subjects found a mean of 20.2 with an sd of 6, study B of 42 subjects found a mean of 27 with an sd of 4, etc.
How do I find /calculate the t-quantile to place into the calculation?