Calculate centred moving averages

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Norah Storey

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Norah Storey 4 years, 2 months ago

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

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Question statement

The following tables shows by quarter over the three years 2007, 2008, 2009 {This} {tothere} {nat} {tothere2} {tothere3} {tothere4}

{table(rows,[" ","Jan-Mar","Apr-June","July-Sep","Oct-Dec"])}

Give any introductory information the student needs.

			Name	Type	Generated Value

ch	integer	3
j8	integer	920
j9	integer	980
tothere3	string	KiwiJet.
j7	integer	900
tothere4	string
y9	rational	2615/2
y8	rational	5195/4
ap9	integer	1050
y3	rational	4895/4
y5	rational	5025/4
y4	rational	4965/4
y7	rational	5125/4
y6	rational	2535/2
rows	list	Nested 3×5 list
m7	integer	2600
tol	integer	0
m9	integer	2690
m8	integer	2670
ap8	integer	1000
tothere2	string
nat	string
ap7	integer	950
ja8	integer	490
ja9	integer	580
this	string	passenger numbers (in hundreds
ja7	integer	400
tol1	integer	1
tothere	string
y10	rational	2635/2

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.

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Generated value: `integer`

→ Used by:

nat
this
tothere
tothere2
tothere3
tothere4

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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4. Gap Gap 3. Number entry
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5. Gap Gap 4. Number entry
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6. Gap Gap 5. Number entry
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7. Gap Gap 6. Number entry
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8. Gap Gap 7. Number entry
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Gap-fill

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

Find the series of (centred) moving averages for these data and complete the table below:

	Jan-Mar	April-June	July-Sep	Oct-Dec
2007	*	*	Gap 0.	Gap 1.
2008	Gap 2.	Gap 3.	Gap 4.	Gap 5.
2009	Gap 6.	Gap 7.	*	*

Advice

	Jan-Mar	April-June	July-Sep	Oct-Dec
2007	*	*	$\var{y3}$	$\var{y4}$
2008	$\var{y5}$	$\var{y6}$	$\var{y7}$	$\var{y8}$
2009	$\var{y9}$	$\var{y10}$	*	*

Let $Y_t$ denote the data table values so $Y_1=\var{ja7},\;Y_2=\var{ap7} ,\ldots, Y_{12}=\var{j9}$

Using the centred moving average formula for quarters:

$Y^*_t=\frac{Y_{t-2}+2(Y_{t-1}+Y_t+Y_{t+1})+Y_{t+2}}{8}$ we obtain the values in the table above.

Thus the moving average for Oct-Dec 2007 is:

$\frac{Y_{2}+2(Y_{3}+Y_4+Y_{5})+Y_{6}}{8}=\frac{\var{ap7} + 2 (\var{m7} + \var{j7} + \var{ja8}) + \var{ap8}}{8} = \var{y4}$

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Taxonomy: mathcentre

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Norah Storey 4 years, 2 months ago

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Generated value: `integer`

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Gap-fill

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Calculate centred moving averages

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Norah Storey 4 years, 2 months ago

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`