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Class survey data investigation and mathematical communication - Mathematics Year 7

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Introduction

What makes a survey conclusion convincing rather than merely attractive? Ask a clear question, describe who was sampled and show how the actual values support a limited conclusion.

You will build a complete investigation portfolio: question, sampling note, table, display and a conclusion with at least two numerical facts and one limitation. All twenty example responses are fictional; no real pupil names, addresses or personal records are needed. A mixed checkpoint connects number, algebra, ratio, geometry, statistics and probability.

Design a clear question and defensible sample

A population is the whole group your question concerns; a sample is the group actually observed. Suppose a fictional school has 80 Year 7 pupils and you want to describe their usual journeys. Twenty volunteers are only a sample, not automatically a representative miniature of all 80. If invitations came mainly from a cycling club, the selection process could overrepresent cyclists, even if the final chart is perfectly drawn.

Define each variable before collecting a response. Journey time is numerical and needs a unit; journey mode is categorical and needs clear response choices. An answerable original question is: “On your most recent ordinary school day, what mode covered the longest part of your journey by time?”Allow Cycle, Walk, Bus, Car, Other, and Prefer not to answer. Ask for approximate total minutes separately, using the same stated journey definition for everyone.

This wording is a design example, not proof that every respondent will understand it identically. A mixed journey needs the longest-part rule; the time question needs an explicit time period and unit. Avoid a leading question such as“Don’t you agree cycling is the best way to arrive?”which asks for approval rather than measuring the stated journey mode.

Plan the sampling note. State the intended population, how invitations are chosen, how many people respond and any non-response. A larger voluntary sample does not automatically remove a selection bias. A balanced invitation or a suitable random selection can improve the design, but practical access and response differences still need consideration. Describe the procedure actually used rather than calling every convenient group random.

Use anonymous aggregate teaching data for this online task. Real classroom enquiries can be organised separately under the teacher’s normal arrangements without names or home addresses in a public course response. The provided twenty values are invented so you can practise the complete reasoning without collecting personal records.

Before making a display, decide what the question asks. A frequency table and separated bars suit mode counts; a list or distribution display can describe journey minutes. A single central average cannot show the entire distribution, and a colourful chart cannot repair unclear wording or an unrepresentative sample. Planning quality affects which conclusions the later calculations can support.

Audit twenty responses and choose a display

Complete original fictional journey-time data, in minutes.

8,10,12,14,15,16,17,17,18,18,
18,19,20,21,22,24,25,26,28,30
Twenty invented values,already in ascending order.

The total is 378 minutes, so $\bar{x} = \frac{378}{20} = 18.9 m i n u t e s$ . The median averages positions 10 and 11, both 18, giving 18 minutes. The range is 30−8=22 minutes. A calculation should retain the observation count and units, not only the final number. The three 18 values also make 18 the most frequent time in this particular list.

The same fictional sample’s separately supplied mode counts.

Journey category	Count	Sample share
Cycle	12	60%
Walk	5	25%
Bus	3	15%
Car	0	0%
Other	0	0%
Prefer not to answer	0	0%

The counts sum to 20 and the shares to 100%. Draw separated labelled bars with the category names and a count scale beginning at 0. Keep zero categories visible in the table so their absence is not confused with an omitted response option. A chart may focus on non-zero bars if its caption still explains the full response set.

For a pie display, the angles are 216° forCycle, 90° forWalk and 54° forBus, with zero angle for the remaining categories. For example $\frac{12}{20} \times 36 0^{\circ} = 21 6^{\circ}$ . Check that the angles sum to 360°. A bar chart gives counts more directly; the pie makes a complete-whole comparison explicit. Both require the stated sample size.

The temperature graph’s months have a natural order, so connecting points communicates change across that order. Journey-mode names are categories, so joining them as if Cycle→Walk→Bus were continuous time would be misleading. Match the display to the variable and question rather than copying the source graphic’s layout.

Use Corbettmaths’ original questionnaire example to identify missing time periods or incomplete response categories. Then evaluate the different journey questions and the fully fictional data here; the video’s mobile-phone spending question is not our data collection. Original: corbettmaths, Questionnaires - Corbettmaths. The written explanations and native tasks work without sound or the external player.

Retain the raw values, counts, formulas and chosen display so another reader can audit your numerical claims. A summary without the table or sampling note conceals important evidence.

Communicate limits and connect six mathematical strands

Write a bounded conclusion. “In this fictional twenty-response sample, 12 selected Cycle, so 60% of responses were Cycle. The median journey time was 18 minutes and the range 22 minutes. Because the example sample is not demonstrated to represent all 80 Year 7 pupils, we cannot infer the whole school’s proportions.” This supplies multiple numerical facts and an explicit limitation without pretending the invented survey really occurred.

The aggregate mode counts and aggregate time list do not say which time belongs to which mode. You therefore cannot conclude that cycling caused longer or shorter journeys, or even calculate each mode’s mean time from these separate summaries. Correlation would not by itself establish causation, and here even the paired data are absent.

A six-strand cumulative checkpoint.

Mathematical strand	Original task	Checked result
Number	Share the 378-minute total equally across 20 observations	18.9 minutes
Algebra	A hypothetical constant-share model predicts C=0.6 n; use n=40	24 responses under that model, not a population finding
Ratio	Compare 12 Cycle with 8 non-Cycle responses	3: 2
Geometry	Find theCyclepie-sector angle	216°
Statistics	Give median and range from the full ordered list	18 minutes and 22 minutes
Probability	Choose uniformly from these 20 fictional responses; chance ofCycle	12/20=0.6

The probability statement concerns one uniform choice from this finite sample, not a randomly chosen person anywhere in the school. The algebraic extension assumes a constant 60% share; it does not establish that 40 new real responses would contain exactly 24 cyclists. State the model when connecting different mathematical strands.

Unfamiliar comparison. A second fictional sample has 8 Cycle choices among 10 responses. Its sample share is 80%, higher than 12/20=60%, although its Cycle count 8 is lower than 12. The denominator changes the interpretation. Compare proportions for like questions, keep sample sizes visible and avoid claiming that the school’s behaviour changed when the samples have different selection methods.

Error clinic and evidence. Correct a claim that“12 cyclists means 12%”by dividing by 20 and multiplying by 100. Correct averaging the distinct journey times instead of all observations; repeated 17 and 18 values still count. Submit the question, sampling note, full table, chosen display, worked checks and limited conclusion. Retain an actual later response after a break; the course does not fabricate a real survey or a learner’s later performance.

Interactive Tasks

Quiz: Test Your Knowledge

What is the sample size in the original fictional investigation? (20) (!80) (!12) (!378)

What is the intended fictional Year 7 population size? (80) (!20) (!12) (!18)

What is 12 out of 20 as a percentage? (60%) (!12%) (!40%) (!80%)

What is the mean of the complete twenty-time list? (18.9 minutes) (!18 minutes) (!22 minutes) (!20 minutes)

What is its median? (18 minutes) (!18.9 minutes) (!22 minutes) (!19 minutes)

What is its range? (22 minutes) (!30 minutes) (!8 minutes) (!18 minutes)

WhichCyclepie-sector angle matches 12 out of 20? (216 degrees) (!60 degrees) (!180 degrees) (!240 degrees)

What is the ratio ofCycle to non-Cycle counts? (3: 2) (!2: 3) (!3: 5) (!12: 20)

What is theCycle share in a separate 8 out of 10 sample? (80%) (!8%) (!60%) (!20%)

What is a valid limitation of these aggregate data? (They do not link each journey time to a mode) (!They prove cycling causes longer journeys) (!They represent every pupil in the school) (!They remove all sampling bias because a chart is drawn)

Memory Game

Population	Whole group targeted by the enquiry
Sample	Subset actually observed
Variable	Attribute or quantity recorded
Category	Response group for a categorical variable
Bias	Systematic distortion from selection or measurement
Conclusion	Claim bounded by the evidence and its limits

Drag and Drop

20	Number of original fictional responses
378 minutes	Total of the original time list
18.9 minutes	Original mean journey time
18 minutes	Original median journey time
216 degrees	Cycle sector for the original sample

Crossword Puzzle

POPULATION	Whole target group
SAMPLE	Observed subset
VARIABLE	Recorded attribute
CATEGORY	Group of response choices
MEDIAN	Middle after ordering
CONCLUSION	Claim supported and limited by evidence

LearningApps

Optional extra practice. Choose an appropriate activity with your teacher. If the external collection is unavailable, use the native activities and independent tasks in this course.

Cloze Text

Open Tasks

Easy

Name population and sample: Distinguish the fictional 80 Year 7 pupils from 20 respondents.
Improve question wording: Remove the leading cycling wording and supply a time period and complete choices.
Check response totals: Show counts 20 andshares 100% including zero categories.
Find ordered positions: Identify positions 10 and 11 and calculate the median.

Standard

Build the investigation portfolio: Submit question, sampling note, raw values, table and a justified display.
Calculate centre and spread: Show total 378, mean 18.9, median 18 andrange 22 with units.
Write a limited conclusion: Include two numerical facts and at least one sampling or data limitation.
Complete the six-strand checkpoint: Explain the different assumptions behind arithmetic, algebra, ratio, geometry, statistics and probability statements.

Advanced

Compare unequal samples: Compare 12/20 with 8/10 without confusing count and proportion.
Evaluate a causal claim: Explain why separate mode counts and time values do not identify mode-specific journey times.
Defend a display choice: Compare categorical bars, pie shares and a time-series line using the actual source-image limits.
Retrieve and audit later: Keep actual later calculations and a correction of a percentage, count or sampling error.

Learning Check

Question and sampling design: Submit an answerable journey enquiry and sampling note.
Full numerical dataset: Calculate the actual twenty-time summaries.
Table and display: Represent the original mode counts.
Conclusion with two facts and one limit: Make an evidence-bounded claim.
Cumulative and unfamiliar transfer: Solve all six strands and compare another sample.
Audit and later evidence: Correct errors and retain genuine work.

Worked checks and assessment guidance

Define mode/time separately, time period, minutes, longest-part rule and complete categories. Population 80 versus sample 20; voluntary or cycling-club selection can bias coverage. The example is fictional, no real personal records are needed.
Ordered values 8, 10, 12, 14, 15, 16, 17, 17, 18, 18, 18, 19, 20, 21, 22, 24, 25, 26, 28, 30 total 378. Mean 18.9, median 18, range 22, mode 18. Repeated observations remain in the calculation.
Cycle 12, Walk 5, Bus 3, remaining categories 0, total 20. Shares 60/25/15%, pie 216/90/54 degrees. Use a labelled bar scale/count table or a justified complete-whole display; sourceFirmaA/Bchart is not this survey.
SampleCycle share 60% andmedian 18 minutes/range 22 are numerical facts. No demonstrated representative sampling and no paired mode/time data mean no whole-school or causal conclusion follows.
378/20=18.9; constant-shareC=.6 ngives 24 at 40 onlyasmodel; 12: 8=3: 2; pie 216; median 18/range 22; uniformsampleP(Cycle)=.6. New 8/10=80% exceeds 60% despitelowercount 8.
12 is 60% of 20, not 12%; include all repeats in mean/median. Keep sampling note, source limits, full working and actual later response; do not fabricate a real class study or delayed score.

Learning evidence

Keep a complete fictional-data investigation portfolio with two numerical facts, one limitation and the six-strand checkpoint. Actual later work and real classroom enquiries require their own evidence.

OER and Wikipedia

Department for Education: England mathematics programme of study, Key Stage 3, probability,statistics,geometry and mathematical reasoning. Year 7 sequencing and the survey enrichment are editorial within KS3. All course examples,models,fictional data and worked answers are original. Actual Commons sources retain their creator/licence credits below; original-publisher videos supplement the written explanations. Reviewed 12 November 2026.

Simple bar chart.svg, Masur, Public domain. Unchanged original; caption and learning activities are original.

Graph of monthly temperature variations in south-west England.png, Jolly Janner, Public domain. Unchanged original; caption and learning activities are original.