The business question. You have learned the full descriptive statistics toolkit: organising data (Modules 1–3), summarising one variable (Modules 4–7), and analysing two variables (Modules 8–9). This module puts it all together with a start-to-finish walkthrough on a fresh dataset, a common-pitfalls checklist, and an original mock exam mapped back to every module so you can pinpoint exactly what to revise.
1 Theory
1.1 Complete walkthrough — Lakeside Bakery
The lakeside-bakery.csv dataset contains two outlets (Riverside, Hilltop) × 60 days = 120 rows. Variables: outlet, day, date, day_of_week, month, weather, temperature_c, foot_traffic, customer_count, items_sold, daily_revenue_eur, waste_kg, satisfaction_rating.
Step 1 — variable typing. outlet, weather, day_of_week, month (ordinal), satisfaction_rating (ordinal) are qualitative. temperature_c, daily_revenue_eur, waste_kg are quantitative continuous. day, foot_traffic, customer_count, items_sold are quantitative discrete.
Step 2 — frequency tables and charts. Build frequency tables for weather (nominal) and satisfaction_rating (ordinal) per outlet. Use bar charts (nominal) and ordered bar charts (ordinal). Identify the modal category for each.
Step 3 — five-number summary and boxplot. For daily_revenue_eur per outlet: compute min, Q1, median, Q3, max, IQR, fences. Draw side-by-side boxplots. Check for outliers.
Step 4 — centre, spread, shape. Compute mean, median, grouped mode, variance, standard deviation, CV, skewness for daily_revenue_eur per outlet. Compare outlets.
Step 5 — contingency table. Cross weather with daily_revenue_eur class (€50 bins) per outlet. Compute conditional distributions (revenue class given weather). Look for visible dependence.
Step 6 — scatter plot, correlation, regression. Plot temperature_c vs daily_revenue_eur per outlet. Compute covariance, correlation \(r\), \(r^2\), regression line. Interpret.
1.2 Common pitfalls checklist
- Unequal-width histogram heights — use density \(n_i/h_i\), not raw counts, when class widths differ (Module 3).
- \(n\) vs \(n-1\) — use sample formulas (
.S) by default; population formulas (.P) only when you have the entire population (Module 6). - Correlation vs causation — \(r\) measures linear association, not cause and effect (Module 9).
- \(r\) vs \(r^2\) — \(r\) is correlation (direction + strength); \(r^2\) is explained share (always 0 to 1) (Module 9).
QUARTILE.INCvsQUARTILE.EXC— the course uses exclusive (position \((n+1)p\)); do not mix them (Module 5).- Ordinal treated as ratio —
satisfaction_rating1–5 has no equal intervals; median, not mean (Module 1). - Extrapolation — regression predictions outside the observed \(X\) range are unjustified (Module 9).
- Raw counts vs conditional % — compare rows with different totals using conditional distributions (Module 8).
- Grouped mean/mode as exact — they are approximations; prefer raw data when available (Modules 3–4).
- Mean/median/mode ordering heuristic — for near-symmetric data, the gaps are tiny; trust the Fisher-Pearson skewness using all raw data (Module 7).
- Fence rule vs standard deviations — 1.5×IQR is for boxplots; 2σ is for normal distributions — different tools (Module 5).
- Intercept as real prediction — if \(X=0\) is not meaningful, the intercept is just a mathematical anchor (Module 9).
- Excel locale — French Excel uses
;and localised function names; use the Excel functions page to translate (Module 1). - Line chart vs scatter plot — line charts imply sequence; scatter plots show relationship between two variables (Module 8).
1.3 Notation recap
This block comes after the mock exam debrief (see the time plan). Read each formula aloud with the class, then follow the link to the module that introduced it: its notation decoder, where the module has one, names every symbol.
| Indicator | Formula | Read aloud | Module |
|---|---|---|---|
| Mean | \(\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i\) | “add up all \(n\) values and divide by \(n\)” | Module 4 |
| Interquartile range | \(IQR = Q_3 - Q_1\) | “the third quartile minus the first quartile” | Module 5 |
| Sample variance | \(s^2 = \frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})^2\) | “add up each value’s squared distance from the mean, divide by \(n-1\)” | Module 6 |
| Standard deviation | \(s = \sqrt{s^2}\) | “s is the square root of the variance, back in the original unit” | Module 6 |
| Coefficient of variation | \(CV = \frac{s}{\bar{x}} \times 100\%\) | “the standard deviation as a percentage of the mean” | Module 6 |
Skewness (SKEW) |
\(\frac{n}{(n-1)(n-2)}\sum_{i=1}^{n}\left(\frac{x_i-\bar{x}}{s}\right)^3\) | “cube each standardised deviation, add them up, apply the small-sample factor” | Module 7 |
| Covariance | \(\text{Cov}(X,Y) = \frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y})\) | “multiply the two deviations for each individual, add up, divide by \(n-1\)” | Module 9 |
| Correlation | \(r = \frac{\text{Cov}(X,Y)}{s_X\, s_Y}\) | “the covariance divided by the product of the two standard deviations” | Module 9 |
| Regression slope | \(b = \frac{\text{Cov}(X,Y)}{s_X^2}\), \(a = \bar{y} - b\,\bar{x}\) | “the covariance divided by the variance of X; the line passes through the point of means” | Module 9 |
2 Worked example — Lakeside Bakery (summary)
| Statistic | Riverside | Hilltop |
|---|---|---|
| \(n\) | 60 | 60 |
| Mean revenue (€) | 205.69 | 216.91 |
| Median revenue (€) | 184.94 | 195.16 |
\(Q_1\) / \(Q_3\) (€, QUARTILE.EXC) |
156.66 / 261.25 | 151.62 / 265.92 |
| Std. dev. (€) | 83.48 | 81.96 |
| CV | 40.6% | 37.8% |
Skewness (SKEW) |
+0.93 | +0.60 |
| Outliers (1.5×IQR) | 2 high | none |
| \(r\)(temp, revenue) | −0.087 | 0.125 |
| Regression slope (€ per °C) | −1.78 | 2.38 |
Both outlets are right-skewed (mean above median) with high relative variability (CV near 40%). Hilltop has a slightly higher average and slightly lower CV; Riverside is more skewed and has two unusually high days. Temperature tells us almost nothing about revenue at either outlet (\(|r| < 0.13\)): look at weather categories instead (Module 8).
3 Proof / derivation
Let a dataset be partitioned into \(k\) groups (e.g., franchises). Group \(j\) has \(n_j\) observations with mean \(\bar{x}_j\). The overall mean is \[ \bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i = \frac{1}{n}\sum_{j=1}^{k} \sum_{i \in \text{group } j} x_i = \frac{1}{n}\sum_{j=1}^{k} n_j \bar{x}_j = \sum_{j=1}^{k} \frac{n_j}{n} \bar{x}_j. \]
This is exactly a weighted mean of the group means, with weights \(w_j = n_j/n\) (the group’s share of total observations). For “The Wandering Fork”, the overall 240-day mean revenue is the weighted mean of the Harbour 120-day mean and the Campus 120-day mean, with equal weights (120/240 = 0.5 each): \(0.5 \times 413.49 + 0.5 \times 455.03 = 434.26\) €, which is exactly what =AVERAGE(tblFork[daily_revenue_eur]) returns.
4 Visual intuition
The full walkthrough on Lakeside Bakery data is the visual consolidation of the entire course: the frequency tables and bar charts (Module 2) show the qualitative shape; the boxplots (Module 5) show the five-number summary and outliers at a glance; the histogram (Module 3) shows the revenue distribution shape; the scatter plots (Module 8) show the temperature–revenue relationship; and the regression lines (Module 9) quantify that relationship. Together, these pictures tell the complete story that the numbers alone cannot.
5 Interactive demo
TODO: an interactive full-workflow dashboard (upload CSV, auto-generate all tables/charts) would be a capstone OJS demo.
6 Exercises
The exercises for this module are the mock exam below. Two short by-hand review exercises (4–5) follow it, for the notation recap block.
6.1 Mock exam — Modules 1–9
This is an originally-authored mock exam on “The Wandering Fork” and Lakeside Bakery data, mirroring the format and difficulty of the Midterm Exam (35%, 45 min) and Final Exam (65%, 90 min) described in the syllabus: a multiple-choice section followed by computational exercises. It does not reproduce any verbatim question or answer key from the source exam files.
Part A — Multiple choice (1 point each)
“The Wandering Fork”’s satisfaction_rating (1–5) is: (a) Quantitative discrete (b) Qualitative ordinal (c) Qualitative nominal (d) Quantitative continuous Answer: (b). The categories have a natural order (1 < 2 < 3 < 4 < 5) but the distances between them are not necessarily equal.
Revise: Module 1.
In any relative frequency table for a qualitative variable, the percentages sum to: (a) 100% exactly (b) Approximately 100% (rounding may cause 99.9% or 100.1%) (c) The sample size \(n\) (d) 1 Answer: (b). Rounding often makes the sum 99.9% or 100.1%; the exact algebraic sum is 1 (or 100%), but printed percentages are rounded.
Revise: Module 2.
When class widths are unequal, the bar height in a histogram must represent: (a) Absolute frequency \(n_i\) (b) Relative frequency \(f_i\) (c) Density \(n_i/h_i\) (d) Cumulative frequency \(N_i^{+}\) Answer: (c). Area = height × width must equal frequency; with unequal widths, height = density = \(n_i/h_i\).
Revise: Module 3.
“The Wandering Fork” Harbour 30-day revenue has fences at 171.52 and 1065.07. The observed minimum is 407.59 and maximum is 886.56. How many outliers? (a) 0 (b) 1 (c) 2 (d) Cannot be determined Answer: (a). Both extremes lie inside the fences.
Revise: Module 5.
For a right-skewed distribution, the typical ordering is: (a) \(\bar{x} < Me < Mo\) (b) \(\bar{x} = Me = Mo\) (c) \(\bar{x} > Me > Mo\) (d) No consistent ordering Answer: (c). The long right tail pulls the mean above the median above the mode.
Revise: Module 4.
\(CV = 21.82\%\) for Harbour 30-day daily revenue. This means: (a) The standard deviation is 21.82% of the mean (b) 21.82% of days are within one standard deviation (c) The variance is 21.82% of the mean (d) The data is 21.82% skewed Answer: (a). \(CV = s/\bar{x} \times 100\%\).
Revise: Module 6.
Three skewness formulas give different signs for the same near-symmetric data. Which one uses all raw observations and is the course standard? (a) Pearson skewness coefficient (b) Yule-Kendall skewness coefficient (c) Fisher-Pearson sample skewness (Excel’s SKEW) (d) They are all equally authoritative Answer: (c). The Fisher-Pearson coefficient uses every raw observation; the others use grouped estimates or only the five-number summary.
Revise: Module 7.
To compare revenue distributions for Sunny vs Rainy days fairly, you should use: (a) Raw counts from the contingency table (b) Column percentages (c) Row percentages (conditional distribution of revenue given weather) (d) The grand total Answer: (c). Row percentages rescale each weather type to its own total, enabling fair comparison.
Revise: Module 8.
\(r = 0.621\) for temperature vs revenue (Harbour, 30 days). This means: (a) Temperature causes revenue to increase (b) 62.1% of revenue variability is explained by temperature (c) There is a moderate positive linear relationship (d) The regression slope is 0.621 Answer: (c). \(r\) measures linear association strength and direction; \(r^2 = 0.386\) is the explained share.
Revise: Module 9.
For Harbour’s first 30 days the regression line is \(\widehat{\text{revenue}} = -22.01 + 28.71 \times \text{temperature\_c}\). Predicting revenue at \(40\) °C is:
- Reliable — the line is the best fit
- Unreliable — extrapolation beyond the data range (16.4–27.1 °C)
- Exact — the line passes through all points
- Impossible — the intercept is negative Answer: (b). Extrapolation beyond observed \(X\) values is unjustified.
Revise: Module 9.
Part B — Computational exercises (6 points each)
Using the Harbour 120 days of wandering-fork.xlsx, compute the complete descriptive summary for daily_revenue_eur: (a) Class table with classes of width €100 starting at €0. (b) Five-number summary, IQR, fences, outliers. (c) Mean, median, grouped mode. (d) Sample variance, standard deviation, CV. (e) Fisher-Pearson skewness. (f) Comment on symmetry and variability using the course conventions. Solution. (a) Classes: \([0,100[\) (9), \([100,200[\) (11), \([200,300[\) (17), \([300,400[\) (24), \([400,500[\) (21), \([500,600[\) (10), \([600,700[\) (16), \([700,800[\) (7), \([800,900[\) (3), \([900,1000[\) (0), \([1000,1100[\) (2); total 120. Modal class \([300,400[\). (b) Min=51.21, Q1=267.89, Me=391.47, Q3=567.32, Max=1050.00, IQR=299.43, fences=-181.25/1016.45, 1 high outlier (1050.00 > 1016.45). (c) Mean=413.49, Me=391.47, grouped Mo ≈ 300 + 100×(24−17)/((24−17)+(24−21)) = 300 + 100×7/10 = 370. (d) \(s^2\)=46,661.10, \(s\)=216.01, CV=52.24%. (e) Skewness = 0.47 (mild right skew). (f) Mild right skew (skewness 0.47), high relative variability (CV 52.2% > 35%), one high outlier. Mean > median (413 > 391) consistent with right skew.
Revise: Module 3 (a), Module 5 (b), Module 4 (c), Module 6 (d), Module 7 (e–f).
Using the Campus 120 days of wandering-fork.xlsx: (a) Build a contingency table: weather (Rows) × daily_revenue_eur class (Columns, €100 bins). Show conditional distributions (% of row total). (b) Create a scatter plot of customer_count vs daily_revenue_eur. (c) Compute covariance, correlation \(r\), \(r^2\), regression line. (d) Predict revenue for a 30-customer day. Is this prediction reliable? (e) Verify the regression line passes through \((\bar{x},\bar{y})\). Solution. (a) Rows: Cloudy 48, Rainy 22, Sunny 50. 27.3% of Rainy days fall below €100 against 4.2% (Cloudy) and 4.0% (Sunny); all six days of €1,100 or more are Sunny. The row profiles differ: visible dependence. (b) Strong, upward, linear cloud with few outliers. (c) Cov=7,223.49, \(r\)=0.970, \(r^2\)=0.940, slope=12.30 € per customer, intercept=−22.75. (d) \(-22.75 + 12.30\times30 = 346.25\) €. Reliable: 30 customers lies inside the observed range (3–106), and \(r^2 = 0.94\). (e) \(\bar{x}\)=38.84, \(\bar{y}\)=455.03: \(-22.75 + 12.30\times38.84 = 454.98 \approx \bar{y}\) (the small gap is rounding of the coefficients). ✓
Revise: Module 8 (a–b), Module 9 (c–e).
Open lakeside-bakery.csv. For the Riverside outlet (60 days): (a) Classify all 13 variables by type and level of measurement. (b) Build frequency tables and charts for weather and satisfaction_rating. (c) Compute the five-number summary, boxplot, and outliers for daily_revenue_eur. (d) Compute mean, median, mode, variance, std, CV, skewness for daily_revenue_eur. (e) Build a contingency table: weather × daily_revenue_eur class (€50 bins). Compute conditional distributions. (f) Scatter plot, correlation, regression for temperature_c vs daily_revenue_eur. (g) Summarise the key differences between Riverside and Hilltop in three sentences. Solution. (a) Qualitative nominal: outlet, weather, day_of_week. Qualitative ordinal: month, satisfaction_rating. Quantitative discrete: day, foot_traffic, customer_count, items_sold. Quantitative continuous: temperature_c, daily_revenue_eur, waste_kg. (b) Weather: Sunny/Cloudy/Rainy frequencies; satisfaction: 1–5 frequencies. Bar charts for both. (c) Min=66.93, Q1=156.66, Me=184.94, Q3=261.25, Max=472.24, IQR=104.58, fences=−0.21/418.12, 2 high outliers (431.34, 472.24). (d) Mean=205.69, Me=184.94, modal class [150,200[ (22 days), grouped Mo ≈ 150 + 50×13/(13+14) ≈ 174.07, \(s\)=83.48, CV=40.6%, skew=+0.93 (clear right skew; Mo < Me < mean). (e) 63.6% of Rainy days earn below €150, against 20.0% of Cloudy and 6.9% of Sunny days: revenue clearly depends on weather. (f) \(r\)=−0.087, \(r^2\)=0.008, slope=−1.78, intercept=243.51: no linear link between temperature and revenue. (g) Hilltop earns slightly more on average (216.91 vs 205.69) with slightly lower relative spread (CV 37.8% vs 40.6%). Riverside is more right-skewed and has two outlier days; Hilltop has none. At both outlets weather matters, temperature does not.
Revise: Module 1 (a), Module 2 (b), Module 5 (c), Modules 4, 6 and 7 (d), Module 8 (e), Module 9 (f).
6.2 Review exercises (by hand)
For the notation recap block, after the mock exam debrief. No calculator needed except for a single division in Exercise 4.
Read \(r = \frac{\text{Cov}(X,Y)}{s_X\, s_Y}\) aloud as one sentence. Why is \(r\) easier to interpret than the covariance?
Read \(CV = \frac{s}{\bar{x}} \times 100\%\) aloud. Riverside has \(s = 83.48\) € and \(\bar{x} = 205.69\) €: check the \(CV\) of 40.6% in the summary table.
Solution. (a) “\(r\) is the covariance of \(X\) and \(Y\) divided by the product of their standard deviations.” The division removes the unit (°C·€), so \(r\) is a pure number between \(-1\) and \(1\). (b) “The standard deviation as a percentage of the mean.” \(83.48 / 205.69 = 0.406\), i.e. \(CV = 40.6\%\) ✓.
Revise: Module 9 (a), Module 6 (b).
Write in symbols:
“for each individual, multiply the two deviations from the means, add up the products, and divide by \(n-1\)”;
“the slope is the covariance divided by the variance of \(X\)”;
“the third quartile minus the first quartile”.
A regression line has \(\bar{x} = 20\), \(\bar{y} = 400\) and \(b = 10\). Compute the intercept \(a\) and the prediction at \(x = 25\).
Solution. (a) \(\text{Cov}(X,Y) = \frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y})\). (b) \(b = \dfrac{\text{Cov}(X,Y)}{s_X^2}\). (c) \(IQR = Q_3 - Q_1\). (d) \(a = \bar{y} - b\,\bar{x} = 400 - 10 \times 20 = 200\), so \(\hat{y} = 200 + 10 \times 25 = 450\).
Revise: Module 9 (a, b, d), Module 5 (c).
7 Common mistakes
- Unequal-width histogram heights — use density \(n_i/h_i\), not raw counts, when class widths differ (Module 3).
- \(n\) vs \(n-1\) — use sample formulas (
.S) by default; population formulas (.P) only when you have the entire population (Module 6). - Correlation vs causation — \(r\) measures linear association, not cause and effect (Module 9).
- \(r\) vs \(r^2\) — \(r\) is correlation (direction + strength); \(r^2\) is explained share (always 0 to 1) (Module 9).
QUARTILE.INCvsQUARTILE.EXC— the course uses exclusive (position \((n+1)p\)); do not mix them (Module 5).- Ordinal treated as ratio —
satisfaction_rating1–5 has no equal intervals; median, not mean (Module 1). - Extrapolation — regression predictions outside the observed \(X\) range are unjustified (Module 9).
- Raw counts vs conditional % — compare rows with different totals using conditional distributions (Module 8).
- Grouped mean/mode as exact — they are approximations; prefer raw data when available (Modules 3–4).
- Mean/median/mode ordering heuristic — for near-symmetric data, the gaps are tiny; trust the Fisher-Pearson skewness using all raw data (Module 7).
- Fence rule vs standard deviations — 1.5×IQR is for boxplots; 2σ is for normal distributions — different tools (Module 5).
- Intercept as real prediction — if \(X=0\) is not meaningful, the intercept is just a mathematical anchor (Module 9).
- Excel locale — French Excel uses
;and localised function names; use the Excel functions page to translate (Module 1). - Line chart vs scatter plot — line charts imply sequence; scatter plots show relationship between two variables (Module 8).
8 Exit check
Five minutes, no calculator needed except for question 5.
- Read \(\text{Cov}(X,Y)=\frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y})\) aloud as a sentence.
satisfaction_rating(1–5) is ordinal. Which centre indicator do you report, and why not the mean?- Riverside has \(r = -0.087\) between temperature and revenue. Interpret it in one sentence, and give \(r^2\).
- Why does the sample variance divide by \(n-1\) rather than \(n\)?
- Riverside revenue runs from €66.93 to €472.24, with \(IQR = 104.58\). Compute the range. Which of the two spread measures do you trust more here, and why?
- “For each day, multiply the deviation of \(x\) from its mean by the deviation of \(y\) from its mean, add up the \(n\) products, and divide by \(n-1\).” (Module 9)
- The median (or the mode): the gaps between 1, 2, 3, 4, 5 are not equal, so averaging the codes has no meaning. (Module 1)
- There is almost no linear link between temperature and revenue; \(r^2 = 0.087^2 \approx 0.008\), so temperature explains under 1% of the revenue variability. (Module 9)
- The deviations \(x_i-\bar{x}\) sum to 0, so only \(n-1\) of them are free; dividing by \(n-1\) corrects for \(\bar{x}\) being estimated from the same sample (Bessel’s correction). (Module 6)
- Range \(= 472.24 - 66.93 = 405.31\) €. The \(IQR\): the range is set by the two extreme days (both high outliers), while the \(IQR\) covers the middle 50% of days and ignores them. (Modules 5–6)
9 Homework — Excel lab
Replicate the walkthrough in Excel: reproduce the Lakeside Bakery summary you reviewed in class with the functions of Modules 1–9, then run the full walkthrough on the second outlet.
Estimated time: about 50–60 minutes. Any spreadsheet application works, at home or in a campus computer room.
Follow-up: there is no next module, so check yourself against the solutions on this page (Step 0 and Homework 1–2). If your group has a final-exam review session, bring any remaining question to it.
9.1 Using Excel
All functions from Modules 1–9. The complete list is on the Excel functions page.
| Walkthrough step | Excel function / steps |
|---|---|
| Keep one outlet | Filter outlet, or FILTER(range, outlet_range="Riverside") inside each function |
| Step 2 — frequency tables | =COUNTIF(range,"Sunny"), or a PivotTable with weather in Rows |
| Step 3 — five-number summary | =MIN(range), =QUARTILE.EXC(range,1), =MEDIAN(range), =QUARTILE.EXC(range,3), =MAX(range) |
| Step 4 — centre, spread, shape | =AVERAGE(range), =STDEV.S(range), =STDEV.S(range)/AVERAGE(range), =SKEW(range) |
| Step 5 — contingency table | PivotTable: weather in Rows, revenue class in Columns, values shown as % of row total |
| Step 6 — correlation, regression | =COVARIANCE.S(x,y), =CORREL(x,y), =RSQ(y,x), =SLOPE(y,x), =INTERCEPT(y,x) |
9.2 Step 0 — check your class results
- Open
lakeside-bakery.csvand keep the 60 Riverside rows. - For
daily_revenue_eur, compute=AVERAGE,=MEDIAN,=QUARTILE.EXC(range,1),=QUARTILE.EXC(range,3),=STDEV.S,=STDEV.S(range)/AVERAGE(range)and=SKEW. - With
temperature_cas \(x\) and revenue as \(y\), compute=CORREL(x,y),=SLOPE(y,x)and=INTERCEPT(y,x). - Compare every result with the Riverside column of the summary table and with the solution of Exercise 3.
| Indicator | Riverside |
|---|---|
| \(n\) | 60 |
| Mean revenue (€) | 205.69 |
| Median revenue (€) | 184.94 |
\(Q_1\) / \(Q_3\) (€, QUARTILE.EXC) |
156.66 / 261.25 |
| Std. dev. (€) | 83.48 |
| CV | 40.6% |
Skewness (SKEW) |
+0.93 |
| Outliers (1.5×IQR) | 2 high (431.34, 472.24) |
| \(r\)(temp, revenue) | −0.087 |
| Slope / intercept | −1.78 / 243.51 |
The exact \(Q_3\) is 261.245, so some apps display 261.24: both are correct.
Repeat Steps 2–6 of the walkthrough for the Hilltop outlet (60 days) of lakeside-bakery.csv: (a) Modal category of weather and of satisfaction_rating. (b) Five-number summary, IQR, fences and outliers of daily_revenue_eur. (c) Mean, median, grouped mode (€50 classes from €50), standard deviation, CV and skewness. (d) Share of days below €150 for each weather type. (e) \(r\), \(r^2\), slope and intercept of temperature_c vs daily_revenue_eur.
How to. Filter outlet to “Hilltop”, then follow the Using Excel table row by row; use COUNTIFS for the class counts in (c) and (d).
Solution. (a) Weather: Sunny 30, Cloudy 23, Rainy 7 (modal: Sunny). Satisfaction: 2 (18 days), 3 (29), 4 (13) (modal: 3). (b) Min=69.91, Q1=151.62, Me=195.16, Q3=265.92, Max=417.35, IQR=114.31, fences=−19.85/437.39, no outlier. (c) Mean=216.91, Me=195.16, modal class [150,200[ (17 days), grouped Mo ≈ 150 + 50×5/(5+6) ≈ 172.73, \(s\)=81.96, CV=37.8%, skew=+0.60 (moderate right skew; Mo < Me < mean). (d) 71.4% of Rainy days earn below €150, against 30.4% of Cloudy and 6.7% of Sunny days: revenue depends on weather, as at Riverside. (e) \(r\)=0.125, \(r^2\)=0.016, slope=2.38, intercept=166.02: no useful linear link between temperature and revenue. Every value matches the Hilltop column of the summary table.
Compute the mean daily_revenue_eur over all 120 rows of lakeside-bakery.csv. Check the derivation on this page: is it the weighted mean of the two outlet means, with weights \(n_j/n\)?
How to. Put =AVERAGE of the whole column in one cell and =0.5*AVERAGE(FILTER(…,…="Riverside"))+0.5*AVERAGE(FILTER(…,…="Hilltop")) in another.
Solution. Overall mean = 211.30 €. Both outlets have 60 of the 120 days, so \(w_j = 60/120 = 0.5\) and \(0.5 \times 205.69 + 0.5 \times 216.91 = 211.30\) € ✓.
10 Further reading
| Source | Where | What it adds | Time | Verified |
|---|---|---|---|---|
| OpenStax IBS 2e | Chapter 2 Review (from book page 90: summary, practice, homework) | Comprehensive review of all univariate topics | ~10 pages | checked against the PDF contents (T046) |
| OpenStax IBS 2e | Chapter 13 Review (from book page 570: summary, practice, homework) | Comprehensive review of bivariate topics | ~7 pages | checked against the PDF contents (T046) |
| Khan Academy | Unit Exploring bivariate numerical data — practice | Full practice set on correlation and regression | ~30 min (estimate) | link check pending (T048) |
| Khan Academy | Unit Summarizing quantitative data — practice | Full practice set on univariate summaries | ~30 min (estimate) | link check pending (T048) |
OpenStax IBS 2e: Alexander Holmes, Barbara Illowsky and Susan Dean, Introductory Business Statistics 2e, OpenStax, Rice University, https://openstax.org/details/books/introductory-business-statistics-2e, licensed under CC BY-NC-SA 4.0. Sections are cited, not reproduced.
11 What comes next
This course describes data as a snapshot. Two natural sequels are time series (trend, seasonality, moving averages: the 120 days of “The Wandering Fork” are a time series) and index numbers (price and volume indices, base-year comparisons). Both are covered in the next course of the programme, together with probability and the inference tools that this course deliberately leaves out.