What is the difference between standard deviation and standard error?
Standard deviation describes how spread out individual data points are. Standard error describes how much a sample statistic, usually the mean, would vary from sample to sample, and equals SD divided by the square root of n.
Explain it simply
Standard deviation answers: how different are individual students from each other? Standard error answers: if I repeated my survey many times, how much would the average bounce around?
SE of the mean = SD / sqrt(n)
More data makes the average steadier, so SE shrinks as n grows, while the SD of the population does not change.
Example
Daily screen time of students has SD = 20 minutes.
- n = 25: SE = 20 / 5 = 4 minutes
- n = 100: SE = 20 / 10 = 2 minutes
- n = 400: SE = 20 / 20 = 1 minute
Quadrupling the sample halves the error.
import numpy as np
sd = 20
for n in (25, 100, 400):
print(n, sd / np.sqrt(n)) # 25 4.0 / 100 2.0 / 400 1.0What to say in the interview
"SD measures variability within the data; SE measures the precision of an estimate, SD over root n. Report SD to describe the data and SE, or a confidence interval, to describe how reliable a mean is. Since SE shrinks with the square root of n, halving it needs four times the data."
Common mistakes
- Using SE bars when you want to show how spread-out the data is.
- Expecting a bigger sample to reduce the SD. It only reduces the SE.