In Python with pandas, standard error of the mean for the sample data takes a few lines, shown below. It returns 1.28.
Standard error = Standard deviation ÷ √n
Step by step
- Install the libraries (pip install pandas) and save daily.csv next to your script.
- Run the script and compare the printed value with the expected result.
The code
import pandas as pd
df = pd.read_csv("daily.csv")
se_mean = df["website_orders"].sem()
print(round(se_mean, 3))
Expected result on the sample data: 1.28.
What the result means
Standard deviation describes how much days vary; standard error describes how sure you are about the average day. Quadrupling the number of days halves it.
Notes for Python
- pandas methods such as .std(), .var() and .quantile() match Excel's sample versions (STDEV.S, VAR.S, PERCENTILE.INC). NumPy's np.std() and np.var() default to the population version instead.
- pandas skips NaN values in these calculations by default. Count how many rows were used if data might be missing.
Where standard error of the mean misleads
- Do not confuse it with standard deviation; error bars drawn with one when you meant the other are very common.
- It assumes independent observations. Days in a trend or a season are not, so the real uncertainty is larger.
- Use the sample standard deviation (STDEV.S).
The plain-language explanation is on the Standard error of the mean page.
The data
| day | website_orders |
|---|---|
| 1 | 24 |
| 2 | 27 |
| 3 | 22 |
| 4 | 30 |
| 5 | 28 |
| 6 | 25 |
| 7 | 31 |
| 8 | 29 |
| 9 | 26 |
| 10 | 33 |
| 11 | 30 |
| 12 | 28 |
| 13 | 35 |
| 14 | 32 |
| 15 | 29 |
| 16 | 34 |
| 17 | 61 |
| 18 | 31 |
| 19 | 36 |
| 20 | 33 |
| 21 | 30 |
| 22 | 37 |
| 23 | 35 |
| 24 | 32 |
| 25 | 38 |
| 26 | 36 |
| 27 | 34 |
| 28 | 40 |
| 29 | 37 |
| 30 | 39 |
Same method, other tools
Related methods
Learn more about Python
- Python and SQL for data analysis, side by side — 3 min read
- Data analysis methods and techniques, and when to use each — 3 min read
About the data on this page
The figures come from a small made-up dataset, printed above in full so you can check every number by hand. Download it as daily.csv. The results are computed from those rows when the page is built, and the Excel formulas, SQL and Python on these pages are run against the same rows before publishing, so the code and the answers agree.
To get these numbers from your own data without writing formulas, try AnalyzeIt: ask in plain words and it shows the working behind every figure.
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