Data Collection
Data collection is the foundation of statistics. Understanding the types of data, how to collect it fairly, and how to organise it into frequency tables helps us draw meaningful conclusions.
Discrete Whole number values (shoe size, goals scored)
Continuous Any value in a range (height, weight, temperature)
Categorical Non-numerical groups (colour, type, name)
Ordinal Ordered categories (poor/fair/good/excellent)
📖 Learn
Types of Data
Type Description Examples Qualitative Non-numerical (categorical) Colour, nationality, opinion Quantitative Numerical Height, score, count Discrete Countable whole numbers Shoe size (3,4,5…), number of goals Continuous Can take any value in a range Height, temperature, time
💡 Shoe sizes are technically discrete even though they can be half-sizes — the key is they cannot take every value (e.g. there's no size 3.14159).
Sampling Methods
Random sampling Every member of the population has an equal chance. Use random number tables or a random number generator.
Systematic sampling Select every nth item from a list. e.g. every 10th student on a roll.
Stratified sampling Divide population into groups (strata), then sample proportionally from each group.
Convenience sampling Sample whoever is available. Quick but biased.
Stratified sample calculation: number from stratum = (stratum size ÷ total) × sample size
Questionnaire Design
A good questionnaire question should be:
Clear and unambiguous
Not leading (doesn't suggest the answer)
With response boxes that cover all possibilities without overlapping
Anonymous where sensitive information is requested
💡 Bad: "Don't you agree that this school is too noisy?" — leading question!
💡 Bad: Response boxes 1−5, 5−10, 10−15 — 5 and 10 appear in two boxes!
Frequency Tables and Grouped Frequency Tables
A frequency table lists each data value and its count (frequency).
A grouped frequency table organises continuous data into class intervals:
Height (cm) Tally Frequency 150 ≤ h < 160 |||| 4 160 ≤ h < 170 |||| ||| 8 170 ≤ h < 180 |||| | 6
💡 The class width should be equal. Total frequency = total of all values in the frequency column.
Two-Way Tables
A two-way table cross-tabulates two categorical variables. Row and column totals must sum to the grand total.
Boys Girls Total Walk 12 15 27 Bus 18 10 28 Total 30 25 55
✏️ Worked Examples
Example 1: Stratified Sample
A school has 200 students: 80 in Year 7, 70 in Year 8, 50 in Year 9. A stratified sample of 40 is needed. How many from Year 8?
Year 8 fraction = 70/200
Year 8 in sample = (70/200) × 40 = 14 students
Example 2: Reading a two-way table
Complete the missing value in the table: Boys who walk = 12, Girls who walk = 15, Boys who cycle = 8, Total girls = 25. How many girls cycle?
Girls who walk + Girls who cycle = Total girls
15 + Girls who cycle = 25
Girls who cycle = 10
Example 3: Frequency table totals
Frequencies: 4, 7, 12, 9, 3. Find total frequency and the most common group (modal class).
Total = 4 + 7 + 12 + 9 + 3 = 35
Highest frequency = 12 → modal class is group 3
Example 4: Systematic sampling
A factory makes 500 items per day. A quality sample of 25 is needed. What is the sampling interval?
Interval = population ÷ sample size = 500 ÷ 25 = 20
Select every 20th item, starting from a random item between 1 and 20.
🎨 Visualizer
Frequency Table Builder
Enter a comma-separated list of values to build a frequency table automatically.
Build Table
Bar Chart from Frequency Table