`<variance>`

Variance of the child math or number values

<variance> is a Math Operator component that renders the variance of a list of enclosed data values according to the equation:

$\mathbf{Var}(x) = \frac{\sum_{i=1}^n (x_{i} - \bar x)^2}{n-1}$

In this equation, $\bar x$ represents the <mean> of the sample and $n$ the number of data points. By default, the sample variance is calculated. If instead, the population attribute is specified as “true”, the equation becomes:

$\mathbf{Var}(x) = \frac{\sum_{i=1}^n (x_{i} - \bar x)^2}{n}$

Attributes and Properties

Attributes for `<variance>`

Highlighted (3)

displayDigits

integer. Default value: 3. Number of significant digits to display when rendering this number.

format

keyword. Input format.

Value	Description
`text` (default)	Plain-text math notation (e.g., `x^2 + 1`).
`latex`	LaTeX-formatted math (e.g., `x^{2} + 1`).

simplify

keyword. Level of simplification applied to the expression.

Value	Description
`none` (default)	No simplification is applied.
`full`	Fully simplify the expression.
`numbers`	Simplify numeric subexpressions only, leaving symbolic structure intact.
`numbersPreserveOrder`	Like `numbers`, but does not reorder commutative operands.
`normalizeOrder`	Reorder commutative operands into a canonical form without simplifying values.

Number display (5)

avoidScientificNotation

boolean. Default value: false. Whether to render numbers in full decimal form rather than scientific notation.

displayDecimals

integer. Default value: 2. Number of decimal places to display when rendering this number.

displayDigits

integer. Default value: 3. Number of significant digits to display when rendering this number.

displaySmallAsZero

number. Default value: 1e-14. Threshold below which numbers are displayed as zero.

padZeros

boolean. Default value: false. Whether to pad displayed numbers with trailing zeros to fill the requested digits/decimals.

Positioning (2)

anchor

point. Default value: $\left( 0, 0 \right)$. Coordinates of the anchor point used to position this component on a graph.

positionFromAnchor

keyword. Where this component sits relative to its anchor point.

Value	Description
`upperRight`	Place the component above and to the right of the anchor point.
`upperLeft`	Place the component above and to the left of the anchor point.
`lowerRight`	Place the component below and to the right of the anchor point.
`lowerLeft`	Place the component below and to the left of the anchor point.
`top`	Place the component directly above the anchor point.
`bottom`	Place the component directly below the anchor point.
`left`	Place the component directly to the left of the anchor point.
`right`	Place the component directly to the right of the anchor point.
`center` (default)	Center the component on the anchor point.

Other (16)

assumptions

math. Default value: $＿$. Assumptions applied when simplifying or comparing.

createIntervals

boolean. Default value: false. Whether range expressions are interpreted as intervals.

createVectors

boolean. Default value: false. Whether tuple-like expressions are interpreted as vectors.

displayBlanks

boolean. Default value: true. Whether blanks (placeholders) are visibly rendered.

draggable

boolean. Default value: true. Whether the math component can be dragged on a graph.

expand

boolean. Default value: false. Whether to expand the expression.

forceNumeric

boolean. Default value: false. Whether to force the operator to evaluate numerically rather than symbolically.

forceSymbolic

boolean. Default value: false. Whether to force the operator to evaluate symbolically rather than numerically.

functionSymbols

textList. Default value: ["f","g"]. Symbols treated as function names when parsing.

layer

number. Default value: 0. Z-order layer index when shown on a graph.

parseScientificNotation

boolean. Default value: false. Whether to parse expressions like 1e3 as scientific notation.

population

boolean. Default value: false. Whether to use the population formula (rather than sample).

referencesAreFunctionSymbols

reference. References whose names should be treated as function symbols when parsing.

renderMode

text. Default value: inline. How the math is rendered (e.g. "inline", "display").

splitSymbols

boolean. Default value: true. Whether multi-character symbols are split into a product of variables.

unordered

boolean. Default value: false. Whether tuple- or list-like math expressions should be treated as unordered for comparison.

Common to all components (9)

copy

reference. Create an independent copy of another component by reference. Enter a references a $name.

disabled

boolean. Default value: false. Whether this component is disabled and cannot be interacted with.

extend

reference. Extend another component by reference, inheriting its children and attributes. Enter a reference as $name.

fixed

boolean. Default value: false. Whether this component's value is fixed and cannot be modified.

fixLocation

boolean. Default value: false. Whether this component's location is fixed (preventing it from being moved while still allowing other modifications).

hide

boolean. Default value: false. Whether to hide this component from the rendered output.

isResponse

boolean. Default value: false. Whether this component is treated as a response for the purposes of assessment.

name

text. The name used to reference this component from elsewhere in the document.

styleNumber

integer. Default value: 1. The style number used to select this component's visual styling from the available style definitions.

Properties for `<variance name="v">`

Highlighted (3)

$v.displayDigits

integer. Number of significant digits to display when rendering this number.

$v.format

text. Input format.

$v.simplify

text. Level of simplification applied to the expression.

Number display (5)

$v.avoidScientificNotation

boolean. Whether to render numbers in full decimal form rather than scientific notation.

$v.displayDecimals

integer. Number of decimal places to display when rendering this number.

$v.displayDigits

integer. Number of significant digits to display when rendering this number.

$v.displaySmallAsZero

number. Threshold below which numbers are displayed as zero.

$v.padZeros

boolean. Whether to pad displayed numbers with trailing zeros to fill the requested digits/decimals.

Positioning (2)

$v.anchor

point. The coordinates where this component is anchored on the graph.

$v.positionFromAnchor

text. Where this component sits relative to its anchor point.

Other (41)

$v.assumptions

math. Assumptions applied when simplifying or comparing.

$v.backgroundColor

text. Human-readable name for this component's background color, derived from the active style and theme.

$v.columns

[ math ]. The matrix's entries grouped by column.

$v.createIntervals

boolean. Whether range expressions are interpreted as intervals.

$v.createVectors

boolean. Whether tuple-like expressions are interpreted as vectors.

$v.disabled

boolean. Whether this component is disabled and cannot be interacted with.

$v.displayBlanks

boolean. Whether blanks (placeholders) are visibly rendered.

$v.draggable

boolean. Whether the math component can be dragged on a graph.

$v.expand

boolean. Whether to expand the expression.

$v.fixed

boolean. Whether this component's value is fixed and cannot be modified.

$v.fixLocation

boolean. Whether this component's location is fixed (preventing it from being moved while still allowing other modifications).

$v.forceNumeric

boolean. Whether to force the operator to evaluate numerically rather than symbolically.

$v.forceSymbolic

boolean. Whether to force the operator to evaluate symbolically rather than numerically.

$v.functionSymbols

textList. Symbols treated as function names when parsing.

$v.hidden

boolean. Whether this component is hidden from the rendered output.

$v.isNumber

boolean. Whether the expression evaluates to a finite number.

$v.isNumeric

boolean. Whether the expression evaluates to any number (including infinities).

$v.latex

latex. The expression rendered as a LaTeX string.

$v.layer

number. Z-order layer index when shown on a graph.

$v.list

[ math ]. The math expression interpreted as a list (its elements).

$v.matrix

[ math ]. The math expression interpreted as a matrix (its entries by row and column).

$v.matrixSize

numberList. The size of the math expression as a matrix, as a [numRows, numColumns] list.

$v.number

number. The numeric value of the expression (NaN if not a number).

$v.numColumns

integer. The number of columns when the math expression is interpreted as a matrix.

$v.numDimensions

integer. The number of dimensions if the math expression is interpreted as a vector or matrix.

$v.numListItems

integer. The number of items when the math expression is interpreted as a list.

$v.numRows

integer. The number of rows when the math expression is interpreted as a matrix.

$v.parseScientificNotation

boolean. Whether to parse expressions like 1e3 as scientific notation.

$v.population

boolean. Whether to use the population formula (rather than sample).

$v.renderMode

text. How the math is rendered (e.g. "inline", "display").

$v.rows

[ math ]. The matrix's entries grouped by row.

$v.splitSymbols

boolean. Whether multi-character symbols are split into a product of variables.

$v.text

text. The expression rendered as a plain text string.

$v.textColor

text. Human-readable name for this component's text color, derived from the active style and theme.

$v.textStyleDescription

text. Human-readable description of this component's text styling (color and any background color).

$v.unordered

boolean. Whether list-like values are treated as unordered.

$v.value

variance. The math expression value.

$v.vector

[ math ]. The math expression interpreted as a vector (its components).

$v.x

math. The first component of the math expression when interpreted as a vector.

$v.y

math. The second component of the math expression when interpreted as a vector.

$v.z

math. The third component of the math expression when interpreted as a vector.

Common to all components (4)

$v.doenetML

text. The DoenetML source code that produced this component.

$v.hide

boolean. Whether to hide this component from the rendered output.

$v.isResponse

boolean. Whether this component is treated as a response for the purposes of assessment.

$v.styleNumber

integer. The style number used to select this component's visual styling from the available style definitions.

Examples

Example: `<variance>` of a nested list of numbers

The <variance> component renders the variance of a list of numbers separated by spaces.

Example: `<variance>` of a named list

The <variance> component renders the variance of a named <numberList>.

Example: `<variance>` of a user-input list

Since there is no numberInput component, the <mathInput> is used to store a user’s numerical list. This must then be defined as a <numberList>. The named <numberList> is then referenced by the <variance> component to compute the numerical variance.

updateValue variantControl

<variance>

Attributes and Properties

Attributes for <variance>

Properties for <variance name="v">