Probability and Statistics > Basic Statistics > Pooled Sample Standard Error

## Pooled Sample Standard Error: Overview

The standard error of a sample is another name for the standard deviation of a sample (this is also one of the AP Statistics formulas).

There’s a slight difference between standard deviation and pooled sample standard error:

- When we are talking about a population, we talk about standard deviations.
- When we talk about a
**sample**we call it a standard error.

For calculations, you don’t have to worry about that difference: Both are calculated using the same formulas.

A **pooled** standard error accounts for two sample variances and assumes that both of the variances from the two samples are equal. It’s called a “pooled” standard error because you’re **pooling the data from both samples into one**. The formula for the pooled sample standard error is:

SE

_{pooled}= S_{p}√ (1/n_{1}+ 1/n_{2})

## Pooled Sample Standard Error: Steps

**Sample problem**: Calculate the pooled sample standard error for the following data from two samples:

Sample_{1} :n=25, s = 6.

Sample_{2} :n=25, s = 6.

Step 1: **Insert your numbers into the formula. **Use your variance (s) for s_{p} (you can do this because both variances are the same:

SE_{p} = 6 √ (1/25 + 1/25)

Step 2: **Solve:**

6 √ (1/25 + 1/25) ≈ 1.697.

The pooled sample standard error is about 1.697.

*That’s it!*

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