How to Calculate Standard Error

Standard Error is a method of measurement or estimation of standard deviation of sampling distribution associated with an estimation method. The formula to calculate Standard Error is,

Standard Error Formula:

where
SEx̄ = Standard Error of the Mean
s = Standard Deviation of the Mean
n = Number of Observations of the Sample

Standard Error Example:
X = 10, 20,30,40,50
Total Inputs (N) = (10,20,30,40,50)
Total Inputs (N) =5

To find Mean:
Mean (x_m) = (x₁+x₂+x₃...x_n)/N
Mean (x_m) = 150/5
Mean (x_m) = 30

To find SD:
Understand more about Standard Deviation using this Standard Deviation Worksheet or it can be done by using this Standard Deviation Calculator
SD = √(1/(N-1)*((x₁-x_m)²+(x₂-x_m)²+..+(x_n-x_m)²))
= √(1/(5-1)((10-30)²+(20-30)²+(30-30)²+(40-30)²+(50-30)²))
= √(1/4((-20)²+(-10)²+(0)²+(10)²+(20)²))
= √(1/4((400)+(100)+(0)+(100)+(400)))
= √(250)
= 15.811


To Find Standard Error:
Standard Error=SD/ √(N)
Standard Error=15.811388300841896/√(5)
Standard Error=15.8114/2.2361
Standard Error=7.0711

This above worksheet helps you to understand how to perform standard error calculation, when you try such calculations on your own, this standard error calculator can be used to verify your results easily.