How to find the sample mean and sample standard deviation if only given the $n$ sample size and that the sample $95%$ confidence interval is $(x, y)$?
If I was given one of them I would know how to find the other one, but what should I do if both of them are unknown?
[Math] Calculating the sample mean and sample standard deviation from confidence interval
confidence intervalstatistics
Best Answer
A $95$% confidence interval is given by
$$\bar{X} \pm 1.96 \frac{s}{\sqrt{n}}$$
where $n=100$
If your confidence interval is $(x,y)$ then
$$\bar{X}=\frac{x+y}{2}$$
Can you go from here to solve for $s$?