Critique statistical displays and claims

A club has 900 members. An open poll gets 40 replies, and 70% of those respondents favour longer hours. Does this establish that 70% of all members favour longer hours?

A chart compares 12 responses for A and 15 for B. Which statement matches the numbers?

Predict whether changing the baseline changes the data. Compare Zero with Truncated at 10, then inspect the values and visible bar lengths

With baseline 10, what do the visible bar lengths compare?

Separate three checks

A correct calculation can sit inside a misleading display or an unsupported population claim

1. 1Claim and evidence Read exactly what is asserted. Decide whether the supplied numbers support it, contradict it or do not establish it
2. 2Presentation Check labels, units, intervals, baseline, scale and omitted data. Use bar lengths honestly; compare the underlying numbers too
3. 3People and collection Identify the target population, sampling frame, selection method, response count and missing groups

How many more responses does B have than A?

Subtract A’s count from B’s count

B has what percentage more responses than A? Enter the percentage number

Identify the relevant counts and denominator before calculating

Which advice about vertical scales is most accurate?

The morning survey has 20 replies and the afternoon survey 40. Predict whether equal-height percentage bars mean equal numbers of respondents. Switch between Counts and Percentages

Which interpretation remains true in both views?

How many percentage points higher is the morning bus share?

Identify the relevant counts and denominator before calculating

The table records one answer from each of 30 respondents. Which statement is supported by these records?

A report says Late was the most common answer in the same table. How does the evidence relate to that claim?

A survey finds that club members who practise more often also report higher confidence. The headline says extra practice has been proved to cause confidence. What is justified?

A survey about all residents uses a large random sample drawn only from a gym membership list. What remains a problem?

Which item asks neutrally about satisfaction with the timetable alone?

Of 120 invited members, 36 reply and 27 support a proposal. Which report is defensible?

Which reporting plan best respects participants and avoids a misleading impression?

Write a conclusion that can be checked

Use a current statistical report from a public source. This open response needs your own review or a teacher’s feedback; the next questions do not assess a written report

1. 1Identify and trace Record the source, date, precise claim, target population and original data source. A headline or attractive chart is not a substitute for provenance
2. 2Recalculate and inspect Check one numerical comparison, its denominator, the graph’s scale and whether the evidence concerns the same people, measure and period as the claim
3. 3State a qualified conclusion Say what the sample supports, identify a specific limitation or bias, and suggest an improvement. Do not generalise beyond the evidence or claim causation without justification
4. 4Consider ethics Ask whether consent, privacy, fair representation and authority to use the data have been respected. For Aboriginal and Torres Strait Islander community data, consider relevant community governance and data-sovereignty protocols