Glossary

Data Description

Every mathematical symbol and named formula introduced across Modules 1–10 is listed below, with its notation, a plain-language definition, a pronunciation guide (for Greek letters only), and the module where it is first introduced.

Conventions used throughout

Question	Convention	Excel
Quartiles and percentiles	Position \((n+1)\times p\) with interpolation	QUARTILE.EXC, PERCENTILE.EXC
Variance and standard deviation	Sample formulas (\(n-1\)) by default	VAR.S, STDEV.S
Skewness	Adjusted Fisher–Pearson coefficient	SKEW
Kurtosis	Conceptual only: no formula in this course	—

French names for each function are on the Excel functions page.

Percentages and totals (Module 1–2)

Notation	Name	Plain-language definition	Pronunciation (Greek only)	Introduced in
\(p_i\)	Percentage distribution	Share of a total that item \(i\) represents, \(x_i/T\times100\%\)	—	Module 1
\(\Delta\%\)	Percentage change	Relative change between an old and a new value	—	Module 1
\(T\)	Grand total	Sum of all values in a range or all group totals	—	Module 1

Univariate position (Modules 2–5)

Notation	Name	Plain-language definition	Pronunciation (Greek only)	Introduced in
\(n\)	Sample size	Number of observations/individuals	—	Module 2
\(k\)	Number of modalities	Number of distinct categories/classes of a variable	—	Module 2
\(n_i\)	Absolute frequency	Count of observations in modality/class \(i\)	—	Module 2
\(f_i\)	Relative frequency	Share of observations in modality/class \(i\), \(n_i/n\)	—	Module 2
\(h\)	Class width	Width of a class interval in a grouped frequency table	—	Module 3
\([L_i, L_i+h[\)	Half-open class	Class that includes its lower bound \(L_i\) but not its upper bound, so each value belongs to exactly one class	—	Module 3
\(k\) (classes)	Number of classes	Number of intervals in a grouped table; Sturges’ rule suggests \(k \approx 1 + 3.3\log_{10}n\)	—	Module 3
\(m_i\)	Class midpoint	Centre of class \(i\), \((L_i + L_i + h)/2\); where the frequency polygon plots the class	—	Module 3
\(n_i/h_i\)	Density	Count divided by class width; the bar height of a histogram when class widths are unequal	—	Module 3
\(N_i^{+}\)	Increasing cumulative frequency (count)	Running total of counts up to and including class \(i\)	—	Module 3
\(F_i^{+}\)	Increasing cumulative frequency (share)	Running total of relative frequencies up to class \(i\), \(N_i^{+}/n\)	—	Module 3
Ogive	Cumulative frequency curve	Line joining (class upper bound, \(F_i^{+}\)); read it to find shares and percentiles	—	Module 3
\(Me\)	Median	The value splitting an ordered series into two equal halves	—	Module 5
\(Q_1, Q_2, Q_3\)	Quartiles	Values splitting an ordered series into four equal quarters (\(Q_2=Me\))	—	Module 5
\(P_p\)	Percentile	Value such that approximately \(p\%\) of observations are \(\leq\) it	—	Module 5
\(IQR\)	Interquartile range	\(Q_3-Q_1\); spread of the central 50% of the data	—	Module 5
\((n+1)p\)	Quantile position	Rank of the \(p\)-th quantile in the ordered data, interpolated between neighbours (QUARTILE.EXC)	—	Module 5
\(Q_1-1.5\,IQR\), \(Q_3+1.5\,IQR\)	Outlier fences	Values beyond these limits are flagged as outliers on a boxplot	—	Module 5

Univariate center, dispersion, and shape (Modules 4–7)

Notation	Name	Plain-language definition	Pronunciation (Greek only)	Introduced in
\(\bar{x}\)	Sample mean	Arithmetic average of all observations, \(\frac{1}{n}\sum x_i\)	“x-bar”	Module 4
\(Mo\)	Mode	Most frequent value, or the center of the most frequent class for grouped data	—	Module 4
\(\bar{x}_w\)	Weighted mean	\(\sum w_i x_i / \sum w_i\); mean where each value counts according to its weight	“x-bar w”	Module 4
\(w_i\)	Weight	Importance given to value \(x_i\) in a weighted mean (e.g. amount invested, credits)	—	Module 4
\(L, f_0, f_1, f_2\)	Grouped-mode inputs	Modal class lower bound, and the frequencies of the preceding/modal/following classes	—	Module 4
\(s^2\)	Sample variance	Average squared distance of observations from the mean, \(\frac{1}{n-1}\sum(x_i-\bar{x})^2\)	—	Module 6
\(s\)	Sample standard deviation	\(\sqrt{s^2}\); dispersion in the original unit	—	Module 6
\(\sigma^2\), \(\sigma\)	Population variance and standard deviation	Same as \(s^2\), \(s\) but dividing by \(n\); used only when the data are the whole population (VAR.P, STDEV.P)	“sigma”	Module 6
\(CV\)	Coefficient of variation	Unit-free relative dispersion, \(s/\bar{x}\times100\%\)	—	Module 6
\(SKEW\) / \(g_1\)	Fisher-Pearson sample skewness	Bias-corrected, unit-free measure of asymmetry around the mean (Excel’s SKEW)	—	Module 7
Pearson asymmetry coefficient	Pearson skewness coefficient	\((\bar{x}-Mo)/s\); compares the mean to the mode	—	Module 7
\(3(\bar{x}-Me)/s\)	Pearson median skewness	Compares the mean to the median; usable when there is no clear mode	—	Module 7
\(YK\)	Yule-Kendall skewness coefficient	\((Q_3+Q_1-2Me)/(Q_3-Q_1)\); asymmetry from the five-number summary	—	Module 7

Bivariate (Modules 8–9)

Notation	Name	Plain-language definition	Pronunciation (Greek only)	Introduced in
\(n_{ij}\)	Contingency table cell count	Count of individuals with modality \(i\) of one variable and modality \(j\) of the other	—	Module 8
\(n_{i\cdot}\), \(n_{\cdot j}\)	Row / column margin	Row or column total of a contingency table; recovers each variable’s own frequency table	—	Module 8
\(\text{Cov}(X,Y)\)	Sample covariance	Average product of deviations from each variable’s mean, \(\frac{1}{n-1}\sum(x_i-\bar{x})(y_i-\bar{y})\)	—	Module 9
\(r\)	Correlation coefficient	Unit-free strength/direction of the linear relationship between \(X\) and \(Y\), \(-1\le r\le1\)	—	Module 9
\(r^2\)	Coefficient of determination	Share of \(Y\)’s variability explained by a linear link with \(X\)	—	Module 9
\(a, b\)	Regression intercept and slope	Coefficients of the least-squares line \(\hat{y}=a+bx\)	—	Module 9
\(\hat{y}\)	Predicted / fitted value	The value of \(y\) predicted by the regression line for a given \(x\)	—	Module 9

Synthesis (Module 10)

Notation	Name	Plain-language definition	Pronunciation (Greek only)	Introduced in
\(n_j\)	Group size	Number of observations in group \(j\) (e.g. one franchise or outlet)	—	Module 10
\(\bar{x}_j\)	Group mean	Mean of the observations in group \(j\)	“x-bar j”	Module 10
\(\bar{x}=\sum_j \frac{n_j}{n}\bar{x}_j\)	Overall mean from group means	The overall mean is the weighted mean of the group means, with weights \(n_j/n\)	—	Module 10

Synthesis and review (Module 10)

Notation	Name	Plain-language definition	Pronunciation (Greek only)	Introduced in
\(\bar{x}_w\)	Weighted mean	Mean of group means weighted by group sizes, \(\sum w_j \bar{x}_j\) with \(w_j = n_j/n\)	—	Module 10
Mock exam	Original assessment	Newly authored MCQ + computational questions mapping to M1–M9	—	Module 10