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Year 6 Maths Data

Statistical investigations with numerical data

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Theory

A statistical investigation answers a question using data. With numerical data you measure or count: heights, times, temperatures. This Year 6 maths page shows how to turn a broad question into one you can measure, collect data fairly, choose the best graph, and explain what the results show and why measurements vary.

Numerical data are numbers you count or measure. Discrete data are counted and go in whole steps (number of pets). Continuous data are measured and can take any value in between (height, time, mass).

A refined question says exactly what to measure, of whom, and when. "Do we sleep enough?" becomes "How many hours does each student in 6C sleep on each school night for one week?"

Collect data fairly and consistently: use the same tool, the same method and the same time each time, and change only the one thing you are testing.

Choose the display: a line graph for change over time; a side-by-side column graph to compare two groups.

Measurements of the same thing vary a little because of rounding, how the tool is lined up, and small changes in conditions. The range shows how much they vary.

The investigation cycle Four steps in a loop: pose and refine a question; plan and collect the data fairly; record and display it; interpret the results. A dashed arrow returns to the start to ask a new question. 1 Pose and refine a questionwhat exactly will we measure? 2 Plan and collectsame tool, same method, same time 3 Record and displaytable or spreadsheet, then a graph 4 Interpretanswer the question; explain variation
The cycle can start again with a new, better question.
Line graph of a bean plant growing A line graph of the height of a bean plant in centimetres each week: week 0, 3; week 1, 5; week 2, 8; week 3, 10; week 4, 15; week 5, 17. Bean plant height 05101520 Height (cm) 012345 Week
The steepest part, week \(3\) to week \(4\), is the fastest growth: \(5\) cm.
Weekly growth of plants in shade and sun A side-by-side column graph of how many millimetres a row of seedlings grew each week, in the shade and in the sun, over four weeks. Shade: 22, 35, 18, 30. Sun: 28, 40, 26, 34. Shade Sun 0510152025303540 Growth (mm) 22 28 Week 1 35 40 Week 2 18 26 Week 3 30 34 Week 4
Side-by-side columns compare the two groups in each week.

Investigation choices:

DecisionGood choice
Counted datadiscrete (whole numbers)
Measured datacontinuous (can be decimals)
Change over timeline graph
Compare two groupsside-by-side column graph
Record datatable or spreadsheet, one column per measure
How much results varyrange = highest − lowest
Make it measurable. A good question names what to measure, the unit, who or what, and over what time.
Change one thing. In a fair test, everything stays the same except the thing you are testing.

How to run an investigation

  1. Refine the question so it can be answered with numbers.
  2. Plan how to collect: measure, count, observe or survey; same tool and method each time.
  3. Record the data in a table or spreadsheet.
  4. Display it with the right graph.
  5. Interpret: answer the question in context, using the numbers, and say why results might vary.
Example 1 — Discrete or continuous?
Is each discrete or continuous?
(i) The number of books each student read this term
(ii) The time to run \(100\) m
(iii) The mass of each school bag
Solution

(i) Discrete (counted)
(ii) Continuous (measured)
(iii) Continuous (measured)

Example 2 — Refine a question
Make this question measurable: "Do students like sport?"
Solution

For example: "How many minutes of sport does each student in 6C play on a school day?" Each student records a number of minutes.

Example 3 — Choose a collection method
How should a class collect data for "How long are our arm spans?"
Solution

Measure each student with the same tape measure, arms stretched the same way, to the nearest centimetre. Measuring is more accurate than asking students to guess.

Example 4 — Fair test
Two bean plants get different amounts of water: one is watered every day and one every third day. What must stay the same?
Solution

The type of plant, the pot and soil, the sunlight and the day they are measured. Only the watering changes.

Example 5 — Choose a display
Which graph suits each investigation?
(i) A puppy’s mass at the start of each month for a year
(ii) Jump distances of two classes
Solution

(i) Line graph (change over time)
(ii) Side-by-side column graph (comparing groups)

Example 6 — Read the line graph
Use the bean plant graph.
(i) How much did the plant grow altogether?
(ii) In which week did it grow the most?
Solution
\(17 - 3\)\(=\)\(14\)
\(15 - 10\)\(=\)\(5\)
17−3=1415−10=5

(i) \(14\) cm
(ii) From week \(3\) to week \(4\) (\(5\) cm).

Example 7 — Variation
Four students measured the same desk: \(1.21\) m, \(1.24\) m, \(1.19\) m, \(1.23\) m.
(i) What is the range?
(ii) Give one reason the results differ.
Solution
\(1.24 - 1.19\)\(=\)\(0.05\)
1.24−1.19=0.05

(i) \(0.05\) m
(ii) The ruler was lined up slightly differently each time, or the results were rounded differently.

Example 8 — Interpret a comparison
Use the third graph. Did the seedlings in the sun grow more each week? How much more did they grow over the four weeks?
Solution
\(22 + 35 + 18 + 30\)\(=\)\(105\)
\(28 + 40 + 26 + 34\)\(=\)\(128\)
\(128 - 105\)\(=\)\(23\)
128−105=23

Yes, every week. Over four weeks they grew \(128\) mm against \(105\) mm: \(23\) mm more.

Example 9 — Check a conclusion
A report on the bean plant says: "The plant grew the same amount every week." Is that supported?
Solution

No. The weekly growth was \(2\), \(3\), \(2\), \(5\) and \(2\) cm, so it changed from week to week.

Common pitfalls

A question that cannot be measured. "Is sport good?" has no number to record; name a measurement and a unit.
Changing two things at once. If both sunlight and water change, you cannot tell which one made the difference.
The wrong graph. Use a line graph only when the data change over time.
Claiming too much. Results from one class do not prove something about every student in Australia.

Frequently asked questions

What is numerical data?

Data made of numbers that are counted or measured.

What is the difference between discrete and continuous data?

Discrete data are counted in whole steps; continuous data are measured and can take any value in between.

How do I make an investigation fair?

Use the same tools and method each time, and change only the one thing you are testing.

Which graph shows change over time?

A line graph.

Why do measurements of the same thing vary?

Small differences in lining up the tool, rounding, and conditions; the range shows how much they vary.

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