Statistics
Z-Scores worksheets
Calculate z-scores, recover original values, and compare relative positions across data sets with positive standard deviations.
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Variance and Standard Deviation worksheets
Calculate population and sample spread from small data sets with explicit n and n - 1 denominators, units, and final rounding.
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Treat each data set as the stated population or sample. Show the mean and sum of squared deviations, divide by n or n - 1 as stated, and round only the final variance and standard deviation to the nearest tenth. Include the given units.
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Variance worksheets state whether each data set is a population or sample and show the corresponding denominator. Z-score worksheets provide the mean and a positive standard deviation, so students can focus on centered, scaled comparisons.
Learning objective
What this activity builds
Find the mean, sum of squared deviations, variance, and standard deviation while applying the stated population or sample convention.
Worked example
Treat 2, 4, 6 as a population. Find the population variance and standard deviation.
Mean = 4; sum of squared deviations = 8; variance = 8/3, approximately 2.7; standard deviation is approximately 1.6.
Population variance divides by n = 3. The standard deviation returns to the original data units.
Teaching notes
Make the practice count
- Have students label the data as a population or sample before calculating.
- Keep the sum of squared deviations unrounded until the final variance and standard deviation.
- Discuss why variance uses squared units while standard deviation uses the original units.
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Choose your options, update the preview, then download the exact same pages.
Choose population, sample, or both; select data set sizes and integer or tenths values. Keep the seed to reproduce the same worksheet.
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