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
| 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 |
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French names for each function are on the Excel functions page.
Percentages and totals (Module 1–2)
| \(p_i\) |
Percentage distribution |
Share of a total that item \(i\) represents, \(x_i/T\times100\%\) |
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Module 1 |
| \(\Delta\%\) |
Percentage change |
Relative change between an old and a new value |
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Module 1 |
| \(T\) |
Grand total |
Sum of all values in a range or all group totals |
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Module 1 |
Univariate position (Modules 2–5)
| \(n\) |
Sample size |
Number of observations/individuals |
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Module 2 |
| \(k\) |
Number of modalities |
Number of distinct categories/classes of a variable |
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Module 2 |
| \(n_i\) |
Absolute frequency |
Count of observations in modality/class \(i\) |
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Module 2 |
| \(f_i\) |
Relative frequency |
Share of observations in modality/class \(i\), \(n_i/n\) |
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Module 2 |
| \(h\) |
Class width |
Width of a class interval in a grouped frequency table |
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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 |
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Module 3 |
| \(k\) (classes) |
Number of classes |
Number of intervals in a grouped table; Sturges’ rule suggests \(k \approx 1 + 3.3\log_{10}n\) |
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Module 3 |
| \(m_i\) |
Class midpoint |
Centre of class \(i\), \((L_i + L_i + h)/2\); where the frequency polygon plots the class |
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Module 3 |
| \(n_i/h_i\) |
Density |
Count divided by class width; the bar height of a histogram when class widths are unequal |
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Module 3 |
| \(N_i^{+}\) |
Increasing cumulative frequency (count) |
Running total of counts up to and including class \(i\) |
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Module 3 |
| \(F_i^{+}\) |
Increasing cumulative frequency (share) |
Running total of relative frequencies up to class \(i\), \(N_i^{+}/n\) |
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Module 3 |
| Ogive |
Cumulative frequency curve |
Line joining (class upper bound, \(F_i^{+}\)); read it to find shares and percentiles |
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Module 3 |
| \(Me\) |
Median |
The value splitting an ordered series into two equal halves |
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Module 5 |
| \(Q_1, Q_2, Q_3\) |
Quartiles |
Values splitting an ordered series into four equal quarters (\(Q_2=Me\)) |
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Module 5 |
| \(P_p\) |
Percentile |
Value such that approximately \(p\%\) of observations are \(\leq\) it |
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Module 5 |
| \(IQR\) |
Interquartile range |
\(Q_3-Q_1\); spread of the central 50% of the data |
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Module 5 |
| \((n+1)p\) |
Quantile position |
Rank of the \(p\)-th quantile in the ordered data, interpolated between neighbours (QUARTILE.EXC) |
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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 |
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Module 5 |
Univariate center, dispersion, and shape (Modules 4–7)
| \(\bar{x}\) |
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 |
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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) |
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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 |
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Module 4 |
| \(x_i\) |
\(i\)-th observation |
The value of observation number \(i\) (e.g. day \(i\)’s revenue) |
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Module 4 |
| \(\sum_{i=1}^{n}\) |
Summation |
Add up the expression that follows, for \(i=1, 2, \dots, n\) |
“capital sigma” |
Module 4 |
| \(x_i-\bar{x}\) |
Deviation from the mean |
How far, and in which direction, observation \(i\) is from the mean; deviations always sum to 0 |
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Module 6 |
| \(s^2\) |
Sample variance |
Average squared distance of observations from the mean, \(\frac{1}{n-1}\sum(x_i-\bar{x})^2\) |
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Module 6 |
| \(s\) |
Sample standard deviation |
\(\sqrt{s^2}\); dispersion in the original unit |
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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, \(s/\bar{x}\times100\%\) |
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Module 6 |
| \(\frac{x_i-\bar{x}}{s}\) |
Standardized deviation |
Deviation of observation \(i\) from the mean, measured in standard deviations; it has no unit |
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Module 7 |
| \(\frac{n}{(n-1)(n-2)}\) |
Small-sample correction factor |
Factor in front of the sum in SKEW; close to \(\frac{1}{n}\) for large \(n\), it matters only for small samples |
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Module 7 |
| \(SKEW\) / \(g_1\) |
Fisher-Pearson sample skewness |
Bias-corrected, unit-free measure of asymmetry around the mean (Excel’s SKEW) |
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Module 7 |
| Pearson asymmetry coefficient |
Pearson skewness coefficient |
\((\bar{x}-Mo)/s\); compares the mean to the mode |
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Module 7 |
| \(3(\bar{x}-Me)/s\) |
Pearson median skewness |
Compares the mean to the median; usable when there is no clear mode |
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Module 7 |
| \(YK\) |
Yule-Kendall skewness coefficient |
\((Q_3+Q_1-2Me)/(Q_3-Q_1)\); asymmetry from the five-number summary |
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Module 7 |
Bivariate (Modules 8–9)
| \(n_{ij}\) |
Contingency table cell count |
Count of individuals with modality \(i\) of one variable and modality \(j\) of the other |
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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 |
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Module 8 |
| \(n_{i\cdot}/n\), \(n_{\cdot j}/n\) |
Marginal distribution |
Share of all \(n\) individuals in each modality of one variable, read from the margins of a contingency table (the \(f_i\) of Module 2) |
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Module 8 |
| \(n_{ij}/n_{i\cdot}\), \(n_{ij}/n_{\cdot j}\) |
Conditional distribution |
Share of a cell within its own row (row percentages, “given row \(i\)”) or column (column percentages, “given column \(j\)”); compares groups of different sizes fairly |
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Module 8 |
| \(X\), \(Y\) |
Pair of variables |
Two quantitative variables measured on the same individuals (e.g. temperature and items sold on the same day) |
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Module 9 |
| \(y_i\), \(\bar{y}\) |
\(i\)-th value and mean of \(Y\) |
Same as \(x_i\) and \(\bar{x}\), for the second variable |
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Module 9 |
| \((x_i-\bar{x})(y_i-\bar{y})\) |
Deviation product |
Positive when observation \(i\) is on the same side of both means, negative otherwise; its sum drives the covariance |
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Module 9 |
| \(s_X\), \(s_Y\) |
Standard deviations of \(X\) and \(Y\) |
The sample standard deviation \(s\) (Module 6) of each variable; \(r\) divides the covariance by \(s_X s_Y\) |
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Module 9 |
| \(\text{Cov}(X,Y)\) |
Sample covariance |
Average product of deviations from each variable’s mean, \(\frac{1}{n-1}\sum(x_i-\bar{x})(y_i-\bar{y})\) |
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Module 9 |
| \(r\) |
Correlation coefficient |
Unit-free strength/direction of the linear relationship between \(X\) and \(Y\), \(-1\le r\le1\) |
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Module 9 |
| \(r^2\) |
Coefficient of determination |
Share of \(Y\)’s variability explained by a linear link with \(X\) |
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Module 9 |
| \(a, b\) |
Regression intercept and slope |
Coefficients of the least-squares line \(\hat{y}=a+bx\) |
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Module 9 |
| \(\hat{y}\) |
Predicted / fitted value |
The value of \(y\) predicted by the regression line for a given \(x\) |
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Module 9 |
| \(y_i-\hat{y}_i\) |
Residual (gap to the line) |
Vertical distance between observation \(i\) and the regression line; least squares minimises the sum of their squares |
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Module 9 |
Synthesis (Module 10)
| \(n_j\) |
Group size |
Number of observations in group \(j\) (e.g. one franchise or outlet) |
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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 \(n_j/n\) |
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Module 10 |
Synthesis and review (Module 10)
| \(\bar{x}_w\) |
Weighted mean |
Mean of group means weighted by group sizes, \(\sum w_j \bar{x}_j\) with \(w_j = n_j/n\) |
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Module 10 |
| Mock exam |
Original assessment |
Newly authored MCQ + computational questions mapping to M1–M9 |
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Module 10 |