# Standard Deviation

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

##### Level 1Level 2Level 3Level 4Exam-StyleDescriptionHelpMore Statistics

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: 3, 5, 9, 6, 8, 5 Working: 5, 5, 13, 13 Working: 12, 6, 20, 14 Working: 4, 18, 12, 10 Working:
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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.

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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).

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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.

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