Efofex News

Often, the hardest part of creating a MultiDocs question is setting up a parameter that produces suitable numbers. We have recently released two new options that can help you.

New Option For Range and RangeEx

The Range and RangeEx parameters now have a new option available – ExcludeMultiplesOf

$p=range(low, high, increment(optional), excludemultiplesof(optional))

An example command might be $p=range(200,400,2,10)

This produces a range of values between 200 and 400, incrementing by 2, excluding all multiples of 10

$p will take a value from this set. {202, 204, 206, 208, 212, 214, 216, 218, 222, 224,… 388, 392, 394, 396, 398}

This extension allows you to quickly remove values which might prove too easy for your particular question.

NoCommonFactor Parameter

NoCommonFactor parameters allow you to access numbers which do not share a common factor.

$p=nocommonfactor(number)

$p=nocommonfactor(number,low,high)

Notes:

• low and high are optional and do NOT need to be factors of the number.
• low and high can be higher (or lower) than number
• The nocommonfactor command will return 1.

Examples:

$p=nocommonfactor(12)                $p will be chosen from the set {1,5,7,11}.

$p=nocommonfactor(12,10,36)        $p will be chosen from the set {11,13,17,19,23,25,29,31,35}.

The most common reason for using a nocommonfactor parameter is to create numerators for fractions which cannot be simplified.

Data parameters can now be created with bivariate data.

$b=data((11,12)(15,19)(21,28)(13.2,19.4),(8,16))

Bivariate data is entered as separate data points, wrapped in parentheses, which are then (optionally) separated with your normal separator.

New RandBivariate Parameter

Often, the best way to create random bivariate is to use a randbivariate parameter.

$p=RandBivariate(lowx, highx, slope, intercept, targetr, number)

Generates number random bivariate data points with the x values ranging from lowx to highx. The data will approximately fit a linear regression line with the given slope and intercept with a correlation coefficient of approximately targetr.

If you want data with a negative correlation, you MUST enter a negative slope, NOT a negative targetr.

Statistical Commands

There are a number of new statistical commands that can operate on bivariate data parameters.

regslope($p) will return the slope of the line of best fit for the bivariate data.
regintercept($p) will return the intercept of the line of best fit for the bivariate data
regr($p) will return the correlation coefficient for the bivariate data

Other Commands

$b=data((11,12)(15,19)(21,28)(13.2,19.4),(8,16)) creates 5 data points, each with an x value and a y value.

$b[3] will return (21,28)
xvalue($b[3]) will return 21
yvalue($b[3]) will return 28

Data parameters can now support grouped data.

$g=data(10~20:2,20~30:6,30~40:4,40~50:2)

This data parameter is equivalent to this frequency table.

Each entry in the data parameter is the group definition, separated by a ~, and the frequency, separated by a :.

Statistical Calculator Commands

All statistical commands honour the group and frequency information. For example {mean($g)} will return 29.28

Grouped Data Calculator Commands

The definition of $g creates 4 group entries. If you reference one of the entries, $g[3] for example, you will see 30~40:4. There are two commands which allow you to access the group definition and the frequency of the entry.

{groupdefn($g[3])} will return 30~40
{freq($g[3])} will return 4

Grouping Existing Data

If you have a parameter which contains raw, ungrouped data you can group it using a calculator command.

For example. If

$p=randnormal(50,15,30)

{group($p)} will return the raw data automatically grouped.

Often, the best way to use the group command is within parameter definitions.

$p=randnormal(50,15,30)
$g=group($p)

This will create a set of randomly generated grouped data, perfect for histogram type questions.

Data parameters can now support frequency tables.

$p=data(10:1, 11:3, 12:5, 13:4, 14:3, 15:2)

This data parameter is equivalent to this frequency table.

Each entry in the data parameter is the data value and the frequency, separated by a :.

Statistical Calculator Commands

All statistical commands honour the frequency information. For example {mean($p)} will return 12.61111

Frequency Table Calculator Commands

The definition of $p creates 6 data entries. If you reference one of the entries, $p[3] for example, you will see 12:5. There are two commands which allow you to access the data value and the frequency of the entry.

{datavalue($p[3])} will return 12
{freq($p[3])} will return 5

The inclusion of data parameters and random number generating parameters has prompted more statistical functions which can calculate summary statistics.

For example. If $p=randnormal(50,15,30), $p will return a data parameter with 30 random numbers which have been taken from a probability density function with mean of 50 and standard deviation of 15.

Measures of Central Tendency

mean($p)
median($p)
mode($p)

Note that mode will return one or two modes if they exist.

Measures of Dispersion

sd($p) Sample standard deviation
sdp($p) Population standard deviation
variance($p) Variance
iqr($p) Interquartile range.
range($p) Range

Other Measures

count($p) Counts the number of values in the data parameter (equivalent to $p[0])
lq($p) Lower quartile
max($p) Maximum value
maxref($p) Reference of the maximum value (ie, this will return 3 if the third value is the maximum)
min($p) Minimum value
minref($p) Reference of the minimum value
sum($p) Sum of the values in $p
uq($p) Upper quartile

We have implemented a new parameter and a number of new calculator commands that allow you to work with words. These allow you to implement probability questions like:

If you randomly select a letter from the word MISSISSIPPI, what is the probability that the letter you select will be a vowel.

You could implement this type of question using a LIST parameter.

$m=list(“M”,”I”,”S”,”S”,”I”,”S”,”S”,”I”,”P”,”P”,”I”)

but this quickly becomes onerous, especially if you want to include a range of words in your question.

New Explode Parameter.

The first change we have made is to implement a new Explode parameter.

$x=explode(“MISSISSIPPI”)

This takes the provided word and explodes it into a list – just like typing the extended list command above.

You can combine a list command and an explode command to create a question which deals with lots of different words.

$w=list(“MATHEMATICS”,”STATISTICS”,”ALGEBRA”,”TRIGONOMETRY”,”GEOMETRY”)
$x=explode($w)

This allows you to regenerate to randomly select a word and explode it into a list of letters.

New Calculator Commands

unique($x)

Creates a new list of the unique letters in a list of letters. If $x contains the exploded word MATHEMATICS, {unique($x)} will return the list

“M”,”A”,”T”,”H”,”E”,”I”,”C”,”S”

sort($x)

The sort command will sort a list of letters. If $x contains the exploded word MATHEMATICS, {sort($x)} will return the list”A”,”A”,”C”,”E”,”H”,”I”,”M”,”M”,”S”,”T”,”T”

You will often combine the sort and unique commands.

{sort(unique($x))} will return “A”,”C”,”E”,”H”,”I”,”M”,”S”,”T”

vowels($x)

This command returns a list of vowels in a word.

{vowels(sort(unique($x)))} will return “A”,”E”,”I”

consonants($x)

This command returns a list of consonants in a word.

{consonants(sort(unique($x)))} will return “C”,”H”,”M”,”S”,”T”

NOTE: The letter Y is not returned by either the vowels command or the consonants command.

We have been very busy over the last few months, adding significant new features to our products. Our Efofex Insiders newsletter details all of the finer details of the new options. This week we have already uploaded 5 new articles containing details on using parameters for bivariate data, grouped data, frequency tables and an number of other options.

If you want access to all of the technical changes to the software, our Efofex Insiders Newsletter is the place to be! We will continue to report on more general changes and development themes in our general newsletter.

FX Equation has had the box command for many years. It allows you to create empty boxes or put boxes around various parts of your equation.

Cancelling Parts Of Your Equation

FX Equation has also had a “strike-through” system which tried to allow you to “cancel” various parts of an equation. This was always a difficult task programatically but the addition of parameters to our products has made it impossible.

In the latest versions, we have deprecated (still available but not recommended) the strikethough system and replaced it with explicit cancel and strike commands.

cancel(x2) will cancel using a diagonal line.
strike(x2) will cancel with a horizontal line.

For example, if I type…

(cancel((x-2))(x+2))/(strike(x-2))

FX Equation will produce the following.

The new system is far more reliable.

New Underlining Commands

As part of this upgrade we have also added two new underlining commands, ul() and dul(). These underline and double-underline components of your equation.

x2+ul(3x)-dul(4)

By selecting the dul or ul part of the command you can change the colour of the underline. Ideal for marking the “answer”.

ArcUnder Command

FX Equation has had an arc command for a number of years. This allows you to add an arc above a component of your equation. The latest releases add an arcunder command.

We have been working feverishly on expanding the types of mathematics that can be regenerated using MultiDocs. Our recent efforts have added the ability to create most statistical graphs and perform most statistical calculations.

Visit FX Library and type Statistics in as the search term. This will provide you with a small selection of the new features available. So far we have uploaded a bivariate data question, a cumulative frequency question and a question involving stem & leaf plots.

Like all MultiDocs, our examples are regeneratable at the push of a button. Here’s a graph from the bivariate data question – three different versions of the question in seconds!

MultiDocs are the most exciting addition to Efofex since the release of FX Draw. If you haven’t investigated the power of the new system, we strongly recommend that you take a look!

MultiDocs – Powered by Efofex

As always, our Efofex Insider’s Newsletter will keep you up-to-date with the technical side of changes.

Our introduction of data parameters means that parameters are no longer just 1 number. You often need to work with full list of values.

If we have the following parameter

$p=randnormal(50,10,30)

$p might contain the following data.

52.82, 51.09, 49.33, 47.02, 38.04, 67.23, 55.54, 51.4, … , 37.88, 45.5, 55.23, 49.21, 38.63

The inline calculator can now calculate most summary statistics

{mean($p)} will be replaced with 49.77

{iqr($p)} will be replaced with 10.55

There are a number of commands which produce summary statistics. These are discussed in our online manual.

You also have access to commands like

{sort($p)} which will sort the list in ascending order

{contains($p,50)} which will return true if $p contains the value 50

{count($p,6)} which will return the number of 6’s in $p