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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 1: compare small data sets by estimating their dispersion. You can earn a trophy if you get at least 4 questions correct and you do this activity online.

1. Drag these three sets into order according to their dispersion. The set with the smallest dispersion should be at the top.

7, 2, 3
6, 2, 2
1, 2, 3
Correct Wrong

2. The following is the data collected regarding the length of snakes captured on three consecutive days. Drag these three sets into order according to their standard deviation. The set with the smallest standard deviation should be at the top.

17cm , 34cm, 99cm
22cm, 32cm
23cm, 37cm
Correct Wrong

3. The following sets show the weights of empty containers found in three locations. Drag these three sets into order according to their standard deviation. The set with the smallest standard deviation should be at the top.

3,750 kg, 3,750 kg, 3,750 kg, 3,750 kg, 3,750 kg
3,200 kg, 3,750 kg, 3,750 kg, 4,250 kg
3,200 kg, 3,750 kg
Correct Wrong

4. Drag these three sets into order according to their dispersion. The set with the smallest dispersion should be at the top.

188, 243, 944, 243
11, 99, 67, 23
4.7, 8.17, 5.99, 7.7, 4.65
Correct Wrong

5. Drag these three sets into order according to their standard deviation. The set with the smallest standard deviation should be at the top.

10, 21, 49, 87, 90
10, 80, 49, 31, 90
10, 53, 54, 50, 90
Correct Wrong
Check

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

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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 1

For this introductory exercise you have to consider how spread out the values in the set are and then compare this (called the dispersion or standard deviation) with the other sets in the group.

You can drag the sets up or down until the three sets in the group are in order with the least spread out at the top and the most spread out at the bottom.

It may help to visualise the numbers on a number line and then it would be clearer how spread out the numbers are. For example consider the following two sets:

Set A: {15,14,17,10,19}

Set B: {9,6,14,21,28}

Plotted on a number line they look like this:

Dispersion number line

It is clear from the diagram that the numbers in set B are more spread out than the numbers in set A.

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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