Standard deviation worksheet for Pre-Algebra

Standard deviation is usually an Algebra 1 topic, and Pre-Algebra classes that preview it can treat it as a cousin of the mean absolute deviation. The lists of whole numbers here are chosen so the square root comes out exact, and the small frequency tables are rounded to the hundredth. Other questions ask what happens to the SD when every value is shifted or multiplied, and which of two sets is more spread out. A small value means the data sit close to the mean.

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

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



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: $1, 3, 7, 9, 13, 15$ Find the population standard deviation: $20,$ $21,$ $22,$ $22,$ $23,$ $25,$ $25,$ $26$ Find the population standard deviation: $9,$ $9,$ $9,$ $10,$ $11,$ $14,$ $15,$ $15,$ $16,$ $22$ Find the population standard deviation: $8,$ $15,$ $21,$ $23,$ $24,$ $24,$ $26,$ $27$ Find the population standard deviation: $4, 4, 8, 10, 11, 11$ Find the new mean and standard deviation A data set has mean 47 and standard deviation 3. Each value is multiplied by 3. Find the new mean and standard deviation. A data set has mean 16 and standard deviation 11. 2 is subtracted from each value. Find the new mean and standard deviation. A data set has mean 38 and standard deviation 3. 4 is added to each value. Find the new mean and standard deviation. A data set has mean 31 and standard deviation 6. Each value is multiplied by 3. Find the new mean and standard deviation. A data set has mean 51 and standard deviation 12. 3 is added to each value. Find the new mean and standard deviation. Find the standard deviation from a frequency table $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{cccc} Value & 4 & 6 & 8 \\ Frequency & 7 & 5 & 2 \end{array} \end{aligned}$ $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{cccc} Value & 2 & 3 & 5 \\ Frequency & 3 & 6 & 2 \end{array} \end{aligned}$ $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{cccc} Value & 0 & 2 & 4 \\ Frequency & 5 & 6 & 6 \end{array} \end{aligned}$ $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{cccc} Value & 1 & 2 & 3 \\ Frequency & 6 & 6 & 2 \end{array} \end{aligned}$ $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{cccc} Value & 5 & 6 & 8 \\ Frequency & 7 & 4 & 6 \end{array} \end{aligned}$ Compare standard deviations Which set has the larger standard deviation? Set A: $14$ , $16$ , $12$ , $16$ . Set B: $19$ , $7$ , $20$ , $19$ Which set has the larger standard deviation? Set A: $17$ , $14$ , $18$ , $14$ , $17$ . Set B: $15$ , $8$ , $8$ , $21$ , $17$ Which set has the larger standard deviation? Set A: $7$ , $16$ , $14$ , $22$ , $24$ , $8$ . Set B: $19$ , $18$ , $19$ , $15$ , $15$ , $17$ Which set has the larger standard deviation? Set A: $20$ , $11$ , $20$ , $24$ . Set B: $15$ , $15$ , $17$ , $19$ Which set has the larger standard deviation? Set A: $18$ , $18$ , $19$ , $19$ , $15$ , $16$ . Set B: $21$ , $20$ , $23$ , $10$ , $11$ , $18$ 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:
$1, 3, 7, 9, 13, 15$
Find the population standard deviation:
$20,$ $21,$ $22,$ $22,$ $23,$ $25,$ $25,$ $26$
Find the population standard deviation:
$9,$ $9,$ $9,$ $10,$ $11,$ $14,$ $15,$ $15,$ $16,$ $22$
Find the population standard deviation:
$8,$ $15,$ $21,$ $23,$ $24,$ $24,$ $26,$ $27$
Find the population standard deviation:
$4, 4, 8, 10, 11, 11$

Find the new mean and standard deviation
A data set has mean 47 and standard deviation 3. Each value is multiplied by 3. Find the new mean and standard deviation.
A data set has mean 16 and standard deviation 11. 2 is subtracted from each value. Find the new mean and standard deviation.
A data set has mean 38 and standard deviation 3. 4 is added to each value. Find the new mean and standard deviation.
A data set has mean 31 and standard deviation 6. Each value is multiplied by 3. Find the new mean and standard deviation.
A data set has mean 51 and standard deviation 12. 3 is added to each value. Find the new mean and standard deviation.

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

Compare standard deviations
Which set has the larger standard deviation? Set A: $14$ , $16$ , $12$ , $16$ . Set B: $19$ , $7$ , $20$ , $19$
Which set has the larger standard deviation? Set A: $17$ , $14$ , $18$ , $14$ , $17$ . Set B: $15$ , $8$ , $8$ , $21$ , $17$
Which set has the larger standard deviation? Set A: $7$ , $16$ , $14$ , $22$ , $24$ , $8$ . Set B: $19$ , $18$ , $19$ , $15$ , $15$ , $17$
Which set has the larger standard deviation? Set A: $20$ , $11$ , $20$ , $24$ . Set B: $15$ , $15$ , $17$ , $19$
Which set has the larger standard deviation? Set A: $18$ , $18$ , $19$ , $19$ , $15$ , $16$ . Set B: $21$ , $20$ , $23$ , $10$ , $11$ , $18$



Sigma Prep · sigmaprep.io/worksheets Name Standard DeviationAnswer keyVersion 4 Date Period Answer each question. Round to two places where needed. Find the standard deviation Find the population standard deviation: $1, 3, 7, 9, 13, 15$ $5$ Find the population standard deviation: $20,$ $21,$ $22,$ $22,$ $23,$ $25,$ $25,$ $26$ $2$ Find the population standard deviation: $9,$ $9,$ $9,$ $10,$ $11,$ $14,$ $15,$ $15,$ $16,$ $22$ $4$ Find the population standard deviation: $8,$ $15,$ $21,$ $23,$ $24,$ $24,$ $26,$ $27$ $6$ Find the population standard deviation: $4, 4, 8, 10, 11, 11$ $3$ Find the new mean and standard deviation A data set has mean 47 and standard deviation 3. Each value is multiplied by 3. Find the new mean and standard deviation.mean $141$ , SD $9$ A data set has mean 16 and standard deviation 11. 2 is subtracted from each value. Find the new mean and standard deviation.mean $14$ , SD $11$ A data set has mean 38 and standard deviation 3. 4 is added to each value. Find the new mean and standard deviation.mean $42$ , SD $3$ A data set has mean 31 and standard deviation 6. Each value is multiplied by 3. Find the new mean and standard deviation.mean $93$ , SD $18$ A data set has mean 51 and standard deviation 12. 3 is added to each value. Find the new mean and standard deviation.mean $54$ , SD $12$ Find the standard deviation from a frequency table $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{cccc} Value & 4 & 6 & 8 \\ Frequency & 7 & 5 & 2 \end{array} \end{aligned}$ $1.44$ $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{cccc} Value & 2 & 3 & 5 \\ Frequency & 3 & 6 & 2 \end{array} \end{aligned}$ $1.00$ $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{cccc} Value & 0 & 2 & 4 \\ Frequency & 5 & 6 & 6 \end{array} \end{aligned}$ $1.60$ $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{cccc} Value & 1 & 2 & 3 \\ Frequency & 6 & 6 & 2 \end{array} \end{aligned}$ $0.70$ $\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{cccc} Value & 5 & 6 & 8 \\ Frequency & 7 & 4 & 6 \end{array} \end{aligned}$ $1.32$ Compare standard deviations Which set has the larger standard deviation? Set A: $14$ , $16$ , $12$ , $16$ . Set B: $19$ , $7$ , $20$ , $19$ Set B Which set has the larger standard deviation? Set A: $17$ , $14$ , $18$ , $14$ , $17$ . Set B: $15$ , $8$ , $8$ , $21$ , $17$ Set B Which set has the larger standard deviation? Set A: $7$ , $16$ , $14$ , $22$ , $24$ , $8$ . Set B: $19$ , $18$ , $19$ , $15$ , $15$ , $17$ Set A Which set has the larger standard deviation? Set A: $20$ , $11$ , $20$ , $24$ . Set B: $15$ , $15$ , $17$ , $19$ Set A Which set has the larger standard deviation? Set A: $18$ , $18$ , $19$ , $19$ , $15$ , $16$ . Set B: $21$ , $20$ , $23$ , $10$ , $11$ , $18$ Set B Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Standard DeviationAnswer keyVersion 4

Date Period

Answer each question. Round to two places where needed.

Find the standard deviation
Find the population standard deviation:
$1, 3, 7, 9, 13, 15$ $5$
Find the population standard deviation:
$20,$ $21,$ $22,$ $22,$ $23,$ $25,$ $25,$ $26$ $2$
Find the population standard deviation:
$9,$ $9,$ $9,$ $10,$ $11,$ $14,$ $15,$ $15,$ $16,$ $22$ $4$
Find the population standard deviation:
$8,$ $15,$ $21,$ $23,$ $24,$ $24,$ $26,$ $27$ $6$
Find the population standard deviation:
$4, 4, 8, 10, 11, 11$ $3$

Find the new mean and standard deviation
A data set has mean 47 and standard deviation 3. Each value is multiplied by 3. Find the new mean and standard deviation.mean $141$ , SD $9$
A data set has mean 16 and standard deviation 11. 2 is subtracted from each value. Find the new mean and standard deviation.mean $14$ , SD $11$
A data set has mean 38 and standard deviation 3. 4 is added to each value. Find the new mean and standard deviation.mean $42$ , SD $3$
A data set has mean 31 and standard deviation 6. Each value is multiplied by 3. Find the new mean and standard deviation.mean $93$ , SD $18$
A data set has mean 51 and standard deviation 12. 3 is added to each value. Find the new mean and standard deviation.mean $54$ , SD $12$

Find the standard deviation from a frequency table
$\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{cccc} Value & 4 & 6 & 8 \\ Frequency & 7 & 5 & 2 \end{array} \end{aligned}$ $1.44$
$\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{cccc} Value & 2 & 3 & 5 \\ Frequency & 3 & 6 & 2 \end{array} \end{aligned}$ $1.00$
$\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{cccc} Value & 0 & 2 & 4 \\ Frequency & 5 & 6 & 6 \end{array} \end{aligned}$ $1.60$
$\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{cccc} Value & 1 & 2 & 3 \\ Frequency & 6 & 6 & 2 \end{array} \end{aligned}$ $0.70$
$\begin{aligned} Find the population standard deviation, to the nearest hundredth. \\ \begin{array}{cccc} Value & 5 & 6 & 8 \\ Frequency & 7 & 4 & 6 \end{array} \end{aligned}$ $1.32$

Compare standard deviations
Which set has the larger standard deviation? Set A: $14$ , $16$ , $12$ , $16$ . Set B: $19$ , $7$ , $20$ , $19$ Set B
Which set has the larger standard deviation? Set A: $17$ , $14$ , $18$ , $14$ , $17$ . Set B: $15$ , $8$ , $8$ , $21$ , $17$ Set B
Which set has the larger standard deviation? Set A: $7$ , $16$ , $14$ , $22$ , $24$ , $8$ . Set B: $19$ , $18$ , $19$ , $15$ , $15$ , $17$ Set A
Which set has the larger standard deviation? Set A: $20$ , $11$ , $20$ , $24$ . Set B: $15$ , $15$ , $17$ , $19$ Set A
Which set has the larger standard deviation? Set A: $18$ , $18$ , $19$ , $19$ , $15$ , $16$ . Set B: $21$ , $20$ , $23$ , $10$ , $11$ , $18$ Set B

How to do these

Find the population standard deviation: $1, 3, 3, 9$

The mean is 16 ÷ 4 = 4.
Distances from 4 squared: 9, 1, 1, 25, which add to 36.
36 ÷ 4 = 9, and √9 = 3.

The answer is $3$ .

Where students go wrong

Squaring the data values instead of their distances from the mean. Subtract the mean first and then square, or the answer measures how big the numbers are rather than how spread out.

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.

Pre-Algebra is usually taken around 7th or 8th 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 Pre-Algebra

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?+

Do the standard deviation worksheets come with an answer key?+

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What grade are these standard deviation worksheets for?+

Can I get a different version of the same standard deviation worksheet?+

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

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What do students get wrong with standard deviation?+