Efofex News

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

Efofex parameters have always supported references. These allow you to reference individual values in a parameter.

For example, if you have created a parameter like

$p=shuffle(1,6)

$p might end up being 5, 4, 6, 1, 3, 2

You can reference individual elements of $p using square brackets.

$p[4] = 1
$p[6] = 2

The latest versions allow you to use a reference range.

$p[2,5] = “4, 6, 1, 3”

Reference ranges will automatically be produced with your local separator (in this example, that is a comma).

You can also add your own separator

$p[2,5,+]

will be replaced with “4+6+1+3”

Special Reference Ranges

There are two special reference ranges you can use. The first is the empty reference range.

$p[]

This will list out ALL elements of the set. For the example above, this will produce

“5, 4, 6, 1, 3, 2”

The second special reference range is an elided reference. For this example we will use

$q=range(1,100)

If you listed out this full set, the result would be too long for one line. Instead you can use this notation.

$q[…]

which will automatically produce an elided list.

1, 2, 3, 4, 5, 6, 7, 8 … 96, 97, 98, 99, 100

You can also add your own separator

$q[…,+]

1+2+3+4+5+6+7+8+ … +96+97+98+99+100

Ideal for sequences and series questions!

We have been working frenetically on Efofex parameters and the inline calculator over the last few months and have created a number of new, powerful parameters and commands. This article discusses the new parameter types.

Shuffle Parameters

A shuttle parameter allows you to quickly create a shuffled list. For example,

$p=shuffle(1,6)

will automatically create a shuffled list of the numbers from 1 to 6. This means that $p might be

3, 4, 1, 6, 5, 2 or 4, 5, 1, 2, 6, 3 or any other arrangement.

You will normally access shuffled lists using references.

$p[1] or $p[4] for example.

Coprimes Parameters

A coprimes parameter produces a randomly selected set of (up to 10) coprime numbers from the indicated range.

$p = coprimes(1,50)

This parameter might produce

34, 35, 11, 31… or 4, 21, 19, 43…

This allows you to quickly create new sets of coprime numbers (numbers which share no common factors)

Data Parameters

A data parameter is really just a list of values (a bit like a list parameter). The difference is that data parameters are designed to be worked on as a data set. For example, you can find the mean of a data parameter using a simple calculator command.

A simple data parameter looks just like a list parameter.

$p=data(1,4,6,8,2,4,7,2)

but you will not often write out your own set of data. A more useful way to get a data set is to use one of our random number parameters.

Random Number Parameters

Our random number parameters allow you to quickly create data parameters using random numbers. The two you will use most often are:

$p=randnormal(50,10,30,2)

Which will produce 30 normally distributed random numbers from a population with a mean of 50 and a standard deviation of 10 (rounded to 2 decimal places).

or

$p=randbetween(1,6,30)

Which will produce 30 uniformly distributed random numbers from 1 to 6 (equivalent to rolling a die 30 times)

There are a number of other distributions you can use. These are mentioned in our online help.