Data Collection and Tabulation

Data collection is the systematic process of gathering information from a defined population or sample in order to answer a research question or test a hypothesis. Before any statistical analysis can occur, raw data must be collected using a clearly defined method — whether through surveys, experiments, observations, or existing records. The quality of every conclusion drawn from statistics depends entirely on how carefully the data was collected. Poorly collected data leads to biased or misleading results, no matter how sophisticated the analysis that follows. Once data is collected, organizing it into a structured table — called a frequency table or tally table — makes patterns immediately visible and prepares the data for further analysis such as calculating measures of centre or drawing graphs. Tabulation transforms a chaotic list of raw values into an ordered summary that shows how often each value or range of values appears. This step is essential in every branch of statistics, from opinion polls to medical trials to quality control in manufacturing. In this article you will learn how to design a data collection process, record raw data efficiently using tally marks, construct frequency tables for both discrete and grouped continuous data, and calculate relative frequencies. These skills form the foundation of the entire Statistics unit and connect directly to graphical displays such as histograms, bar charts, and stem-and-leaf plots.

Key takeaways
  • Define the research question and population
  • Choose a data collection method
  • Record raw data using tally marks
  • Construct a frequency table
  • Calculate relative and cumulative frequencies

Define the research question and population

Every data collection project begins with a precise question, for example: 'How many hours per night do Year 10 students sleep?' The population is the entire group you want information about (all Year 10 students in the school). Because surveying every member is often impractical, you may select a sample — a representative subset. A simple random sample gives every member an equal chance of selection and minimises bias.

Choose a data collection method

Common methods include: (1) Questionnaire/Survey — written or digital questions; (2) Experiment — the researcher controls one variable and measures the effect; (3) Observation — recording what happens without interference; (4) Secondary data — using existing datasets (government records, databases). For each method, consider potential sources of bias such as leading questions, non-response bias, or measurement error.

Record raw data using tally marks

As responses are collected, enter each value as a tally mark (|) in the appropriate row of a tally chart. Group every fifth mark as a 'gate' (||||) to make counting easier. For example, a tally of |||| || represents 7. This real-time recording prevents transcription errors and makes the next step — counting frequencies — trivial.

Construct a frequency table

Count the tally marks for each category or class interval to obtain the frequency f. For discrete data (whole number counts) list each possible value. For continuous data (measurements) group values into equal class intervals of width w. A well-formed frequency table has columns: Value/Class | Tally | Frequency (f) | Relative Frequency (f/n) | Cumulative Frequency. The sum of all frequencies must equal the total number of data points n: Σf = n.

Calculate relative and cumulative frequencies

Relative frequency expresses each class's frequency as a proportion of the total: relative frequency = f/n. Multiply by 100 to express as a percentage. Cumulative frequency is the running total of frequencies from the first class up to and including the current class. It answers questions like 'How many students sleep fewer than 8 hours?' Cumulative frequencies are used to draw ogive (cumulative frequency) curves and find medians and percentiles.

The Key Equation

firel=finandFk=∑i=1kfif_i^{\text{rel}} = \frac{f_i}{n} \qquad \text{and} \qquad F_k = \sum_{i=1}^{k} f_i
  • f_i — Class frequency (count): The number of data values that fall in class interval i.
  • n — Total sample size (count): The total number of observations collected; equals Σf over all classes.
  • f_i^{\text{rel}} — Relative frequency (dimensionless (or %)): The proportion of all observations that belong to class i; always between 0 and 1 and all relative frequencies sum to 1.
  • F_k — Cumulative frequency (count): The number of data values in all classes up to and including class k.

Worked Example

Problem. A teacher records the scores (out of 20) of 24 students on a short quiz. The raw scores are: 14, 17, 12, 15, 18, 14, 16, 13, 17, 15, 19, 14, 12, 16, 15, 17, 13, 18, 15, 14, 16, 17, 11, 15. Organise this data into a grouped frequency table using class intervals of width 3, starting at 11. Then calculate the relative frequency and cumulative frequency for each class.

Classff/nF[11,13]55/245[14,16]121/217[17,19]77/2424Σ241—\begin{array}{|c|c|c|c|}\hline \text{Class} & f & f/n & F \\ \hline [11,13] & 5 & 5/24 & 5 \\ [14,16] & 12 & 1/2 & 17 \\ [17,19] & 7 & 7/24 & 24 \\ \hline \Sigma & 24 & 1 & — \\ \hline \end{array}

Answer. Grouped frequency table with classes [11–13], [14–16], [17–19] having frequencies 5, 12, 7; relative frequencies 5/24, 1/2, 7/24; and cumulative frequencies 5, 17, 24.

Figure
Diagram
Grouped Frequency Table – Quiz Scores (n = 24)ClassTallyFreq (f)Rel FreqCum F[11 – 13]|||| |55/24 ≈ 0.2085[14 – 16]|||| |||| ||1212/24 = 0.50017[17 – 19]|||| ||77/24 ≈ 0.29224Total241.000—Key Checks• Sum of frequencies: 5 + 12 + 7 = 24 = n ✓• Sum of relative frequencies: 0.208 + 0.500 + 0.292 = 1.000 ✓• Last cumulative frequency = n = 24 ✓
Origins · 1 minKarl Pearson and how this was discovered
KP
Karl Pearson
1857–1936 · British

Karl Pearson is regarded as one of the founders of modern mathematical statistics. He formalised the use of frequency distributions and frequency tables as core tools for organising data, and introduced the chi-squared test for testing whether observed frequency distributions differ from expected ones. His 1895 paper introduced the concept of the standard deviation and laid out rigorous methods for describing distributions using moments — concepts that still underpin the way statisticians interpret tabulated data today. He also founded the world's first university statistics department at University College London in 1911. Pearson originally trained as a lawyer and only switched to mathematics and statistics in his late twenties. He was so passionate about data that he personally tabulated thousands of measurements of human skulls by hand to study heredity — work that today would be done in seconds by a computer.

  • Frequency Distributions and Histograms — A frequency table is the direct numerical source for a histogram; each class frequency becomes the height (or area) of a bar, so these two concepts are inseparable.
  • Measures of Central Tendency (Mean, Median, Mode) — The mean, median, and mode are all estimated from organised frequency tables; without tabulation, calculating these statistics from large raw datasets would be impractical.
  • Sampling Methods — Understanding how data is collected — random sampling, stratified sampling, systematic sampling — is a prerequisite for evaluating whether the frequencies in a table are representative of the population.
  • Cumulative Frequency and Ogive Curves — The cumulative frequency column of a frequency table is plotted directly to produce an ogive, which is used to find medians, quartiles, and percentiles graphically.