Inferential Statistics • Lesson 6
Standard Error
How much can a sample result change from one sample to another? Standard Error answers this question — and quantifies the precision of an estimate.
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What Does Standard Error Measure?
Standard Error (SE) measures the typical variability of a sample statistic — like the sample mean — across repeated samples of the same size. It answers: 'how much would this estimate move if we drew a different sample?'
Learn by Seeing
Variability of the estimate
Sample 1 → mean 4,850 Sample 2 → mean 5,120 Sample 3 → mean 4,970 Sample 4 → mean 5,060 SE ≈ how far apart these tend to sit
SE describes how much the statistic itself varies, not how much the raw data varies.
Repeated sample means
Sample 1
₹4,850
Sample 2
₹5,120
Sample 3
₹4,970
Sample 4
₹5,060
SE ≈ how far apart these tend to sit
Interactive Activity
What does Standard Error measure?
Hint: It is about the statistic, not the raw observations.
Statistics Analyst Mindset
Every estimate needs a precision
A number without a Standard Error is a number without context. "The average spend was ₹5,000" is only meaningful when you also know how much that estimate would move from sample to sample. SE provides that context.
Estimate
Compute the statistic.
Quantify
Compute the SE.
Interpret
Smaller SE = more precise.
Use
Confidence intervals and tests.
Lesson Summary
What you learned
The typical variability of a sample statistic across samples.
SD describes raw data; SE describes the estimate.
SE = σ / √n when σ is known.
Larger n → smaller SE (shrinks with √n).
Larger samples give more precise estimates.
SE underpins confidence intervals and tests.