Foundations practice
Free Foundations practice with 60 original tasks, worked guidance and links to timed practice and a full mock. These tasks are not live-bank items.
What you will learn
- Practise analytical reasoning in Foundations contexts.
- Practise quantitative data literacy in Foundations contexts.
- Practise communication in Foundations contexts.
- Practise ai digital literacy in Foundations contexts.
- Practise learning agility in Foundations contexts.
These 60 tasks teach the Foundations reasoning process. They are public preparation, not a scored sitting, and they do not reuse protected assessment items.
Before you begin
- Use only the information given. State what remains unknown.
- Attempt a task before opening the guidance.
- Write the evidence for the choice, not only the final answer.
- Use timed practice after an untimed pass, then the full mock.
Practice activities
Analytical Reasoning · foundational
Which assumption must hold for that conclusion to follow? Situation: A neighbourhood market stall. Monday takings were 24 coins; Saturday, after a festival, were 36. A side count of 4 used a different definition from 9.
Review answer guidance
Name the missing premise. If it is unchecked, the conclusion is not shown. The claim in play is that Saturday is always busier. 36 versus 24 is a festival Saturday, not a typical week The extra figure (A side count of 4 used a different definition from 9) is part of what you must not ignore.
Analytical Reasoning · moderate
Which inference is actually supported by the stated facts? Situation: A school bus timetable with delayed departures. Four of twelve morning buses were more than ten minutes late on one wet day. The working copy is dated 9 days later than a 20-page cited copy.
Review answer guidance
Keep the conclusion inside the evidence. Do not import a cause that was not given. The claim in play is that the route is unreliable. one wet day is not the route's usual performance The extra figure (The working copy is dated 9 days later than a 20-page cited copy) is part of what you must not ignore.
Analytical Reasoning · challenging
What alternative explanation still accounts for the difference? Situation: A community clinic appointment sheet. 18 of 80 booked slots were unused, and the sheet does not say whether people cancelled or did not attend. 14 of 31 rows were added after the first total was announced.
Review answer guidance
A change that arrives with another change is not a cause until those extras are ruled out. The claim in play is that patients are wasting appointments. unused is not the same as did-not-attend, and the reason is unstated The extra figure (14 of 31 rows were added after the first total was announced) is part of what you must not ignore.
Analytical Reasoning · foundational
Which of the two arguments is better supported, and why? Situation: A household energy bill with estimated readings. The bill is 40 percent higher than last winter, and two of the four readings are estimates. A second observer recorded 19 where the first sheet shows 42.
Review answer guidance
Score each argument by the evidence it actually cites, not by how confident it sounds. The claim in play is that the household is using much more energy. estimated readings can shift cost between periods The extra figure (A second observer recorded 19 where the first sheet shows 42) is part of what you must not ignore.
Analytical Reasoning · moderate
What counterexample would be enough to refute the general rule? Situation: A local library late-return notice. A book due in 14 days was returned on day 16; the fine table charges 2 coins per day after a 1-day grace. The window used for 5 days is not the window used for 16 days.
Review answer guidance
One well-formed contrary case is enough to show that an unrestricted rule fails. The claim in play is that the fine must be 4 coins. with a 1-day grace, day 16 is one chargeable day, not two The extra figure (The window used for 5 days is not the window used for 16 days) is part of what you must not ignore.
Analytical Reasoning · challenging
Which constraint is being ignored in the recommended action? Situation: A youth club snack budget for a weekend trip. The budget is 90 coins for 15 people; 6 people need a more expensive option that costs twice the standard share. A note in the margin says 10 cases were excluded without a rule, against 27 kept.
Review answer guidance
List the limits that still bind. An option that needs a resource you do not have is not available. The claim in play is that everyone can have the same spend. six double shares consume 12 of 15 units of budget The extra figure (A note in the margin says 10 cases were excluded without a rule, against 27 kept) is part of what you must not ignore.
Analytical Reasoning · foundational
How far can the claim fairly be extended? Situation: A sports day results table by age group. Group A (20 runners) had 8 personal bests; group B (8 runners) had 5. The same label covers 15 events in one table and 38 in the other.
Review answer guidance
Match the claim's scope to the sample, time window and population that were actually observed. The claim in play is that group B trained better. 5/8 is a higher rate than 8/20, but the groups may not be comparable The extra figure (The same label covers 15 events in one table and 38 in the other) is part of what you must not ignore.
Analytical Reasoning · moderate
What evidence is required before the claim can be treated as shown? Situation: A recycling collection calendar with missed streets. 3 of 10 streets were missed in week 1; the notice says 'most collections ran as planned'. An appendix lists 20 exceptions that the summary of 12 does not mention.
Review answer guidance
Identify the comparison, baseline or source that is absent, and withhold the stronger wording until it arrives. The claim in play is that the service is mostly fine. a 30 percent miss rate is not 'most' in the ordinary sense of the word The extra figure (An appendix lists 20 exceptions that the summary of 12 does not mention) is part of what you must not ignore.
Analytical Reasoning · challenging
Which wording is stronger than the evidence permits? Situation: A weather warning posted on a community board. The warning covers 18:00–22:00; a club night is advertised as 'doors 17:30, ends late'. A side count of 6 used a different definition from 23.
Review answer guidance
Replace 'proves' and 'always' with what the observations actually cover. The claim in play is that the event is unaffected because it starts before 18:00. the overlap after 18:00 is inside the warning The extra figure (A side count of 6 used a different definition from 23) is part of what you must not ignore.
Analytical Reasoning · foundational
Which disputed definition would change the result? Situation: A shared kitchen rota for a student hostel. Two people are listed for Friday; the rule is one cook and one cleaner, and both names appear under cook. The working copy is dated 11 days later than a 34-page cited copy.
Review answer guidance
If two sides count different things, agree the definition before arguing about the number. The claim in play is that Friday is fully covered. cleaning has no owner if both names are cooks The extra figure (The working copy is dated 11 days later than a 34-page cited copy) is part of what you must not ignore.
Analytical Reasoning · moderate
How did the way the cases were chosen affect the conclusion? Situation: A ferry timetable and ticket price list. The 09:00 sailing is 12 coins; the 12:00 is 8 coins but arrives 90 minutes later for a 10:30 appointment. 16 of 45 rows were added after the first total was announced.
Review answer guidance
A volunteer, leftover or convenience sample cannot stand in for the group the claim names. The claim in play is that the cheaper sailing is better value. value depends on arriving before 10:30, which the 12:00 cannot do The extra figure (16 of 45 rows were added after the first total was announced) is part of what you must not ignore.
Analytical Reasoning · challenging
Which other variable moved at the same time as the supposed cause? Situation: A food-bank stock sheet after a donation drive. Cans rose from 40 to 70; fresh bread is listed as 0 with a note 'not counted'. A second observer recorded 21 where the first sheet shows 19.
Review answer guidance
Name the co-occurring change and say what comparison would separate the two. The claim in play is that stock is healthy. an uncounted essential with a zero is not evidence of health The extra figure (A second observer recorded 21 where the first sheet shows 19) is part of what you must not ignore.
Analytical Reasoning · foundational
What comparison is required before calling one option better? Situation: A class test mark sheet. The mean is 62; one mark of 12 sits with 24 other marks between 58 and 71. The window used for 7 days is not the window used for 30 days.
Review answer guidance
Better than what, for whom, over which period, on which measure. The claim in play is that the class average shows a weak group. the mean is pulled by one extreme mark The extra figure (The window used for 7 days is not the window used for 30 days) is part of what you must not ignore.
Analytical Reasoning · moderate
When would the recommended rule not apply? Situation: A park booking form. Capacity is 40; 28 tickets are sold and 16 complimentary places are reserved. A note in the margin says 12 cases were excluded without a rule, against 41 kept.
Review answer guidance
State the boundary condition. A rule without a stated exception is being oversold. The claim in play is that 12 places remain. 28 plus 16 is 44, which already exceeds capacity The extra figure (A note in the margin says 12 cases were excluded without a rule, against 41 kept) is part of what you must not ignore.
Analytical Reasoning · challenging
Who has the burden of proof for the disputed claim? Situation: A water-saving poster. It says use fell 50 percent after a campaign; the table shows 80 units then 40, but the second month was a holiday shutdown. The same label covers 17 events in one table and 15 in the other.
Review answer guidance
The party asserting a general effect must produce the comparison; the other party need not disprove a slogan. The claim in play is that the campaign halved use. the holiday shutdown is a competing explanation The extra figure (The same label covers 17 events in one table and 15 in the other) is part of what you must not ignore.
Analytical Reasoning · foundational
What mechanism is asserted, and what would count against it? Situation: A cycling-club mileage log. Three riders logged 10, 12 and 40 kilometres; the captain reports 'about 20 km each'. An appendix lists 22 exceptions that the summary of 26 does not mention.
Review answer guidance
A story about how an effect happens is not evidence that it happened. The claim in play is that 20 km is a fair summary. the mean is 20.7 because of one 40 km ride; the median is 12 The extra figure (An appendix lists 22 exceptions that the summary of 26 does not mention) is part of what you must not ignore.
Analytical Reasoning · moderate
Which two statements in the account cannot both be true? Situation: A lost-property log. 12 umbrellas and 3 phones were logged in a week; the notice says phones are the main problem. A side count of 8 used a different definition from 37.
Review answer guidance
Put the statements side by side. If they conflict, at least one needs a source or a revision. The claim in play is that phones dominate losses. 12 umbrellas outnumber 3 phones The extra figure (A side count of 8 used a different definition from 37) is part of what you must not ignore.
Analytical Reasoning · challenging
Why is the measured proxy a poor stand-in for the stated outcome? Situation: A homework club sign-in. Sign-ins rose from 10 to 15 after a poster; the club also moved next to the canteen that week. The working copy is dated 13 days later than a 11-page cited copy.
Review answer guidance
Say what the proxy actually captures and what part of the outcome it misses. The claim in play is that the poster worked. the location change arrived at the same time The extra figure (The working copy is dated 13 days later than a 11-page cited copy) is part of what you must not ignore.
Analytical Reasoning · foundational
What time-order problem undermines the causal claim? Situation: A charity raffle. 200 tickets at 2 coins; 3 prizes cost 90, 40 and 20 coins; 30 tickets remain unsold. 18 of 22 rows were added after the first total was announced.
Review answer guidance
A cause must precede its effect. If the 'result' was already trending, the intervention is not shown to be responsible. The claim in play is that the raffle has 400 coins to give. unsold tickets are not income; sold income is 340 coins The extra figure (18 of 22 rows were added after the first total was announced) is part of what you must not ignore.
Analytical Reasoning · moderate
From this case, which generalisation is unwarranted? Situation: A classroom temperature log. Readings at 09:00 are 16, 17, 16; at 14:00 they are 23, 24, 22, taken by a window in sun. A second observer recorded 4 where the first sheet shows 33.
Review answer guidance
A single setting does not licence a rule about all settings of that type. The claim in play is that the heating is broken in the morning. the afternoon sensor sits in sun, so the comparison is not like-for-like The extra figure (A second observer recorded 4 where the first sheet shows 33) is part of what you must not ignore.
Analytical Reasoning · challenging
Which unstated premise does the author need? Situation: A step-count challenge. Ava's watch shows 8,000; Ben's phone shows 5,500; they walked together. The window used for 9 days is not the window used for 44 days.
Review answer guidance
Write the suppressed step. If that step is false, the argument collapses. The claim in play is that Ava walked further. two devices are not the same measure The extra figure (The window used for 9 days is not the window used for 44 days) is part of what you must not ignore.
Analytical Reasoning · foundational
Which rival hypothesis is most worth testing next? Situation: A bake-sale price list. Cakes are 3 coins, or 5 for 12 coins; a customer wants 4. A note in the margin says 14 cases were excluded without a rule, against 18 kept.
Review answer guidance
Pick the alternative that would produce the same observations, then name the test that could split them. The claim in play is that four singles is the only option. four singles cost 12, the same as the five-pack, so the pack is not cheaper for four The extra figure (A note in the margin says 14 cases were excluded without a rule, against 18 kept) is part of what you must not ignore.
Analytical Reasoning · moderate
Which quantifier in the claim is unjustified? Situation: A river-level board. Yesterday 1.2 m, today 1.4 m; the danger mark is 1.8 m. A post says the river is 'up 20 percent, so almost in flood'. The same label covers 19 events in one table and 29 in the other.
Review answer guidance
All, most, some and none are different claims. Keep the one the data can support. The claim in play is that 20 percent up means near danger. 1.4 versus 1.8 is still 0.4 m below danger; percent of yesterday is the wrong comparison The extra figure (The same label covers 19 events in one table and 29 in the other) is part of what you must not ignore.
Analytical Reasoning · challenging
Where does the analogy break? Situation: A club membership list. 40 members, 12 new this month, 9 left; the chair says membership is up 12. An appendix lists 5 exceptions that the summary of 40 does not mention.
Review answer guidance
Name the property that holds in the source case but not in the target case. The claim in play is that net membership rose by 12. net change is 12 minus 9, which is 3 The extra figure (An appendix lists 5 exceptions that the summary of 40 does not mention) is part of what you must not ignore.
Analytical Reasoning · foundational
What decision rule is being used, and is it stated? Situation: A science-fair judging sheet. Scores are 8, 8, 3; the 3 is from a judge who saw only the poster, not the talk. A side count of 10 used a different definition from 14.
Review answer guidance
If the threshold is implicit, make it explicit before treating the verdict as fair. The claim in play is that the mean of 6.3 is the team's score. the incomplete judging is not the same observation as the other two The extra figure (A side count of 10 used a different definition from 14) is part of what you must not ignore.
Analytical Reasoning · moderate
Which source is weakest, and why does that matter here? Situation: A bus-pass refund rule. Refunds need 10 unused days in a 30-day pass; 8 days remain and 3 were public holidays when buses did not run. The working copy is dated 15 days later than a 25-page cited copy.
Review answer guidance
Match the source type to the claim type. An opinion column cannot carry a prevalence claim. The claim in play is that the unused days are 11. whether holidays count as unused is the missing rule The extra figure (The working copy is dated 15 days later than a 25-page cited copy) is part of what you must not ignore.
Analytical Reasoning · challenging
What was left out that would most change the decision? Situation: A plant-watering rota. Plants need 200 ml every 3 days; a jug is 250 ml with no marks; someone watered 'about a jug' yesterday and today. 20 of 36 rows were added after the first total was announced.
Review answer guidance
Identify the missing group, time period or cost, and say how it would move the recommendation. The claim in play is that the plants are on schedule. two days in a row is not every 3 days, and the volume is unmeasured The extra figure (20 of 36 rows were added after the first total was announced) is part of what you must not ignore.
Analytical Reasoning · foundational
What would you need to see to reverse the current conclusion? Situation: A spelling-test report. The class 'improved 100 percent' from 8 to 16 correct out of 20. A second observer recorded 6 where the first sheet shows 10.
Review answer guidance
State a specific observation that would count the other way. If none exists, the claim is unfalsifiable. The claim in play is that the class doubled to full competence. 16/20 is 80 percent, not competence, even though 8 to 16 is a doubling The extra figure (A second observer recorded 6 where the first sheet shows 10) is part of what you must not ignore.
Analytical Reasoning · moderate
How does aggregation hide an important subgroup difference? Situation: A cinema club vote. 18 votes for film A, 12 for B, 10 abstained of 40 members. The window used for 11 days is not the window used for 21 days.
Review answer guidance
A total can be right while every important subgroup moves the other way. Ask for the split. The claim in play is that A won with most of the club. 18 of 40 is not most of the club; it is most of the votes cast The extra figure (The window used for 11 days is not the window used for 21 days) is part of what you must not ignore.
Analytical Reasoning · challenging
What is the cost of doing nothing, given only the stated facts? Situation: A rain-gauge notebook. Monday 0 mm, Tuesday 12 mm, Wednesday 'gauge overflowed'. The report averages 6 mm a day. A note in the margin says 16 cases were excluded without a rule, against 32 kept.
Review answer guidance
Inaction is an option. Compare it with the proposal using the same outcome and the same unknowns. The claim in play is that 6 mm is the mean of the three days. an overflow is not 0, and you cannot average a missing third day as if it were 0 or 12 The extra figure (A note in the margin says 16 cases were excluded without a rule, against 32 kept) is part of what you must not ignore.
Quantitative Data Literacy · foundational
What percentage change is actually shown, and what is still unknown? Situation: A neighbourhood market stall. Monday takings were 24 coins; Saturday, after a festival, were 36. The same label covers 21 events in one table and 43 in the other.
Review answer guidance
Compute the change from the stated baseline. Percent change without a base, period or definition is incomplete. The claim in play is that Saturday is always busier. 36 versus 24 is a festival Saturday, not a typical week The extra figure (The same label covers 21 events in one table and 43 in the other) is part of what you must not ignore.
Quantitative Data Literacy · moderate
Which ratio should be compared, rather than the raw totals? Situation: A school bus timetable with delayed departures. Four of twelve morning buses were more than ten minutes late on one wet day. An appendix lists 7 exceptions that the summary of 17 does not mention.
Review answer guidance
Divide each count by its own eligible population and period before ranking. The claim in play is that the route is unreliable. one wet day is not the route's usual performance The extra figure (An appendix lists 7 exceptions that the summary of 17 does not mention) is part of what you must not ignore.
Quantitative Data Literacy · challenging
How should the base rate change the reading of the count? Situation: A community clinic appointment sheet. 18 of 80 booked slots were unused, and the sheet does not say whether people cancelled or did not attend. A side count of 12 used a different definition from 28.
Review answer guidance
A large count from a large group can be a lower rate than a small count from a small group. The claim in play is that patients are wasting appointments. unused is not the same as did-not-attend, and the reason is unstated The extra figure (A side count of 12 used a different definition from 28) is part of what you must not ignore.
Quantitative Data Literacy · foundational
The chart's axis does not start at zero. What is the responsible reading? Situation: A household energy bill with estimated readings. The bill is 40 percent higher than last winter, and two of the four readings are estimates. The working copy is dated 17 days later than a 39-page cited copy.
Review answer guidance
Describe the difference in units, not the visual height. A truncated axis exaggerates change. The claim in play is that the household is using much more energy. estimated readings can shift cost between periods The extra figure (The working copy is dated 17 days later than a 39-page cited copy) is part of what you must not ignore.
Quantitative Data Literacy · moderate
What is the chance of the stated event on the information given? Situation: A local library late-return notice. A book due in 14 days was returned on day 16; the fine table charges 2 coins per day after a 1-day grace. 22 of 13 rows were added after the first total was announced.
Review answer guidance
Use the given counts as the sample space. Do not import an outside probability. The claim in play is that the fine must be 4 coins. with a 1-day grace, day 16 is one chargeable day, not two The extra figure (22 of 13 rows were added after the first total was announced) is part of what you must not ignore.
Quantitative Data Literacy · challenging
How should missing values change the reported rate? Situation: A youth club snack budget for a weekend trip. The budget is 90 coins for 15 people; 6 people need a more expensive option that costs twice the standard share. A second observer recorded 8 where the first sheet shows 24.
Review answer guidance
Recalculate under more than one assumption for the missing cases and say whether the ranking survives. The claim in play is that everyone can have the same spend. six double shares consume 12 of 15 units of budget The extra figure (A second observer recorded 8 where the first sheet shows 24) is part of what you must not ignore.
Quantitative Data Literacy · foundational
Which weighted comparison is the fair one? Situation: A sports day results table by age group. Group A (20 runners) had 8 personal bests; group B (8 runners) had 5. The window used for 13 days is not the window used for 35 days.
Review answer guidance
Weight by the size of each group, not by the number of groups. The claim in play is that group B trained better. 5/8 is a higher rate than 8/20, but the groups may not be comparable The extra figure (The window used for 13 days is not the window used for 35 days) is part of what you must not ignore.
Quantitative Data Literacy · moderate
What order-of-magnitude estimate is defensible from the figures given? Situation: A recycling collection calendar with missed streets. 3 of 10 streets were missed in week 1; the notice says 'most collections ran as planned'. A note in the margin says 18 cases were excluded without a rule, against 9 kept.
Review answer guidance
Round to the precision the data support. A precise-looking figure from rough inputs is a false exactness. The claim in play is that the service is mostly fine. a 30 percent miss rate is not 'most' in the ordinary sense of the word The extra figure (A note in the margin says 18 cases were excluded without a rule, against 9 kept) is part of what you must not ignore.
Quantitative Data Literacy · challenging
What per-person figure is required before comparing the two groups? Situation: A weather warning posted on a community board. The warning covers 18:00–22:00; a club night is advertised as 'doors 17:30, ends late'. The same label covers 4 events in one table and 20 in the other.
Review answer guidance
Totals are not comparable when the groups differ in size. Divide by headcount. The claim in play is that the event is unaffected because it starts before 18:00. the overlap after 18:00 is inside the warning The extra figure (The same label covers 4 events in one table and 20 in the other) is part of what you must not ignore.
Quantitative Data Literacy · foundational
The two percentages cover different time windows. What must you do first? Situation: A shared kitchen rota for a student hostel. Two people are listed for Friday; the rule is one cook and one cleaner, and both names appear under cook. An appendix lists 9 exceptions that the summary of 31 does not mention.
Review answer guidance
Put both rates on the same period, or refuse the comparison. The claim in play is that Friday is fully covered. cleaning has no owner if both names are cooks The extra figure (An appendix lists 9 exceptions that the summary of 31 does not mention) is part of what you must not ignore.
Quantitative Data Literacy · moderate
Which part-whole mistake is being made? Situation: A ferry timetable and ticket price list. The 09:00 sailing is 12 coins; the 12:00 is 8 coins but arrives 90 minutes later for a 10:30 appointment. A side count of 14 used a different definition from 42.
Review answer guidance
A percentage of a subset is not the same as a percentage of the whole. The claim in play is that the cheaper sailing is better value. value depends on arriving before 10:30, which the 12:00 cannot do The extra figure (A side count of 14 used a different definition from 42) is part of what you must not ignore.
Quantitative Data Literacy · challenging
What is the conditional rate, not the overall rate? Situation: A food-bank stock sheet after a donation drive. Cans rose from 40 to 70; fresh bread is listed as 0 with a note 'not counted'. The working copy is dated 19 days later than a 16-page cited copy.
Review answer guidance
Restrict the denominator to the group named in the question. The claim in play is that stock is healthy. an uncounted essential with a zero is not evidence of health The extra figure (The working copy is dated 19 days later than a 16-page cited copy) is part of what you must not ignore.
Quantitative Data Literacy · foundational
What expected value follows from the stated chances and amounts? Situation: A class test mark sheet. The mean is 62; one mark of 12 sits with 24 other marks between 58 and 71. 5 of 27 rows were added after the first total was announced.
Review answer guidance
Multiply each amount by its probability and add. Do not pick the most vivid outcome. The claim in play is that the class average shows a weak group. the mean is pulled by one extreme mark The extra figure (5 of 27 rows were added after the first total was announced) is part of what you must not ignore.
Quantitative Data Literacy · moderate
Why might the mean mislead relative to the median here? Situation: A park booking form. Capacity is 40; 28 tickets are sold and 16 complimentary places are reserved. A second observer recorded 10 where the first sheet shows 38.
Review answer guidance
A single extreme value pulls the mean. Report both, or use the median when the tail matters. The claim in play is that 12 places remain. 28 plus 16 is 44, which already exceeds capacity The extra figure (A second observer recorded 10 where the first sheet shows 38) is part of what you must not ignore.
Quantitative Data Literacy · challenging
The figure is an index, not a count. What does a one-point change mean? Situation: A water-saving poster. It says use fell 50 percent after a campaign; the table shows 80 units then 40, but the second month was a holiday shutdown. The window used for 15 days is not the window used for 12 days.
Review answer guidance
Read the index definition. A point on an index is not a person, a pound or a percent unless the documentation says so. The claim in play is that the campaign halved use. the holiday shutdown is a competing explanation The extra figure (The window used for 15 days is not the window used for 12 days) is part of what you must not ignore.
Quantitative Data Literacy · foundational
Where did rounding create a false exactness? Situation: A cycling-club mileage log. Three riders logged 10, 12 and 40 kilometres; the captain reports 'about 20 km each'. A note in the margin says 20 cases were excluded without a rule, against 23 kept.
Review answer guidance
Keep the uncertainty that rounding removed. Do not treat a rounded input as a precise fact. The claim in play is that 20 km is a fair summary. the mean is 20.7 because of one 40 km ride; the median is 12 The extra figure (A note in the margin says 20 cases were excluded without a rule, against 23 kept) is part of what you must not ignore.
Quantitative Data Literacy · moderate
Which unit conversion is required before the comparison is valid? Situation: A lost-property log. 12 umbrellas and 3 phones were logged in a week; the notice says phones are the main problem. The same label covers 6 events in one table and 34 in the other.
Review answer guidance
Convert to one unit. Mixing hours with minutes, or local currency with another, is not a comparison. The claim in play is that phones dominate losses. 12 umbrellas outnumber 3 phones The extra figure (The same label covers 6 events in one table and 34 in the other) is part of what you must not ignore.
Quantitative Data Literacy · challenging
How does double-counting affect the total? Situation: A homework club sign-in. Sign-ins rose from 10 to 15 after a poster; the club also moved next to the canteen that week. An appendix lists 11 exceptions that the summary of 45 does not mention.
Review answer guidance
If categories overlap, adding them inflates the whole. Use a unique-count. The claim in play is that the poster worked. the location change arrived at the same time The extra figure (An appendix lists 11 exceptions that the summary of 45 does not mention) is part of what you must not ignore.
Quantitative Data Literacy · foundational
Why is the percentage unstable at this sample size? Situation: A charity raffle. 200 tickets at 2 coins; 3 prizes cost 90, 40 and 20 coins; 30 tickets remain unsold. A side count of 16 used a different definition from 19.
Review answer guidance
A few observations swinging the other way would reverse a large-looking percentage. The claim in play is that the raffle has 400 coins to give. unsold tickets are not income; sold income is 340 coins The extra figure (A side count of 16 used a different definition from 19) is part of what you must not ignore.
Quantitative Data Literacy · moderate
A total is reported without a denominator. What must you obtain? Situation: A classroom temperature log. Readings at 09:00 are 16, 17, 16; at 14:00 they are 23, 24, 22, taken by a window in sun. The working copy is dated 21 days later than a 30-page cited copy.
Review answer guidance
Ask for the eligible population and period. Rank rates, not raw totals. The claim in play is that the heating is broken in the morning. the afternoon sensor sits in sun, so the comparison is not like-for-like The extra figure (The working copy is dated 21 days later than a 30-page cited copy) is part of what you must not ignore.
Quantitative Data Literacy · challenging
Two points are not a trend. What extra series is required? Situation: A step-count challenge. Ava's watch shows 8,000; Ben's phone shows 5,500; they walked together. 7 of 41 rows were added after the first total was announced.
Review answer guidance
Ask for the values before and after the highlighted pair, and for any other change in that window. The claim in play is that Ava walked further. two devices are not the same measure The extra figure (7 of 41 rows were added after the first total was announced) is part of what you must not ignore.
Quantitative Data Literacy · foundational
The share rose while the total fell. What does that mean? Situation: A bake-sale price list. Cakes are 3 coins, or 5 for 12 coins; a customer wants 4. A second observer recorded 12 where the first sheet shows 15.
Review answer guidance
A larger share of a smaller whole can be fewer people. Report both the share and the count. The claim in play is that four singles is the only option. four singles cost 12, the same as the five-pack, so the pack is not cheaper for four The extra figure (A second observer recorded 12 where the first sheet shows 15) is part of what you must not ignore.
Quantitative Data Literacy · moderate
The gap is reported in percentage points. How is that different from percent? Situation: A river-level board. Yesterday 1.2 m, today 1.4 m; the danger mark is 1.8 m. A post says the river is 'up 20 percent, so almost in flood'. The window used for 17 days is not the window used for 26 days.
Review answer guidance
Percentage points are a subtraction of two rates. Percent of a rate is a different number. The claim in play is that 20 percent up means near danger. 1.4 versus 1.8 is still 0.4 m below danger; percent of yesterday is the wrong comparison The extra figure (The window used for 17 days is not the window used for 26 days) is part of what you must not ignore.
Quantitative Data Literacy · challenging
How should you normalise before ranking the two sites? Situation: A club membership list. 40 members, 12 new this month, 9 left; the chair says membership is up 12. A note in the margin says 22 cases were excluded without a rule, against 37 kept.
Review answer guidance
Use the same definition, the same hours, and the same eligible group. The claim in play is that net membership rose by 12. net change is 12 minus 9, which is 3 The extra figure (A note in the margin says 22 cases were excluded without a rule, against 37 kept) is part of what you must not ignore.
Quantitative Data Literacy · foundational
What range of rates is consistent with the missing data? Situation: A science-fair judging sheet. Scores are 8, 8, 3; the 3 is from a judge who saw only the poster, not the talk. The same label covers 8 events in one table and 11 in the other.
Review answer guidance
Compute the rate if all missing cases are successes, and if all are failures. Report that interval. The claim in play is that the mean of 6.3 is the team's score. the incomplete judging is not the same observation as the other two The extra figure (The same label covers 8 events in one table and 11 in the other) is part of what you must not ignore.
Quantitative Data Literacy · moderate
At what point do the two options cost the same? Situation: A bus-pass refund rule. Refunds need 10 unused days in a 30-day pass; 8 days remain and 3 were public holidays when buses did not run. An appendix lists 13 exceptions that the summary of 22 does not mention.
Review answer guidance
Set the two cost expressions equal and solve. That break-even is the decision boundary given these figures. The claim in play is that the unused days are 11. whether holidays count as unused is the missing rule The extra figure (An appendix lists 13 exceptions that the summary of 22 does not mention) is part of what you must not ignore.
Quantitative Data Literacy · challenging
After the stated adjustment, what residual difference remains? Situation: A plant-watering rota. Plants need 200 ml every 3 days; a jug is 250 ml with no marks; someone watered 'about a jug' yesterday and today. A side count of 18 used a different definition from 33.
Review answer guidance
Subtract the explained portion. Do not treat the remainder as noise without saying so. The claim in play is that the plants are on schedule. two days in a row is not every 3 days, and the volume is unmeasured The extra figure (A side count of 18 used a different definition from 33) is part of what you must not ignore.
Quantitative Data Literacy · foundational
What happens to the headline figure if the extreme observation is set aside? Situation: A spelling-test report. The class 'improved 100 percent' from 8 to 16 correct out of 20. The working copy is dated 4 days later than a 44-page cited copy.
Review answer guidance
Recompute without it. If the story depends on one point, say so. The claim in play is that the class doubled to full competence. 16/20 is 80 percent, not competence, even though 8 to 16 is a doubling The extra figure (The working copy is dated 4 days later than a 44-page cited copy) is part of what you must not ignore.
Quantitative Data Literacy · moderate
What share of the eligible group is actually in the dataset? Situation: A cinema club vote. 18 votes for film A, 12 for B, 10 abstained of 40 members. 9 of 18 rows were added after the first total was announced.
Review answer guidance
Coverage is counted over the group the claim names, not over the files you happened to receive. The claim in play is that A won with most of the club. 18 of 40 is not most of the club; it is most of the votes cast The extra figure (9 of 18 rows were added after the first total was announced) is part of what you must not ignore.
Quantitative Data Literacy · challenging
How many significant figures are justified? Situation: A rain-gauge notebook. Monday 0 mm, Tuesday 12 mm, Wednesday 'gauge overflowed'. The report averages 6 mm a day. A second observer recorded 14 where the first sheet shows 29.
Review answer guidance
Match the output precision to the roughest input. Extra decimals are not extra knowledge. The claim in play is that 6 mm is the mean of the three days. an overflow is not 0, and you cannot average a missing third day as if it were 0 or 12 The extra figure (A second observer recorded 14 where the first sheet shows 29) is part of what you must not ignore.