Descriptive Stats (P): find sample mean, range and variance

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Christian Lawson-Perfect

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9 years, 5 months ago

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Christian Lawson-Perfect 9 years, 5 months ago

Saved a checkpoint:

Rejigged so it's three parts.
Displayed the data in a table.
Changed the setting to toilet visits instead of number of anti-depressants taken, because that's both grim and unrealistic.
Wrote some advice.

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Christian Lawson-Perfect 9 years, 5 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 9 years, 5 months ago

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Hayley Moore 9 years, 8 months ago

Created this.

Name	Status	Author	Last Modified
Descriptive Stats (P): find sample mean, range and variance	Ready to use	Hayley Moore	01/06/2016 09:47
Descriptive Stats (P): find sample mean, range and variance	draft	Xiaodan Leng	11/07/2019 07:02

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Question statement

Joe makes a variable number of visits to the toilet each day. He recorded his activities as follows:

{table([data],['Monday','Tuesday','Wednesday','Thursday','Friday','Saturday','Sunday'])}

Compute the following descriptive statistics of the data. Round your answers to 2 decimal places.

Give any introductory information the student needs.

			Name	Type	Generated Value

Mon	integer	1
Tues	integer	2
Wed	integer	2
Thurs	integer	2
Fri	integer	4
Sat	integer	4
Sun	integer	4
data	list	[ 1, 2, 2, 2, 4, 4, 4 ]
range	number	3
variance	number	1.3469387755
mean	number	2.7142857143

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..4)

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

data

Advice

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add
Part c) Gap-fill
1. Gap Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Mean: Unnamed gap

Advice

a)

The mean of a set of data is the sum of the data, divided by the number of values in the set. In this case, the mean is

$\simplify[]{({mon}+{tues}+{wed}+{thurs}+{fri}+{sat}+{sun})/7} = \var{precround(mean,2)} \text{ (to 2 d.p.)}$

b)

The range of a set of data is the difference between the greatest and least values in the set. In this case, the range is

$\simplify[]{{max(data)}-{min(data)} = {range}}$

c)

The variance of a sample $x_1,x_2, \dots, x_n$ is given by the following formula:

$\text{Variance} = \sum \frac{(x_i-\mu)^2}{n}$

{table([['$x_i$']+data,['$x_i-\\mu$']+map(x-mean,x,data),['$(x_i-\\mu)^2$']+map((x-mean)^2,x,data)],[])}

Now,

$\text{Variance} = \frac{1}{7} \sum (x_i-\mu)^2 = \var{precround(variance,2)} \text{ (to 2 d.p.)}$

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Part	Test	Passed?
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Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
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Number entry
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Descriptive Stats (P): find sample mean, range and variance

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Christian Lawson-Perfect 9 years, 5 months ago

Christian Lawson-Perfect 9 years, 5 months ago

Christian Lawson-Perfect 9 years, 5 months ago

Hayley Moore 9 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

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Error

Descriptive Stats (P): find sample mean, range and variance

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 9 years, 5 months ago

Christian Lawson-Perfect 9 years, 5 months ago

Christian Lawson-Perfect 9 years, 5 months ago

Hayley Moore 9 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

Generated value: `integer`