Module 1 — What is statistics? Data types and measurement

Data Description | Part I — Organising data

Modified

October 7, 2026

The business question. A food-truck owner opens a spreadsheet with 120 rows of daily data: weather, temperature, customers, items sold, revenue, and more. Before computing any number or drawing any chart, what kind of information is in each column? Does “weather” behave like “revenue”? Can you average “satisfaction rating”? This module teaches you to look at a dataset and answer those questions — the first step in every statistical analysis.

Learning objectives

By the end of this module, you will be able to:

Distinguish descriptive statistics (summarising what happened) from inferential statistics (drawing conclusions about a larger population).
Identify the population, the statistical individual, and the variable in a business context.
Classify a variable as qualitative (nominal or ordinal) or quantitative (discrete or continuous).
State the four levels of measurement (nominal, ordinal, interval, ratio) and explain which arithmetic operations each allows.
Open the Wandering Fork dataset, recognise its grain (one row = one franchise-day), and perform basic Excel operations: cell references, sorting, filtering, and the functions SUM, COUNT, COUNTA, AVERAGE, IF.

Time plan

Block	Minutes	What you do
Theory	75	Descriptive vs inferential, population/individual/variable, variable types, levels of measurement, the Wandering Fork dataset
Excel lab	45	Open the CSV/Excel Table, relative/absolute/mixed references, `SUM`, `COUNT`, `COUNTA`, `AVERAGE`, `IF`, sort/filter, English vs French locale
Exercises	60	Four by-hand and two Excel exercises
Total	180

Theory

Descriptive vs inferential statistics

Definition — descriptive statistics

Descriptive statistics summarise and organise data that you already have: frequency tables, charts, means, standard deviations, correlations. They describe the sample at hand and make no claim about any larger group.

Definition — inferential statistics

Inferential statistics use a sample to draw conclusions about a population that you did not fully observe: confidence intervals, hypothesis tests, regression with p-values. This course stops at descriptive statistics; the next course (Inferential Statistics, MS04) continues from here.

In plain words: if you have the revenue of all 120 trading days and you compute the average, that is descriptive. If you have 30 days and you estimate the average of all possible trading days, that is inferential.

Population, individual, variable

Definition — population, individual, variable

A population is the set of elements being studied. It is finite if you can count its members exactly (e.g., the 120 trading days of the Harbour truck), and infinite otherwise (e.g., all possible future trading days). A statistical individual is one element of the population (one franchise-day). A variable is a characteristic observed on each individual (e.g., weather, daily_revenue_eur).

Variable types

Definition — qualitative vs quantitative

A qualitative variable takes categories as values (e.g., weather: Sunny, Cloudy, Rainy). A quantitative variable takes numbers as values (e.g., daily_revenue_eur: 460.48, 500.02, …).

Definition — nominal vs ordinal (qualitative)

A qualitative variable is nominal if its categories have no natural order (e.g., weather, promo_active). It is ordinal if the categories have a natural order (e.g., satisfaction_rating: 1 < 2 < 3 < 4 < 5). The order matters, but the distances between categories are not necessarily equal.

Definition — discrete vs continuous (quantitative)

A quantitative variable is discrete if its possible values are countable (e.g., customer_count: 39, 38, 38, …). It is continuous if it can take any value in an interval (e.g., daily_revenue_eur, temperature_c).

Levels of measurement

The four levels — what arithmetic is allowed

Level	Example	Allowed operations
Nominal	`weather`, `promo_active`	Count, mode, `=`, `≠`
Ordinal	`satisfaction_rating`, `month`	Everything nominal + order (`<`, `>`), median, percentiles
Interval	Temperature in °C (no true zero)	Everything ordinal + addition/subtraction of differences, mean, standard deviation
Ratio	`daily_revenue_eur`, `customer_count`, `temperature` in Kelvin	Everything interval + multiplication/division, ratios, geometric mean, coefficient of variation

In plain words: you can always count and find the mode. With ordinal data you can also sort and find the median. With interval data you can add and subtract differences (so the mean makes sense). With ratio data you can also multiply and divide (so ratios like “twice as much” and the coefficient of variation make sense). Most business data are ratio.

A common trap

satisfaction_rating is stored as the numbers 1, 2, 3, 4, 5, but it is ordinal, not ratio. The step from 1 to 2 is not necessarily the same as from 4 to 5. Computing an arithmetic mean of satisfaction ratings is technically questionable — the median is safer. Module 4 discusses this in detail.

Worked example

We use the Harbour 30-day subset (sheet harbour_30d) to illustrate the concepts of this module.

Column	Type	Level	Example values (first 5 days)
`weather`	Qualitative, nominal	Nominal	Cloudy, Sunny, Rainy, Cloudy, Sunny
`temperature_c`	Quantitative, continuous	Interval	21.9, 20.4, 16.4, 18.5, 24.1
`customer_count`	Quantitative, discrete	Ratio	39, 38, 38, 38, 53
`daily_revenue_eur`	Quantitative, continuous	Ratio	460.48, 500.02, 418.65, 508.80, 646.19
`satisfaction_rating`	Qualitative, ordinal	Ordinal	3, 4, 2, 3, 4

Step 1 — population and individual. The population is the 30 trading days of the Harbour truck (finite). Each row is one statistical individual (one franchise-day).

Step 2 — variable classification. weather is qualitative nominal (categories with no order). temperature_c is quantitative continuous (any value in an interval). customer_count is quantitative discrete (countable integers). daily_revenue_eur is quantitative continuous (ratio level, true zero). satisfaction_rating is qualitative ordinal (ordered categories, unequal steps).

Step 3 — allowed operations. For weather you can count and find the mode (Sunny appears most often). For temperature_c you can compute the mean and standard deviation (interval level). For daily_revenue_eur you can also compute ratios (e.g., “day 5 revenue is 1.5× day 3 revenue”) and the coefficient of variation (ratio level).

Using Excel

The complete list of function names, with their French equivalents, is on the Excel functions page.

Concept	Excel function / steps
Open the data	Data → Get Data → From Text/CSV (for `.csv`) or double-click `wandering-fork.xlsx`
Cell reference	`A1` (relative), `$A$1` (absolute), `$A1` or `A$1` (mixed); press F4 to cycle
Sum of a range	`=SUM(range)`
Count of numbers	`=COUNT(range)`
Count of non-empty cells	`=COUNTA(range)`
Average	`=AVERAGE(range)`
Conditional value	`=IF(condition, value_if_true, value_if_false)`
Sort	Select the table → Data → Sort
Filter	Select the table → Data → Filter (or Table → Filter)
English vs French locale	English Excel uses commas between arguments (`SUM(A1,A2)`); French Excel uses semicolons (`SOMME(A1;A2)`). Function names also differ — see the Excel functions page.

Quick check: does your Excel use English or French names?

Type =AVERAGE( in a cell. If Excel suggests AVERAGE, you are in English locale. If it suggests MOYENNE, you are in French locale. The course writes all formulas with English names; use the Excel functions page to translate.

Proof / derivation

Derivation — relative frequencies sum to 1 (click to expand)

Let a qualitative variable have $k$ categories with absolute frequencies $n_1, \dots, n_k$ and total $n = \sum_{i=1}^{k} n_i$. The relative frequency of category $i$ is $f_i = n_i / n$. Summing over all categories: \[ \sum_{i=1}^{k} f_i = \sum_{i=1}^{k} \frac{n_i}{n} = \frac{1}{n}\sum_{i=1}^{k} n_i = \frac{n}{n} = 1. \] In percentages, $\sum f_i \times 100\% = 100\%$. This is exactly the same property we saw for percentage distributions in the Excel warm-up (Module 1’s derivation), now applied to categories instead of line items. If your frequency table’s percentages do not sum to (very close to) 100%, a category was missed or a count was wrong.

Visual intuition

Think of the population as a bag of coloured balls. A qualitative variable is the colour of each ball — you can sort them into piles (nominal) or line them up by shade (ordinal). A quantitative variable is a number written on each ball — you can count them (discrete) or measure them on a ruler (continuous). The level of measurement tells you which ruler you are allowed to use: a ruler with no numbers (nominal), a ruler with only order marks (ordinal), a ruler with equal spacing but no true zero (interval), or a ruler with a true zero (ratio).

Interactive demo

Important

TODO: an interactive variable-type classifier (drag a column name to its type and level) would be a good Shinylive demo for this module.

Exercises

Exercise 1 (by hand) — Classify the variables (click for solution)

For each column of the Wandering Fork dataset, state: (a) qualitative or quantitative? (b) if qualitative: nominal or ordinal? (c) if quantitative: discrete or continuous? (d) level of measurement?

Solution. See the data dictionary table in the Theory section above. For example: weather → qualitative, nominal, nominal level; customer_count → quantitative, discrete, ratio level; satisfaction_rating → qualitative, ordinal, ordinal level.

Exercise 2 (by hand) — Population and individual (click for solution)

A marketing manager wants to know the average basket size of customers who visited the shop last month. The shop had 2,450 transactions last month. What is the population? What is the statistical individual? What is the variable of interest?

Solution. Population = the 2,450 transactions (finite). Statistical individual = one transaction. Variable of interest = basket size (quantitative, continuous, ratio level).

Exercise 3 (by hand) — Levels of measurement and allowed operations (click for solution)

For each variable, say whether the operation makes sense: (a) Mean of weather. (b) Median of satisfaction_rating. (c) Ratio of two daily_revenue_eur values (e.g., “today’s revenue is 1.3× yesterday’s”). (d) Difference of two temperature_c values (e.g., “today is 3°C warmer than yesterday”).

Solution. (a) No — weather is nominal, no mean. (b) Yes — ordinal data have a median. (c) Yes — revenue is ratio, ratios are meaningful. (d) Yes — temperature in °C is interval, differences are meaningful (but ratios are not, because 0°C is not “no temperature”).

Exercise 4 (by hand) — Descriptive vs inferential (click for solution)

A company surveys 500 customers and finds that 62% are satisfied. Is this descriptive or inferential? What if the company has 10,000 customers total and uses the 62% to estimate how many of the 10,000 are satisfied?

Solution. The 62% from the 500 surveyed is descriptive (it summarises the sample). Using it to estimate the 10,000 is inferential (it draws a conclusion about the population).

Exercise 5 (Excel) — Open the dataset and explore (click for solution)

Open wandering-fork.xlsx. (a) Filter franchise to “Harbour”. How many rows? (b) In column N (daily_revenue_eur), compute =SUM, =COUNT, =COUNTA, =AVERAGE for the filtered rows. (c) Sort by daily_revenue_eur descending. What is the highest revenue day for Harbour?

Solution. (a) 120 rows (all Harbour days). (b) SUM ≈ 49,618.46, COUNT = 120, COUNTA = 120, AVERAGE ≈ 413.49. (c) The highest Harbour revenue is €1,050.00 (day 80).

Exercise 6 (Excel) — English vs French function names (click for solution)

Your colleague uses French Excel. You send them the formula =AVERAGE(N2:N121). What must they change it to?

Solution. =MOYENNE(N2:N121) (function name) and the argument separator becomes a semicolon if the range is written with cell references: =MOYENNE(N2;N121) — but structured references like tblFork[daily_revenue_eur] work the same in both locales. See the Excel functions page for the full list.

Common mistakes

Watch out

Treating ordinal numbers as ratio. satisfaction_rating is 1–5, but =AVERAGE on it is questionable; use the median.
Forgetting to lock the total in a percentage distribution. The denominator must be absolute ($D$8) or a structured reference (tblFork[daily_revenue_eur]), otherwise copying the formula shifts the total.
Confusing the population with the sample. The 120 Harbour days are a finite population in this course. In real life, they would often be a sample of all possible trading days.
Using COUNT when you need COUNTA. COUNT only counts numbers; COUNTA counts everything non-empty (text, dates, errors).

Source	Where	What it adds	Time	Verified
OpenStax IBS 2e	§1.1 Definitions of Statistics, Probability, and Key Terms (book pages 5–10)	Formal definitions of population, sample, parameter, statistic	~5 pages	checked against the PDF contents (T046)
OpenStax IBS 2e	§1.2 Data, Sampling, and Variation in Data and Sampling (book pages 10–22)	Sampling methods, variation, qualitative vs quantitative	~12 pages	checked against the PDF contents (T046)
OpenStax IBS 2e	§1.3 Levels of Measurement (book pages 22–30)	The four levels with examples	~8 pages	checked against the PDF contents (T046)
Khan Academy	Unit Study design in the Statistics and probability course; look for lessons on statistical questions, sampling methods, and types of studies	Videos and practice on population vs sample, observational studies vs experiments	~30–45 min (estimate)	link check pending (T048)