How to interpret Standard Error results
Descriptive statistics summarize a dataset's center, spread, and shape. They're the first step in understanding any quantitative dataset.
Measures of center
- Mean: sensitive to outliers. One extreme value pulls it dramatically. Best for symmetric distributions.
- Median: resistant to outliers. Better for skewed distributions (income, home prices) or datasets with extreme values.
- Mode: most frequent value. Useful for categorical data and multimodal distributions.
Measures of spread
- Standard deviation: average distance from the mean. For a normal distribution, ≈68% of values fall within 1 SD, 95% within 2 SD.
- IQR (Interquartile Range): Q3 − Q1. The range containing the middle 50% of data. Resistant to outliers — used in box plots.
- Range: max − min. Extremely sensitive to outliers; rarely the best spread measure.
Identifying outliers
A common rule: a value is an outlier if it's more than 1.5 × IQR below Q1 or above Q3. For z-score-based detection, values beyond ±3 are flagged (occur in <0.3% of a normal distribution).
Frequently Asked Questions
How accurate are the results?
The Standard Error applies a standard formula to your inputs — accuracy depends on how precisely you measure those inputs. For planning and estimation, results are reliable. For high-stakes or professional decisions, cross-check the output with a domain expert or primary source.
What sample size do I need for reliable results?
It depends on the desired confidence level, margin of error, and population variance. For a typical survey (95% confidence, ±5% margin), n ≈ 385 for a large population. Smaller samples are fine for exploratory analysis, but don't over-interpret the results — widen your confidence intervals to reflect the uncertainty.