Why organise and analyse?
When you collect information (by asking people, measuring, reading or watching), you get raw data. Raw data is a messy pile. It does not answer your question yet.
Two jobs turn the pile into an answer:
- Organise means to put the data in order: sort it, count it, and write it in a table or draw it as a chart.
- Analyse means to look closely for a pattern: which group is biggest, how two groups differ, and what it may mean.
Always keep your first question in front of you. Only keep the facts that help to answer it.
Classifying: sorting into groups
Classifying means putting things into groups by a rule. A good rule has three features:
- Clear. Two people using the rule get the same groups. "Made of paper or not" is clear. "Looks nice" is not.
- One rule at a time. Do not change the rule halfway.
- No overlap, nothing left out. Every item fits in exactly one group.
You can sort the same things by different rules. Bin items can be sorted by material, by place found, or by whether they can be recycled. Each rule shows a different pattern.
Comparing: same and different
Comparing means looking at two sets side by side to see what is the same and what is different.
- Use the same groups for both sets.
- Use the same scale on the chart.
- If the sets have different sizes, compare percentages, not raw counts. 10 out of 20 (50%) is a bigger share than 16 out of 40 (40%).
- Write one sentence for what is similar and one for what is different.
Thinking tools and charts
A thinking tool is a picture that helps you organise ideas. Pick the tool that fits the job:
- Table or tally chart: count quickly while collecting.
- Bar chart: compare the size of groups. Bars start at zero and have equal width.
- Line graph: show change over time.
- Venn diagram: sort by two rules at once. Two overlapping circles; the middle holds items that fit both.
- Mind web: show how ideas link to one main topic.
- Cause and effect chain (or fishbone): show reasons behind a problem.
Statistical analysis: mode, mean, median, range
Numbers describe a data set in short.
- Mode: the value that appears most often.
- Mean: add all values, then divide by how many values there are.
- Median: the middle value when the values are in order (if two are in the middle, take their average).
- Range: largest value minus smallest value. It tells how spread out the data is.
- Percentage: part ÷ whole × 100.
One very big value (an outlier) pulls the mean up, but the median hardly moves. So check both.
Finding the pattern and saying it fairly
Write the pattern in one clear sentence with numbers: "Paper is the most common waste: 5 of 12 items (about 42%)." Then be honest about limits:
- A small sample may not show the whole truth.
- Two things happening together does not mean one causes the other.
- A pattern gives a new question, such as "Why does Class B have more plastic?", which starts the next inquiry.
Try it: sort your own data
Find 12 or more items at home (spoons, socks, coins, books, snacks). 1) Spread them out. 2) Choose a rule and make groups. 3) Count each group and draw a bar chart. 4) Change the rule and see how the groups change. 5) Write one sentence about the pattern. In the 3D scene, tap the buttons in the last step to do the same.
Key formulas and definitions
- Mean = sum of all values ÷ number of values
- Mode = the value that occurs most often
- Median = middle value of the ordered list
- Range = largest value − smallest value
- Percentage = (part ÷ whole) × 100
- Venn counts: A or B = A + B − both
Worked examples
1. Bin counts are paper 5, plastic 4, food 2, metal 1. Find the mean, mode and range of the counts.
Mean = (5 + 4 + 2 + 1) ÷ 4 = 12 ÷ 4 = 3. Mode (most common group) = paper. Range = 5 − 1 = 4.
2. What percentage of the 12 items is plastic (4 items)?
Percentage = 4 ÷ 12 × 100 = 33.3%, so about one third.
3. Sort pen, pencil, banana, ruler, apple, carrot into groups with one rule.
Rule: what kind of thing is it? Stationery: pen, pencil, ruler (3). Fruit: banana, apple (2). Vegetable: carrot (1). Every item is in one group, none left out.
4. Class B bin counts are paper 3, plastic 7, food 1, metal 1. Compare with Class A (5, 4, 2, 1).
Both total 12, so counts can be compared. Similar: food and metal are small in both. Different: Class A's biggest group is paper (5), Class B's is plastic (7). B has 3 more plastic items (7 − 4) and 2 fewer paper items (5 − 3).
5. In a class of 30, 18 like cricket, 12 like football and 5 like both. How many like only cricket, only football, and neither?
Only cricket = 18 − 5 = 13. Only football = 12 − 5 = 7. Either or both = 13 + 7 + 5 = 25. Neither = 30 − 25 = 5.
6. Plastic bottles found on five days: 6, 8, 7, 30, 9. Find the mean and median. Which is the better 'typical' value?
Mean = (6 + 8 + 7 + 30 + 9) ÷ 5 = 60 ÷ 5 = 12. Ordered: 6, 7, 8, 9, 30, so the median is 8. The 30 is an outlier that pulls the mean up, so the median 8 describes a typical day better.
Common mistakes
- Using a rule that is not clear, such as "nice" and "not nice", so two people make different groups.
- Changing the rule halfway, or putting one item in two groups of the same sorting.
- Comparing raw counts when the sets have different sizes. Use percentages.
- Saying "this causes that" just because two things appear together, or giving a firm conclusion from a very small sample.