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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
No calculator

This is level 2: without a calculator find the standard deviation of a small data set. You can earn a trophy if you get at least 4 questions correct and you do this activity online.


4, 2, 5, 8, 6

Working:

Correct Wrong


3, 5, 9, 6, 8, 5

Working:

Correct Wrong


5, 5, 13, 13

Working:

Correct Wrong


12, 6, 20, 14

Working:

Correct Wrong


4, 18, 12, 10

Working:

Correct Wrong
Check

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

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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© Transum Mathematics :: This activity can be found online at:
www.Transum.org/go/?Num=815

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 2

The objective of this exercise is to give you a small amount of practice calculating standard deviation using pen and paper just so that you get a 'feel' for the concept.

Example: find the standard deviation of the following values: {6,18,6,18}

Find the sum: 6 + 18 + 6 + 18 = 48

Find the mean: 48 ÷ 4 = 12

Find the difference between each number and the mean then square that difference. Add the squares:

(6-12)² + (18-12)² + (6-12)² + (18-12)²

= 36 + 36 + 36 + 36 = 144

Divide this by the number of items:

144 ÷ 4 = 36

This is the variance. Find the square root of the variance to give a standard deviation of 6.

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.

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