#set document(title: "3.4 Chapter 3 Formulas", author: "Rachel Webb")
#set page(width: 8.5in, height: auto, margin: 1in)
#import "@preview/cetz:0.5.2"
#set text(font: ("STIX Two Text", "Libertinus Serif", "New Computer Modern"), size: 10.5pt, lang: "en")
#show math.equation: set text(font: ("STIX Two Math", "New Computer Modern Math"))
#set par(justify: true, leading: 0.62em, spacing: 0.9em)
#set enum(spacing: 1.1em)   // room between list items so tall inline fractions don't collide
#set list(spacing: 1.1em)
#set table(stroke: 0.5pt + rgb("#c7ccd3"))

#let BLUE = rgb("#183B6F")     // brand navy — section bars + example/solution labels (white on navy 11.09:1)
#let ORANGE = rgb("#A94509")   // brand primary-700 — AA-safe deep orange for TEXT (5.93:1 on white; raw brand #F37021 is 2.94:1 and must never carry text)
#let RED = rgb("#DC2626")      // brand error-600
#let GREEN = rgb("#059669")    // brand success-600 (decoration only; small green text uses green-text #007942)

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#show heading.where(level: 4): it => text(fill: BLUE, weight: "bold", size: 10.5pt, it.body)

#let examplebox(label, title, body) = block(width: 100%, breakable: true,
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  #body]

// rail = decorative left rule (raw brand token); labelcolor = AA-safe label text shade
#let notebox(label, rail, labelcolor, tint, body) = block(width: 100%, breakable: true, fill: tint,
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    #text(fill: labelcolor, weight: "bold", size: 7.5pt, tracking: 0.5pt)[#upper(label)]
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#let solutionbox(body) = block(above: 4pt, below: 8pt)[
  #text(fill: BLUE, weight: "bold", size: 8.5pt)[Solution] #linebreak() #body]

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// Standardize inlined figure sizes: measure the natural CeTZ canvas, then scale to a
// consistent envelope (aspect-aware; see build_typst.py FIG_* constants). Unlike the
// print preamble, dimensions are FLOORED: in an editor a user can trim a figure to a
// degenerate 1-D shape (a bare line), and w/h or tw/w would then divide by zero.
#let _STD_W = 3.5
#let _WIDE_W = 5.6
#let _MAX_H = 3.4
#let _ASPECT_WIDE = 2.2
#let _UPSCALE_MAX = 1.15
#let stdfig(body) = context {
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}

#show figure: set block(breakable: false)
#set figure(gap: 8pt)
#show figure.caption: set text(size: 8.5pt, fill: rgb("#555"))


    
== 3.4#h(0.6em)Chapter 3 Formulas


    #figure(table(
  columns: 2, align: left, inset: 6pt,
  table.header([#strong[Sample Mean:] #math.equation(block: false, alt: "x bar equals the fraction ∑ x over n")[$overline(x) = frac(∑ x, n)$]], [#strong[Population Mean:] #math.equation(block: false, alt: "μ equals the fraction ∑ x over N")[$μ = frac(∑ x, N)$]]),
  [#strong[Weighted Mean:] #math.equation(block: false, alt: "x bar equals the fraction Σ open parenthesis x w close parenthesis over ∑ w")[$overline(x) = frac(Σ ( x w ), ∑ w)$]], [#strong[Range] = Max – Min],
  [#strong[Sample Standard Deviation:] s = #math.equation(block: false, alt: "the square root of the fraction ∑ open parenthesis x minus x bar close parenthesis squared over n minus 1")[$sqrt(frac(∑ ( x − overline(x) )^(2), n − 1))$]], [#strong[Population Standard Deviation] = σ],
  [#strong[Sample Variance:] s#super[2] = #math.equation(block: false, alt: "the fraction Σ open parenthesis x minus x bar close parenthesis squared over n minus 1")[$frac(Σ ( x − overline(x) )^(2), n − 1)$]], [#strong[Population Variance] = σ#super[2]],
  [#strong[Coefficient of Variation:] CVar = #math.equation(block: false, alt: "open parenthesis the fraction s over x bar times 100 close parenthesis")[$( frac(s, overline(x)) · 100 )$]], [#strong[Z-Score:] z = #math.equation(block: false, alt: "the fraction x minus x bar over s")[$frac(x − overline(x), s)$]],
  [#strong[Percentile Index:] i = #math.equation(block: false, alt: "the fraction open parenthesis n plus 1 close parenthesis times p over 100")[$frac(( n + 1 ) · p, 100)$]], [#strong[Interquartile Range:] IQR = #emph[Q#sub[3]] – #emph[Q#sub[1]]],
  [#strong[Empirical Rule:] z = 1, 2, 3 #math.equation(block: false, alt: "⇒")[$⇒$] 68%, 95%, 99.7%], [#strong[Outlier Lower Limit:]#emph[Q#sub[1]] – (1.5·IQR)],
  [#strong[Chebyshev’s Inequality:] #math.equation(block: false, alt: "open parenthesis open parenthesis 1 minus the fraction 1 over open parenthesis z close parenthesis squared close parenthesis times 100 close parenthesis")[$( ( 1 − frac(1, ( z )^(2)) ) · 100 )$]], [#strong[Outlier Upper Limit:] #emph[Q#sub[3]] + (1.5·IQR)],
))