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# Standard Error Calculator

Enter raw or summary data and hit the calculate button to find standard error

## Standard Error Calculator

Standard Error Calculator is used to determine the standard error of the group data or sample data using the standard deviation and sample size.

## What is Standard Error?

The **standard error** is a statistical term that measures the variability or uncertainty in the estimates or measurements of a statistical sample variation. In simple terms, **standard error** quantifies the average amount of variation or error we can expect in the estimate of a **population **parameter based on a **sample**.

It provides an indication of how reliable the **sample statistic** is in representing the population parameters estimation. It measures the precision or dispersion of the sample statistic with the true population parameter.

The **standard error** in numerical form is calculated using the **standard deviation **of the sample data and the sample size. It is simply denoted as “**SE**”.

**The formula for Standard Error**

The formula of standard error in mathematical form is stated below.

Standard Error (**SE**) = (Standard Deviation of the Sample) / √Sample Size

Where,

**σ**= Standard deviation,**n**= Sample Size

## How to find the numerical value of Standard Error?

**Example 1:**

If the sample size of statistical data is **5 **and the sample data is **34, 12, 13, 15, and 10** then find the Standard error.

**Solution:**

**Step 1: **Write the data from the given sample data.

Input Data = {34, 12, 13, 15, 10}, sample size = n = 5

**Step 2: **Write the formula of the Standard error.

`Standard error = σ/√n`

**Step 3:** Write the formula of Standard deviation.

`STD (σ) = √(∑ (x - x̄)`

^{2}/n – 1)

**Step 4: **Using the formula of mean find the standard error.

x̄ = (Sum of all Values Number of values)/sample size

x̄ = (34+12+13+15+105)/5

x̄ = 845/5

**x̄ = 16.8**

∑(x - x̄)^{2} = ( 34 - 16.8 )^{2} + ( 12 - 16.8 )^{2} + ( 13 - 16.8 )^{2} + ( 15 - 16.8 )^{2} + ( 10 - 16.8 )^{2}

∑ (x-x̄)^{2} = (17.2)^{2} + (4.8)^{2} + (3.8)^{2} + (1.8)^{2} + (-6.8)^{2}

`∑ (x - x̄)`

^{2} = **382.8**

**Step 5: **Put the value in the formula of “**Step 3**” and simplify.

`STD (σ) = √{(∑ (x - x̄)`

^{2})/(n – 1)}

= √ {382.8/(5 – 1)}

= √ {382.8/4}

= √ 95.7

`STD (σ) = `

**9.78264**

**Step 6: **Finally, put the above values in the Standard error formula.

`SE = 9.78264/√5`

**SE = 4.37493**

**Example 2:**

If the standard deviation is **56 **and the sample size is **6 **then find the standard error.

**Solution:**

**Step 1: **Write the data from the above conditions.

σ = 56, n = 6.

**Step 2: **Write the formula of standard error.

`SE = σ/√n`

**Step 3:** Put the values in the above formula.

Standard error (SE) = 56/√5

**SE = 22.8619**