# Calculating the sample mean and sample standard deviation from confidence interval

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?

• Your question would be more clear if you have a specific example. – Remy Feb 26 '18 at 5:25
• Sure, the question says "Using a sample of size n=100, a paper reported a large sample 95% confidence interval for the true mean of a population to be (3:7552;5:2448). What were the sample mean and sample standard deviation?" – George S Feb 26 '18 at 5:28

## 1 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 $s$?

• Thank you very much, that's more than clear – George S Feb 26 '18 at 5:31
• Yes, I just didn't know that we can get the sample mean that way – George S Feb 26 '18 at 5:31