Teaching · For Teachers · Research and data

How spread out
the scores are,
step by step.

Paste a column of scores. The calculator gives the standard deviation and variance for a sample or a whole group, shows each score’s distance from the mean and its z-score, and flags the scores that sit far from the rest.

Calculate the spreadWhat you get
$12one-time · every device you sign in on
Buy · $12

Included with Caveat Classroom and Whole-school licenses. Or get it in the For Teachers toolkit, $79 for 72 items.

The standard deviation calculator

The worked example is made up: ten fall oral reading fluency scores. Use codes, not student names. Nothing you type leaves this browser.

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What you get

Teaching · For Teachers$12 · included with Classroom and Whole-school licenses

What you finish with
The standard deviation, variance, mean, sum of squares and coefficient of variation, the full deviation table with z-scores, and the share of scores within one and two standard deviations. It prints as a summary and downloads as a spreadsheet.
Who it is for
Teachers doing action research, data teams and instructional leaders, school psychologists and graduate students in education.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. Up to 1,000 scores. Prints a summary; downloads a spreadsheet (.csv); export and import a file.
Access
$12 one-time, yours on every device you sign in on; the tool opens once you are signed in with it. Included with Caveat Classroom and Whole-school licenses. Also in the For Teachers toolkit ($79) and the Teaching Suite pass ($199), and 1 more bundle. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The For Teachers space in Caveat Teaching.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Say what the scores are.
  2. Choose sample or population.
  3. Paste the scores.
  4. Read the standard deviation and the steps, then the table for scores far from the mean.
  5. Print the summary or download the spreadsheet.

Calculate the spread

How the standard deviation is worked out

The typical distance from the mean.

The worked example, from scores to spreadMean97970 ÷ 10Squared deviations1,522sum of (x − 97)²Variance169.111,522 ÷ (10 − 1)Standard deviation13.00√169.11The worked example, from scores to spreadMean97970 ÷ 10Squared deviations1,522sum of (x − 97)²Variance169.111,522 ÷ (10 − 1)Standard deviation13.00√169.11
Four steps for the fluency scores: the mean, the squared distances from it added up, that total shared over n − 1, and the square root to return to words per minute, 13.00.

Sample or population

The variance is the average squared distance from the mean, and the standard deviation is its square root, in the same units as the scores. When the scores are a sample standing for a larger group, divide the sum of squares by n − 1 rather than n; this corrects for the sample mean sitting closer to its own scores than the true mean does. When the scores are the whole group, divide by n.

Reading the result

In roughly bell-shaped data about 68 percent of scores fall within one standard deviation of the mean and about 95 percent within two. A z-score says how many standard deviations a score is from the mean. The coefficient of variation, SD divided by mean, compares spread across measures on different scales; it means little when scores can be negative or the mean is near zero.

Sources

  1. NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.5.6, Measures of Scale (itl.nist.gov).
  2. Institute of Education Sciences, What Works Clearinghouse. Procedures and Standards Handbook, Version 5.0 (2022): standard deviations in effect size calculations.
  3. Glass, G. V., and Hopkins, K. D. (1996). Statistical Methods in Education and Psychology (3rd ed.). Allyn and Bacon: variance, standard deviation and the n − 1 divisor.
  4. National Center for Education Statistics. NCES Statistical Standards (nces.ed.gov): reporting measures of variability.

The worked example is made up. Use student codes, not names. Your scores stay in this browser. Support: team@caveatacademic.com.