Variance worksheet for Statistics

Find the mean, square each distance from it, and average the squares: that is the population variance. A sample divides by one less than the count. It is the standard deviation before the square root, so its units are squared.

Also taught in Algebra 1 and Algebra 2, each at its own level and with its own examples.

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Pick more than one for a sheet that mixes them.

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Sigma Prep · sigmaprep.io/worksheets Name Variance Date Period Find each variance. Round to two places where needed. Find the population variance: $4, 5, 7, 8, 9, 9, 10, 12$ Find the population variance: $5,$ $6,$ $7,$ $9,$ $10,$ $14,$ $15,$ $15,$ $18$ Find the population variance: $6, 9, 11, 12, 12, 14, 20$ Find the population variance: $4, 6, 10, 10, 14, 16$ Find the population variance: $9, 10, 15, 23, 23$ Find the population variance: $13,$ $14,$ $15,$ $16,$ $16,$ $16,$ $20,$ $20,$ $21,$ $39$ Find the population variance: $4, 8, 9, 10, 12, 12, 15$ Find the population variance: $1,$ $3,$ $3,$ $4,$ $5,$ $12,$ $12,$ $12,$ $14,$ $14$ Find the population variance: $6, 10, 11, 11, 12, 16$ Find the population variance: $14,$ $15,$ $16,$ $16,$ $21,$ $21,$ $21,$ $22,$ $25$ Find the population variance: $17, 17, 18, 25, 28$ Find the population variance: $15,$ $16,$ $16,$ $20,$ $22,$ $27,$ $28,$ $32$ Find the population variance: $10,$ $10,$ $10,$ $15,$ $16,$ $17,$ $17,$ $19,$ $21,$ $25$ Find the population variance: $4, 4, 4, 14, 14$ Find the population variance: $7, 8, 8, 13, 14, 17, 31$ Find the population variance: $8, 8, 8, 11, 15, 18, 20, 32$ Find the population variance: $14, 17, 19, 21, 21, 28$ Find the population variance: $7,$ $9,$ $13,$ $14,$ $15,$ $16,$ $17,$ $17,$ $18$ Find the population variance: $11,$ $12,$ $12,$ $13,$ $18,$ $19,$ $24,$ $25,$ $28$ Find the population variance: $15,$ $16,$ $17,$ $18,$ $21,$ $22,$ $22,$ $24,$ $27,$ $28$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Variance

Date Period

Find each variance. Round to two places where needed.

Find the population variance:
$4, 5, 7, 8, 9, 9, 10, 12$
Find the population variance:
$5,$ $6,$ $7,$ $9,$ $10,$ $14,$ $15,$ $15,$ $18$
Find the population variance:
$6, 9, 11, 12, 12, 14, 20$
Find the population variance:
$4, 6, 10, 10, 14, 16$
Find the population variance: $9, 10, 15, 23, 23$
Find the population variance:
$13,$ $14,$ $15,$ $16,$ $16,$ $16,$ $20,$ $20,$ $21,$ $39$
Find the population variance:
$4, 8, 9, 10, 12, 12, 15$
Find the population variance:
$1,$ $3,$ $3,$ $4,$ $5,$ $12,$ $12,$ $12,$ $14,$ $14$
Find the population variance:
$6, 10, 11, 11, 12, 16$
Find the population variance:
$14,$ $15,$ $16,$ $16,$ $21,$ $21,$ $21,$ $22,$ $25$
Find the population variance:
$17, 17, 18, 25, 28$
Find the population variance:
$15,$ $16,$ $16,$ $20,$ $22,$ $27,$ $28,$ $32$
Find the population variance:
$10,$ $10,$ $10,$ $15,$ $16,$ $17,$ $17,$ $19,$ $21,$ $25$
Find the population variance: $4, 4, 4, 14, 14$
Find the population variance:
$7, 8, 8, 13, 14, 17, 31$
Find the population variance:
$8, 8, 8, 11, 15, 18, 20, 32$
Find the population variance:
$14, 17, 19, 21, 21, 28$
Find the population variance:
$7,$ $9,$ $13,$ $14,$ $15,$ $16,$ $17,$ $17,$ $18$
Find the population variance:
$11,$ $12,$ $12,$ $13,$ $18,$ $19,$ $24,$ $25,$ $28$
Find the population variance:
$15,$ $16,$ $17,$ $18,$ $21,$ $22,$ $22,$ $24,$ $27,$ $28$



Sigma Prep · sigmaprep.io/worksheets Name VarianceAnswer keyVersion 1 Date Period Find each variance. Round to two places where needed. Find the population variance: $4, 5, 7, 8, 9, 9, 10, 12$ $6$ Find the population variance: $5,$ $6,$ $7,$ $9,$ $10,$ $14,$ $15,$ $15,$ $18$ $19.11$ Find the population variance: $6, 9, 11, 12, 12, 14, 20$ $16.29$ Find the population variance: $4, 6, 10, 10, 14, 16$ $17.33$ Find the population variance: $9, 10, 15, 23, 23$ $36.8$ Find the population variance: $13,$ $14,$ $15,$ $16,$ $16,$ $16,$ $20,$ $20,$ $21,$ $39$ $51$ Find the population variance: $4, 8, 9, 10, 12, 12, 15$ $10.57$ Find the population variance: $1,$ $3,$ $3,$ $4,$ $5,$ $12,$ $12,$ $12,$ $14,$ $14$ $24.4$ Find the population variance: $6, 10, 11, 11, 12, 16$ $8.67$ Find the population variance: $14,$ $15,$ $16,$ $16,$ $21,$ $21,$ $21,$ $22,$ $25$ $12.89$ Find the population variance: $17, 17, 18, 25, 28$ $21.2$ Find the population variance: $15,$ $16,$ $16,$ $20,$ $22,$ $27,$ $28,$ $32$ $35.75$ Find the population variance: $10,$ $10,$ $10,$ $15,$ $16,$ $17,$ $17,$ $19,$ $21,$ $25$ $22.6$ Find the population variance: $4, 4, 4, 14, 14$ $24$ Find the population variance: $7, 8, 8, 13, 14, 17, 31$ $60$ Find the population variance: $8, 8, 8, 11, 15, 18, 20, 32$ $60.75$ Find the population variance: $14, 17, 19, 21, 21, 28$ $18.67$ Find the population variance: $7,$ $9,$ $13,$ $14,$ $15,$ $16,$ $17,$ $17,$ $18$ $12.67$ Find the population variance: $11,$ $12,$ $12,$ $13,$ $18,$ $19,$ $24,$ $25,$ $28$ $36.89$ Find the population variance: $15,$ $16,$ $17,$ $18,$ $21,$ $22,$ $22,$ $24,$ $27,$ $28$ $18.2$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

VarianceAnswer keyVersion 1

Date Period

Find each variance. Round to two places where needed.

Find the population variance:
$4, 5, 7, 8, 9, 9, 10, 12$ $6$
Find the population variance:
$5,$ $6,$ $7,$ $9,$ $10,$ $14,$ $15,$ $15,$ $18$ $19.11$
Find the population variance:
$6, 9, 11, 12, 12, 14, 20$ $16.29$
Find the population variance:
$4, 6, 10, 10, 14, 16$ $17.33$
Find the population variance: $9, 10, 15, 23, 23$ $36.8$
Find the population variance:
$13,$ $14,$ $15,$ $16,$ $16,$ $16,$ $20,$ $20,$ $21,$ $39$ $51$
Find the population variance:
$4, 8, 9, 10, 12, 12, 15$ $10.57$
Find the population variance:
$1,$ $3,$ $3,$ $4,$ $5,$ $12,$ $12,$ $12,$ $14,$ $14$ $24.4$
Find the population variance:
$6, 10, 11, 11, 12, 16$ $8.67$
Find the population variance:
$14,$ $15,$ $16,$ $16,$ $21,$ $21,$ $21,$ $22,$ $25$ $12.89$
Find the population variance:
$17, 17, 18, 25, 28$ $21.2$
Find the population variance:
$15,$ $16,$ $16,$ $20,$ $22,$ $27,$ $28,$ $32$ $35.75$
Find the population variance:
$10,$ $10,$ $10,$ $15,$ $16,$ $17,$ $17,$ $19,$ $21,$ $25$ $22.6$
Find the population variance: $4, 4, 4, 14, 14$ $24$
Find the population variance:
$7, 8, 8, 13, 14, 17, 31$ $60$
Find the population variance:
$8, 8, 8, 11, 15, 18, 20, 32$ $60.75$
Find the population variance:
$14, 17, 19, 21, 21, 28$ $18.67$
Find the population variance:
$7,$ $9,$ $13,$ $14,$ $15,$ $16,$ $17,$ $17,$ $18$ $12.67$
Find the population variance:
$11,$ $12,$ $12,$ $13,$ $18,$ $19,$ $24,$ $25,$ $28$ $36.89$
Find the population variance:
$15,$ $16,$ $17,$ $18,$ $21,$ $22,$ $22,$ $24,$ $27,$ $28$ $18.2$

How to do these

Find the population variance:
$2, 4, 4, 4, 5, 5, 7, 9$

The mean is 5.
The squared distances are 9, 1, 1, 1, 0, 0, 4, 16, totaling 32.
32 over 8.

The answer is $4$ .

Where students go wrong

Averaging the distances without squaring them. Positive and negative distances cancel, and the answer comes out near zero for any set.

Also called population variance, sample variance or measures of spread.

Questions about these worksheets

Yes. Every variance sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Statistics is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the variance questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Averaging the distances without squaring them. Positive and negative distances cancel, and the answer comes out near zero for any set.

Variance worksheet for Statistics

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How to do these

Where students go wrong

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