Standard Deviation in Excel: How to Calculate, Interpret, and Report It Correctly in APA Format
4 min read
Standard deviation is the first descriptive statistic every thesis results section reports - and the one most often calculated wrong or confused with standard error. The wrong Excel formula gives you the wrong number silently. Reporting SEM instead of SD makes your data look far more consistent than it is. This guide shows you which formula to use, how to distinguish SD from SEM, and the exact APA format.
Key takeaways
- Always use =STDEV.S() for thesis data - it calculates sample SD; =STDEV.P() is only for complete populations, not samples.
- SD describes your sample's spread; SEM describes precision of your estimate - for descriptive tables, always report SD.
- APA format: always pair M and SD together - 'M = 70.4, SD = 8.3' - never report one without the other.
- The coefficient of variation (SD/M × 100) allows comparing variability across variables measured on different scales.
- If two groups have the same mean but different SDs, variances are unequal - run Levene's test and use Welch's t-test.
What Standard Deviation Actually Measures
Standard deviation (SD) measures how spread out the values in a dataset are around the mean. A small SD means most values are close to the mean. A large SD means values are spread out widely.
Example: two classes both have a mean exam score of 70. Class A has SD = 5 (most students scored 65–75). Class B has SD = 20 (scores ranged from 30 to 100). Same mean, very different distributions.
SD is always in the same units as the original variable. If you measured weight in kilograms, SD is in kilograms.
Excel Formulas: STDEV.S vs. STDEV.P - Which to Use
Use the correct formula for your data type. Using the wrong one silently gives you a slightly different number.
| Formula | Calculates | When to Use | Divides by |
|---|---|---|---|
| =STDEV.S(range) | Sample SD | Thesis data - a sample from a larger population (almost always) | n − 1 |
| =STDEV.P(range) | Population SD | Only if your dataset IS the entire population (very rare) | n |
| =STDEV(range) | Sample SD (legacy) | Same as STDEV.S - works but less explicit | n − 1 |
If you surveyed 80 students at one university, that is a sample - use =STDEV.S(). Only use =STDEV.P() if you have data on every member of the entire population (e.g., all students in a single class with no intention to generalise).
SD vs. SEM: Which to Report in Your Thesis
This is the single most common descriptive statistics mistake in student theses.
| Statistic | What It Measures | When to Report It | Formula |
|---|---|---|---|
| SD (Standard Deviation) | Spread of individual values in your sample | Descriptive tables, group comparisons | =STDEV.S() |
| SEM (Standard Error) | Precision of your sample mean estimate | Confidence intervals, error bars in figures | =STDEV.S() / SQRT(N) |
APA Format for Reporting SD in Your Thesis
APA format requires M (mean) and SD (standard deviation) always together. Never report one without the other.
- In text:
- "The mean exam score was M = 70.4 (SD = 8.3)."
- or: "Participants scored M = 70.4, SD = 8.3 on the exam."
In a results table: use column headers M and SD (not "Mean" and "Standard Deviation").
Do not use parentheses in table cells - the column headers provide the label.
APA uses two decimal places for means and SDs unless precision requires more.
Frequently asked questions
Should I report standard deviation or standard error in my results table?
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What is a normal or acceptable standard deviation?
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My standard deviation is larger than my mean - is that a problem?
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Can I calculate standard deviation in Excel without the Data Analysis ToolPak?
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What does it mean if two groups have the same mean but different standard deviations?
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Further reading
Thesis Data Analysis: The 5 Critical Steps Students Skip (With Checklist)
· Data analysisHow to Prepare Your Thesis Data: Step-by-Step Guide for SPSS, Excel, and Jamovi
· Data preparationAPA Statistics Reporting: Copy-Paste Templates for Every Test in Your Thesis
· APA reportingThe 5 Thesis Statistics Mistakes That Cost Students Their Grade (And How to Catch Them Before Your Defense)
· Common mistakes
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Statoria Team
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We build Statoria to help bachelor and master students get through their thesis data analysis without stress. Our guides are written by researchers with experience in social science statistics and student supervision.
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