Transum Software

Standard Deviation

Find how 'spread out' data is by estimating and calculating this measure of dispersion

Level 1 Level 2 Level 3 Level 4 Exam-Style Description Help More Statistics

Give your answers correct to three significant figures.

This is level 4: use a calculator find the standard deviation of grouped data. You can earn a trophy if you get at least 4 questions correct and you do this activity online.

1. The number of minutes, rounded to the nearest five minutes, a group of students took to eat their lunch is shown in the following frequency table:

Number of minutes1520253035

Find the standard deviation of the times.

Correct Wrong

2. The table shows the weights of 79 boulders found in a volcano crater:

Weight(w kg)0<w≤1010<w≤2020<w≤3030<w≤4040<w≤50

Find an estimate of the standard deviation of the weights of the boulders.

Correct Wrong

The table shows the times people took to solve a puzzle:

Time in secondsFrequency

3. Find an estimate of the mean of the times.

Correct Wrong

4. Find an estimate of the variance of the times.

Correct Wrong

5. Find an estimate of the standard deviation of the times.

Correct Wrong

This is Standard Deviation level 4. You can also try:
Level 1 Level 2 Level 3


Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales:

"I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!"

Comment recorded on the 21 October 'Starter of the Day' page by Mr Trainor And His P7 Class(All Girls), Mercy Primary School, Belfast:

"My Primary 7 class in Mercy Primary school, Belfast, look forward to your mental maths starters every morning. The variety of material is interesting and exciting and always engages the teacher and pupils. Keep them coming please."

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.

Featured Activity



Find your way through the maze encountering mathematical operations in the correct order to achieve the given total. This is an addictive challenge that begins easy but develops into quite a difficult puzzle.


There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now:


Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.


If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if should go offline for whatever reason, there is a mirror site at that contains most of the resources that are available here on

When planning to use technology in your lesson always have a plan B!

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


©1997-2024 WWW.TRANSUM.ORG

© Transum Mathematics :: This activity can be found online at:

Description of Levels



Level 1 - Compare small data sets by estimating their dispersion

Level 2 - Without a calculator find the standard deviation of a small data set

Level 3 - Use a calculator find the standard deviation of a data set

Level 4 - Use a calculator find the standard deviation of grouped data

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More Statistics Resources including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

What is Standard Deviation?

This great video is from Jeremy Jones.

Help with Level 4

Different calculators will have different ways for you to calculate the standard deviation. The manual that came with your calculator is your best source of information.

Here are some screen shots showing the method for a TInSpire.

Example: find the standard deviation of the following times:

Number of seconds115120125130135
" Standard deviation on a TInSpire

1. Type the values into a list and call that list t. Type the frequencies into a list called f. Put the cursor at the top of the next column.

2. Press the menu button - Statistics - Stat Calculations - One-variable Statistics

3. In the first input box scroll down to find 't and in the second input box scroll down to find 'f then press the OK button

4. Scroll down column E to find the standard deviation, σ

Before entering grouped data into the calculator you need to find the mid-points of the groups of data. When you have done that follow the instructions above.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up