Test Results Standard Deviation Calculator
Describe how test results vary around their mean using population or sample standard deviation.
How to use Test Results Standard Deviation Calculator
1. Enter Test Results Values as matching lists where weights are used; separate numbers with commas, spaces, semicolons or new lines. 2. Choose Population or Sample mode. 3. Select Calculate or press Enter, then read standard deviation. 4. Copy result copies the answer; Reset clears the form. Do not use thousands separators inside lists.
Why use this tool?
Compare score variability for assessments with compatible scales and conditions.
How the calculation works
Find the arithmetic mean, add the squared deviations from that mean, divide by count for Population or count − 1 for Sample, then take the square root. Sample requires at least two observations. Use a common scoring scale. The tool does not assign letter grades, determine a student’s rank, apply a grading curve or compare scores with national norms. Results use up to six decimal places, or six significant digits in scientific notation for nonzero magnitudes below 0.000001. Calculations use browser floating-point arithmetic. Each list supports up to 20,000 numbers. Entry and result magnitudes must not exceed 9,007,199,254,740,991; unrepresentable variance or weighted products are rejected. General descriptive-statistics reference: https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm. Weighted conventions are defined explicitly on this page.
Example
For test results 60,70,80,90 in Population mode, the standard deviation is 11.18034.
Practical tip
Use Population when describing the complete set of interest, or Sample when using observations to estimate a wider population’s variability.
Frequently asked questions
Which standard-deviation mode should I choose?
Population divides squared deviations by n. Sample divides by n − 1 and requires at least two values. Choose according to what the observations represent, not to obtain a preferred answer.
Does this assign grades or rank students?
Use a common scoring scale. The tool does not assign letter grades, determine a student’s rank, apply a grading curve or compare scores with national norms.
How should I separate numbers and interpret rounding?
Use commas, spaces, semicolons or new lines between entries. Enter 1000 rather than 1,000: commas separate observations. Repeated values are retained. Displayed results are rounded as stated; keep original readings for later calculations.