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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
Frequency3710104

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
Frequency516222610

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
[0,20[12
[20,40[18
[40,60[9
[60,80[9
[80,100[2

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

Instructions

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.

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Description of Levels

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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.

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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
Frequency41118173
" 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

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