nuExam06 - Mean & Standard deviation - Numbas at mathcentre.ac.uk

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Michael Proudman 5 years, 9 months ago

Created this as a copy of Exam06 - Mean & Standard deviation.

Name	Status	Author	Last Modified
Standard deviation of a list of numbers	Ready to use	Christian Lawson-Perfect	13/12/2019 15:54
Standard deviation of a list of numbers with hints	Ready to use	Julie Crowley	13/09/2018 14:01
Michael's copy of Standard deviation of a list of numbers with hints	draft	Michael Proudman	07/12/2021 09:49
Simon's copy of population Standard deviation of a list of numbers with hints	draft	Simon Thomas	13/05/2019 11:04
Simon's copy of sample Standard deviation of a list of numbers with hints	draft	Simon Thomas	13/05/2019 11:17
Exam06 - Mean & Standard deviation	draft	Michael Proudman	07/12/2021 09:54
nuExam06 - Mean & Standard deviation	draft	Michael Proudman	07/12/2021 09:54
Standard deviation of a list of numbers with hints	draft	Xiaodan Leng	10/07/2019 23:33
Yvonne's copy of Standard deviation of a list of numbers	Ready to use	Yvonne Wancke	26/02/2021 11:09
Standard deviation list of numbers EXAM	Ready to use	Yvonne Wancke	19/04/2023 15:26
Standard deviation list of numbers EXAM PRAC	Ready to use	Yvonne Wancke	06/01/2023 11:50
Mean 2 list of numbers EXAM	Ready to use	Yvonne Wancke	19/04/2023 15:32

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

data	list	List of 8 items
sigma	number	6.4213997695
x	integer	8
mean	number	11.375
var	number	41.234375

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random(1..30),x)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `list`

[ 7, 11, 13, 24, 11, 2, 6, 17 ]

← Depends on:

→ Used by:

mean
sigma

This variable doesn't seem to be used anywhere.

Advice

To calculate the population standard deviation, $\sigma$, we can use the formula:

Population standard deviation, $\sigma = \sqrt{\frac{\Sigma (x-\text{mean})^2}{n}}$

(note this is slightly different to the formula used to calculate the sample standard deviation, $s$)

So we must:

Find the mean:
- mean = $\frac{(\var{data[0]}+\var{data[1]}+...)}{\var{x}}=\var{mean}$
subtract the mean individually from each of our values:
- we obtain $\var{data[0]}-\var{mean}=\var{data[0]-mean}$, $\var{data[1]}-\var{mean}=\var{data[1]-mean}$, etc.
square each result
- $(\var{data[0]-mean})^2=\var{(data[0]-mean)^2}$, $(\var{data[1]-mean})^2=\var{(data[1]-mean)^2}$, etc.
add up these results. This is the '$\Sigma (x-\text{mean})^2$' part in the formula
- $\var{(data[0]-mean)^2}+\var{(data[1]-mean)^2}+... = \var{x*var}$
divide by the number of values
- $\var{x*var} \div \var{x} = \var{var}$
finally, find the square root to obtain the standard deviation:
- $\sigma$= $\sqrt{\var{var}}=\var{precround(sigma,2)}$

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This question is used in the following exam:

HNC Engineering Maths Exam by Michael Proudman in Assessment Exercises.

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nuExam06 - Mean & Standard deviation

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

Michael Proudman 5 years, 9 months ago

Error in variable testing condition

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Warning

Generated value: `list`

Parts

Number entry

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nuExam06 - Mean & Standard deviation

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Michael Proudman 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Number entry

Advanced settings

Generated value: `list`