Question

Given a standard deviation of 3.5 and a sample size of 5, what is the standard error?Round to nearest hundredth

Answer 1

To calculate the standard error (SE) of a sample, you can use the formula:

\[
SE = \frac{\sigma}{\sqrt{n}}
\]

Where:
- \(\sigma\) is the standard deviation,
- \(n\) is the sample size.

Given:
- \(\sigma = 3.5\)
- \(n = 5\)

Substituting the values into the formula:

\[
SE = \frac{3.5}{\sqrt{5}}
\]

First, calculate the square root of 5:

\[
\sqrt{5} \approx 2.236
\]

Now, substitute that back into the equation for SE:

\[
SE = \frac{3.5}{2.236} \approx 1.566
\]

Now, rounding to the nearest hundredth:

\[
SE \approx 1.57
\]

Thus, the standard error is approximately **1.57**.