Standard deviation worksheet for Statistics

Find the mean, square each distance from it, average the squares, and take the square root: that is the population standard deviation. A sample divides by one less than the count instead. Variance is the same number before the root. Easy lists are built so the root comes out whole; frequency tables are rounded to the hundredth.

Also taught in Algebra 1, Algebra 2 and Pre-Algebra, 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 Standard Deviation Date Period Answer each question. Round to two places where needed. Find the standard deviation Find the population standard deviation: $4, 5, 7, 8, 9, 9, 10, 12$ Find the population standard deviation: $17,$ $18,$ $20,$ $20,$ $20,$ $27,$ $28,$ $28,$ $29$ Find the population standard deviation: $7, 7, 8, 15, 17, 18, 19$ Find the population standard deviation: $14,$ $15,$ $16,$ $17,$ $21,$ $21,$ $22,$ $23,$ $25,$ $26$ Find the population standard deviation: $3, 5, 8, 9, 9, 14$ Find the new mean and standard deviation A data set has mean 48 and standard deviation 4. Each value is multiplied by 3, and then 12 is added to it. Find the new mean and standard deviation. A data set has mean 43 and standard deviation 8. Each value is multiplied by 2. Find the new mean and standard deviation. A data set has mean 27 and standard deviation 11. Each value is multiplied by 3, and then 3 is subtracted from it. Find the new mean and standard deviation. A data set has mean 23 and standard deviation 9. Each value is multiplied by 5, and then 5 is subtracted from it. Find the new mean and standard deviation. A data set has mean 48 and standard deviation 9. Each value is multiplied by 2. Find the new mean and standard deviation. Find the standard deviation from a frequency table $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 5 & 6 & 8 & 9 \\ Frequency & 3 & 3 & 2 & 2 \end{array} \end{aligned}$ $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 0 & 1 & 2 & 4 \\ Frequency & 5 & 1 & 4 & 4 \end{array} \end{aligned}$ $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 4 & 6 & 8 & 9 \\ Frequency & 7 & 3 & 6 & 1 \end{array} \end{aligned}$ $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 3 & 4 & 6 & 8 \\ Frequency & 6 & 6 & 6 & 5 \end{array} \end{aligned}$ $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 5 & 6 & 7 & 8 \\ Frequency & 1 & 4 & 3 & 2 \end{array} \end{aligned}$ Compare standard deviations Which set has the larger standard deviation? Set A: $19$ , $20$ , $19$ , $22$ , $23$ , $20$ . Set B: $27$ , $24$ , $20$ , $18$ , $23$ , $27$ Which set has the larger standard deviation? Set A: $29$ , $26$ , $28$ , $29$ , $28$ . Set B: $23$ , $21$ , $23$ , $29$ , $27$ Which set has the larger standard deviation? Set A: $23$ , $26$ , $32$ , $30$ . Set B: $29$ , $29$ , $27$ , $27$ Which set has the larger standard deviation? Set A: $11$ , $15$ , $13$ , $16$ , $6$ . Set B: $10$ , $8$ , $8$ , $8$ , $9$ Which set has the larger standard deviation? Set A: $6$ , $11$ , $5$ , $3$ . Set B: $7$ , $7$ , $9$ , $6$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Standard Deviation

Date Period

Answer each question. Round to two places where needed.

Find the standard deviation
Find the population standard deviation:
$4, 5, 7, 8, 9, 9, 10, 12$
Find the population standard deviation:
$17,$ $18,$ $20,$ $20,$ $20,$ $27,$ $28,$ $28,$ $29$
Find the population standard deviation:
$7, 7, 8, 15, 17, 18, 19$
Find the population standard deviation:
$14,$ $15,$ $16,$ $17,$ $21,$ $21,$ $22,$ $23,$ $25,$ $26$
Find the population standard deviation:
$3, 5, 8, 9, 9, 14$

Find the new mean and standard deviation
A data set has mean 48 and standard deviation 4. Each value is multiplied by 3, and then 12 is added to it. Find the new mean and standard deviation.
A data set has mean 43 and standard deviation 8. Each value is multiplied by 2. Find the new mean and standard deviation.
A data set has mean 27 and standard deviation 11. Each value is multiplied by 3, and then 3 is subtracted from it. Find the new mean and standard deviation.
A data set has mean 23 and standard deviation 9. Each value is multiplied by 5, and then 5 is subtracted from it. Find the new mean and standard deviation.
A data set has mean 48 and standard deviation 9. Each value is multiplied by 2. Find the new mean and standard deviation.

Find the standard deviation from a frequency table
$\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 5 & 6 & 8 & 9 \\ Frequency & 3 & 3 & 2 & 2 \end{array} \end{aligned}$
$\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 0 & 1 & 2 & 4 \\ Frequency & 5 & 1 & 4 & 4 \end{array} \end{aligned}$
$\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 4 & 6 & 8 & 9 \\ Frequency & 7 & 3 & 6 & 1 \end{array} \end{aligned}$
$\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 3 & 4 & 6 & 8 \\ Frequency & 6 & 6 & 6 & 5 \end{array} \end{aligned}$
$\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 5 & 6 & 7 & 8 \\ Frequency & 1 & 4 & 3 & 2 \end{array} \end{aligned}$

Compare standard deviations
Which set has the larger standard deviation? Set A: $19$ , $20$ , $19$ , $22$ , $23$ , $20$ . Set B: $27$ , $24$ , $20$ , $18$ , $23$ , $27$
Which set has the larger standard deviation? Set A: $29$ , $26$ , $28$ , $29$ , $28$ . Set B: $23$ , $21$ , $23$ , $29$ , $27$
Which set has the larger standard deviation? Set A: $23$ , $26$ , $32$ , $30$ . Set B: $29$ , $29$ , $27$ , $27$
Which set has the larger standard deviation? Set A: $11$ , $15$ , $13$ , $16$ , $6$ . Set B: $10$ , $8$ , $8$ , $8$ , $9$
Which set has the larger standard deviation? Set A: $6$ , $11$ , $5$ , $3$ . Set B: $7$ , $7$ , $9$ , $6$



Sigma Prep · sigmaprep.io/worksheets Name Standard DeviationAnswer keyVersion 1 Date Period Answer each question. Round to two places where needed. Find the standard deviation Find the population standard deviation: $4, 5, 7, 8, 9, 9, 10, 12$ $2.45$ Find the population standard deviation: $17,$ $18,$ $20,$ $20,$ $20,$ $27,$ $28,$ $28,$ $29$ $4.59$ Find the population standard deviation: $7, 7, 8, 15, 17, 18, 19$ $5.04$ Find the population standard deviation: $14,$ $15,$ $16,$ $17,$ $21,$ $21,$ $22,$ $23,$ $25,$ $26$ $4.02$ Find the population standard deviation: $3, 5, 8, 9, 9, 14$ $3.46$ Find the new mean and standard deviation A data set has mean 48 and standard deviation 4. Each value is multiplied by 3, and then 12 is added to it. Find the new mean and standard deviation.mean $156$ , SD $12$ A data set has mean 43 and standard deviation 8. Each value is multiplied by 2. Find the new mean and standard deviation.mean $86$ , SD $16$ A data set has mean 27 and standard deviation 11. Each value is multiplied by 3, and then 3 is subtracted from it. Find the new mean and standard deviation.mean $78$ , SD $33$ A data set has mean 23 and standard deviation 9. Each value is multiplied by 5, and then 5 is subtracted from it. Find the new mean and standard deviation.mean $110$ , SD $45$ A data set has mean 48 and standard deviation 9. Each value is multiplied by 2. Find the new mean and standard deviation.mean $96$ , SD $18$ Find the standard deviation from a frequency table $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 5 & 6 & 8 & 9 \\ Frequency & 3 & 3 & 2 & 2 \end{array} \end{aligned}$ $1.55$ $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 0 & 1 & 2 & 4 \\ Frequency & 5 & 1 & 4 & 4 \end{array} \end{aligned}$ $1.61$ $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 4 & 6 & 8 & 9 \\ Frequency & 7 & 3 & 6 & 1 \end{array} \end{aligned}$ $1.89$ $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 3 & 4 & 6 & 8 \\ Frequency & 6 & 6 & 6 & 5 \end{array} \end{aligned}$ $1.87$ $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 5 & 6 & 7 & 8 \\ Frequency & 1 & 4 & 3 & 2 \end{array} \end{aligned}$ $0.92$ Compare standard deviations Which set has the larger standard deviation? Set A: $19$ , $20$ , $19$ , $22$ , $23$ , $20$ . Set B: $27$ , $24$ , $20$ , $18$ , $23$ , $27$ Set B Which set has the larger standard deviation? Set A: $29$ , $26$ , $28$ , $29$ , $28$ . Set B: $23$ , $21$ , $23$ , $29$ , $27$ Set B Which set has the larger standard deviation? Set A: $23$ , $26$ , $32$ , $30$ . Set B: $29$ , $29$ , $27$ , $27$ Set A Which set has the larger standard deviation? Set A: $11$ , $15$ , $13$ , $16$ , $6$ . Set B: $10$ , $8$ , $8$ , $8$ , $9$ Set A Which set has the larger standard deviation? Set A: $6$ , $11$ , $5$ , $3$ . Set B: $7$ , $7$ , $9$ , $6$ Set A Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Standard DeviationAnswer keyVersion 1

Date Period

Answer each question. Round to two places where needed.

Find the standard deviation
Find the population standard deviation:
$4, 5, 7, 8, 9, 9, 10, 12$ $2.45$
Find the population standard deviation:
$17,$ $18,$ $20,$ $20,$ $20,$ $27,$ $28,$ $28,$ $29$ $4.59$
Find the population standard deviation:
$7, 7, 8, 15, 17, 18, 19$ $5.04$
Find the population standard deviation:
$14,$ $15,$ $16,$ $17,$ $21,$ $21,$ $22,$ $23,$ $25,$ $26$ $4.02$
Find the population standard deviation:
$3, 5, 8, 9, 9, 14$ $3.46$

Find the new mean and standard deviation
A data set has mean 48 and standard deviation 4. Each value is multiplied by 3, and then 12 is added to it. Find the new mean and standard deviation.mean $156$ , SD $12$
A data set has mean 43 and standard deviation 8. Each value is multiplied by 2. Find the new mean and standard deviation.mean $86$ , SD $16$
A data set has mean 27 and standard deviation 11. Each value is multiplied by 3, and then 3 is subtracted from it. Find the new mean and standard deviation.mean $78$ , SD $33$
A data set has mean 23 and standard deviation 9. Each value is multiplied by 5, and then 5 is subtracted from it. Find the new mean and standard deviation.mean $110$ , SD $45$
A data set has mean 48 and standard deviation 9. Each value is multiplied by 2. Find the new mean and standard deviation.mean $96$ , SD $18$

Find the standard deviation from a frequency table
$\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 5 & 6 & 8 & 9 \\ Frequency & 3 & 3 & 2 & 2 \end{array} \end{aligned}$ $1.55$
$\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 0 & 1 & 2 & 4 \\ Frequency & 5 & 1 & 4 & 4 \end{array} \end{aligned}$ $1.61$
$\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 4 & 6 & 8 & 9 \\ Frequency & 7 & 3 & 6 & 1 \end{array} \end{aligned}$ $1.89$
$\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 3 & 4 & 6 & 8 \\ Frequency & 6 & 6 & 6 & 5 \end{array} \end{aligned}$ $1.87$
$\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{ccccc} Value & 5 & 6 & 7 & 8 \\ Frequency & 1 & 4 & 3 & 2 \end{array} \end{aligned}$ $0.92$

Compare standard deviations
Which set has the larger standard deviation? Set A: $19$ , $20$ , $19$ , $22$ , $23$ , $20$ . Set B: $27$ , $24$ , $20$ , $18$ , $23$ , $27$ Set B
Which set has the larger standard deviation? Set A: $29$ , $26$ , $28$ , $29$ , $28$ . Set B: $23$ , $21$ , $23$ , $29$ , $27$ Set B
Which set has the larger standard deviation? Set A: $23$ , $26$ , $32$ , $30$ . Set B: $29$ , $29$ , $27$ , $27$ Set A
Which set has the larger standard deviation? Set A: $11$ , $15$ , $13$ , $16$ , $6$ . Set B: $10$ , $8$ , $8$ , $8$ , $9$ Set A
Which set has the larger standard deviation? Set A: $6$ , $11$ , $5$ , $3$ . Set B: $7$ , $7$ , $9$ , $6$ Set A

How to do these

Find the population standard deviation:
$2, 4, 4, 4, 5, 5, 7, 9$

The mean is 40 over 8, which is 5.
The squared distances are 9, 1, 1, 1, 0, 0, 4, 16, totaling 32.
32 over 8 is 4, and the root of 4 is 2.

The answer is $2$ .

Where students go wrong

Forgetting the square root at the end, which hands in the variance. And on a sample, dividing by n instead of n - 1.

Also called measures of spread, sample standard deviation or population standard deviation.

What you can put on this worksheet

Standard deviation: Find the population standard deviation:
$21, 24, 28, 30, 32$ → $4$
After every value changes: A data set has mean 37 and standard deviation 8. Each value is multiplied by 2. Find the new mean and standard deviation. → mean $74$ , SD $16$
From a frequency table: Find the population standard deviation, to the nearest hundredth.
$\begin{array}{cccc} Value & 3 & 5 & 7 \\ Frequency & 1 & 4 & 4 \end{array}$ → $1.33$
Which set is more spread out: Which set has the larger standard deviation? Set A: $30$ , $17$ , $27$ , $21$ , $30$ . Set B: $21$ , $18$ , $20$ , $20$ , $19$ → Set A
From a dot plot or a stem plot: Find the population standard deviation of the data in the dot plot, to the nearest hundredth. — a dot plot from 6 to 10 → $1.36$

Questions about these worksheets

Yes. Every standard deviation 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 standard deviation 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.

You pick from 5: standard deviation, after every value changes, from a frequency table, which set is more spread out and from a dot plot or a stem plot. Tick as many as you want and set how many of each, or let it spread them evenly.

Forgetting the square root at the end, which hands in the variance. And on a sample, dividing by n instead of n - 1.

Standard deviation worksheet for Statistics

Select your difficulty

Find the standard deviation

Find the new mean and standard deviation

Find the standard deviation from a frequency table

Compare standard deviations

Find the standard deviation

Find the new mean and standard deviation

Find the standard deviation from a frequency table

Compare standard deviations

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these standard deviation worksheets free?+

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Is this a free alternative to Kuta Software for standard deviation?+

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