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Sort tables and judge complete sets of claims

Use columns, units, filters and derived ratios to decide each table claim without confusing totals and rates.

Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.

1. What you will learn

Use columns, units, filters and derived ratios to decide each table claim without confusing totals and rates.

2. Recall the tools this format uses

Read conditional statements precisely and keep ratios, percentages and units distinct. A fraction compares a part with a named whole; an implication states a relationship rather than its converse. Before combining quantities, check that they refer to the same population and time period. If an arithmetic operation is uncertain, use the linked mathematics lesson to repair it before adding a timer. The purpose of this lesson is to decide what follows from supplied information, not to test outside knowledge of the scenario.

3. Terms for the decision

4. Sort tables and judge complete sets of claims

A table organizes observations, but its visual order is not evidence of importance or causation. Read the column headings and accompanying definitions before examining a claim. A row might represent a site, a week, a person or a category; treating those units as interchangeable can change a denominator. When the table gives jobs, revenue and staff hours, total revenue and revenue per job answer different questions. Sorting by revenue alone cannot identify the best unit revenue unless job counts are equal.

Table Analysis presents several decisions about the same dataset. Evaluate each statement independently against the exact condition it names. A statement beginning 'every' requires checking all relevant rows. A statement beginning 'at least one' needs only one qualifying row. 'Exactly two' requires both finding two matches and ruling out further matches. Do not let an answer to the first statement set a pattern for the remaining answers; true and false decisions are not required to alternate. All parts belong to one graded item here, so an omitted or incorrect part makes the complete response incorrect.

Sorting is a way to reduce search effort. It preserves row relationships while changing their order. Use the column header to sort ascending or descending, and keep the labels attached to their values. A derived quantity such as revenue per job may need to be computed rather than directly sorted. Write that calculation in a small side list, then compare the results. A row with the greatest total need not have the greatest rate, and the middle row in the original display need not be the median after sorting.

5. Translate a claim into a filter

For 'every site with at least three staff hours earns at least twice its job count in revenue units,' first identify the rows satisfying hours greater than or equal to three. Ignore other rows for that conditional statement. In the remaining rows compare revenue with twice jobs. The statement is false if even one qualifying row fails; a nonqualifying row does not refute it. Keep strict and inclusive boundaries separate: 'more than three' excludes a value of three, whereas 'at least three' includes it. Marking the qualifying labels before doing arithmetic reduces the chance of silently changing the population midway through the calculation.

6. Distinguish a ratio of totals from a mean of ratios

Suppose one site completes ten jobs at two revenue units per job and another completes thirty jobs at four units per job. The unweighted mean of their rates is three. Their combined rate is total revenue divided by total jobs: (20+120)/(10+30)=3.5. The larger site contributes more jobs, so its rate receives more weight. Neither number is inherently wrong; they answer different questions. Look for wording such as 'average across sites' versus 'revenue per job across all sites.' A shortcut that averages displayed percentages can fail whenever their bases differ. Reconstruct the numerator and denominator whenever the requested combined quantity is unclear.

7. Keep sorting and arithmetic auditable

To find an extreme, compare the requested column or derived measure, then check ties. If two sites share a rate, a claim that one is uniquely greatest is false. To find a median, sort all relevant numerical observations and use the center or average of the two central values. To find a range, subtract the minimum from the maximum rather than subtracting the first displayed row from the last. A sorted table may put numbers stored as text in an unexpected order in some software; these controls use numeric comparison for numeric cells. Regardless of the interface, inspect the values after sorting so that the chosen row actually matches the intended extremum.

8. Know what the table cannot establish

A cross-sectional association does not establish a cause. A site with longer hours and more completed jobs might also have more staff or different work. Unless the question supplies a design that addresses those alternatives, treat the relationship as descriptive. Missing values are not automatically zeros, and a table of completed work does not count work merely proposed for a future week. Follow the supplied convention for totals and rounding. If a claim asks whether the data support a statement, outside knowledge about how a business usually operates cannot substitute for the table. Explain a rejected statement with a row, calculation or missing dependency rather than with intuition about the topic.

9. Audit an aggregate before accepting a summary

Suppose a report states that every branch improved its completion rate, yet the overall completion rate fell. This need not be a contradiction. If much more work moved to a branch with a lower completion rate, the combined rate can decline even while each branch improves. For example, one branch completes nine of ten jobs and another completes one of ten: the combined rate is one half. In a later period, the first completes nineteen of twenty and the second completes twenty of one hundred. Both branch rates rose, but the combined rate is thirty-nine of one hundred twenty, below one half.

The example shows why a table claim about 'all branches' differs from a claim about 'all jobs.' The first compares rates within rows; the second combines their numerators and denominators. To audit such a claim, compute each row's rate and then separately calculate the pooled rate. Do not average the two percentages unless the denominators are equal or the question explicitly asks for an unweighted mean across branches. Check whether the reporting categories overlap before summing their counts. A useful answer explanation names the population at each step, so a correct calculation is not attached to the wrong conclusion.

10. Transfer the method to a new decision

A manager comparing four branches might initially favor the largest revenue total. Before making a unit-performance claim, compute revenue per completed job and jobs per paid hour. These measures can rank the branches differently because they answer different operational questions. A branch handling complex jobs may have fewer jobs per hour without being poorly managed; the table alone does not identify job complexity unless it supplies that variable.

For practice, read all three claims once, decide which columns each needs, and choose a useful sorting order. Complete one claim at a time while preserving the population and units. After submission, identify whether a wrong decision came from a missed row, a boundary word, a rate calculation or an unsupported causal interpretation. Recompute using the original unsorted table to check that sorting changed only convenience, not the answer. Keep the whole-item score separate from the component explanations: knowing which part failed directs study even though the item requires every part correct.

11. Avoid a decision based on appearance

Do not infer a result from an attractive label or the order of displayed alternatives. A complete answer must preserve every stated restriction and the scope of the requested conclusion. When a tempting response is wrong, identify the exact missing dependency or violated condition; merely saying that it feels too strong does not explain the error.

12. Worked case 1: sort tables and judge complete sets of claims

1. Read the target and its restrictions

   Deliveries, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

   Deliveries: Deliveries, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred. Site, Jobs, Revenue, Hours; North, 20, 40, 4; East, 30, 30, 2; West, 40, 120, 5; South, 50, 100, 3

   Use columns, units, filters and derived ratios to decide each table claim without confusing totals and rates.

2. Derive the deciding relationship

   Unit revenues are 2, 1, 3 and 2; West is highest. North has 20 jobs; East has 30. Both ratios equal 2, despite different totals.

   Unit revenues are 2, 1, 3 and 2; West is highest. North has 20 jobs; East has 30. Both ratios equal 2, despite different totals.

3. Compare competing responses

   Unit revenues are 2, 1, 3 and 2; West is highest. North has 20 jobs; East has 30. Both ratios equal 2, despite different totals.

   Unit revenues are 2, 1, 3 and 2; West is highest. North has 20 jobs; East has 30. Both ratios equal 2, despite different totals.

4. Select and verify the complete response

   West has the greatest revenue per job.: Yes; North completes more jobs than East.: No; South and North have equal revenue per job.: Yes

   Unit revenues are 2, 1, 3 and 2; West is highest. North has 20 jobs; East has 30. Both ratios equal 2, despite different totals.

13. Worked case 2: sort tables and judge complete sets of claims

1. Read the target and its restrictions

   Support tickets, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

   Support tickets: Support tickets, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred. Site, Jobs, Revenue, Hours; North, 23, 46, 4; East, 33, 33, 2; West, 43, 129, 5; South, 56, 112, 3

   Use columns, units, filters and derived ratios to decide each table claim without confusing totals and rates.

2. Derive the deciding relationship

   Compared with twice every job count, West contributes 43 extra revenue units and East contributes a shortfall of 33; the net is positive. 23 is below 33. West has rate 3 and five hours; East has the fewest hours, two.

   Compared with twice every job count, West contributes 43 extra revenue units and East contributes a shortfall of 33; the net is positive. 23 is below 33. West has rate 3 and five hours; East has the fewest hours, two.

3. Check the information boundary

   Translate a claim into a filter

   For 'every site with at least three staff hours earns at least twice its job count in revenue units,' first identify the rows satisfying hours greater than or equal to three. Ignore other rows for that conditional statement. In the remaining rows compare revenue with twice jobs. The statement is false if even one qualifying row fails; a nonqualifying row does not refute it. Keep strict and inclusive boundaries separate: 'more than three' excludes a value of three, whereas 'at least three' includes it. Marking the qualifying labels before doing arithmetic reduces the chance of silently changing the population midway through the calculation.

4. Compare competing responses

   Compared with twice every job count, West contributes 43 extra revenue units and East contributes a shortfall of 33; the net is positive. 23 is below 33. West has rate 3 and five hours; East has the fewest hours, two.

   Compared with twice every job count, West contributes 43 extra revenue units and East contributes a shortfall of 33; the net is positive. 23 is below 33. West has rate 3 and five hours; East has the fewest hours, two.

5. Select and verify the complete response

   The combined revenue per job exceeds 2.: Yes; Sorting by Jobs puts North before East in ascending order.: Yes; The site with the greatest revenue per job also has the fewest hours.: No

   Compared with twice every job count, West contributes 43 extra revenue units and East contributes a shortfall of 33; the net is positive. 23 is below 33. West has rate 3 and five hours; East has the fewest hours, two.

14. Worked case 3: sort tables and judge complete sets of claims

1. Read the target and its restrictions

   Warehouse picks, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

   Warehouse picks: Warehouse picks, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred. Site, Jobs, Revenue, Hours; North, 28, 56, 4; East, 38, 38, 2; West, 48, 144, 5; South, 66, 132, 3

   Use columns, units, filters and derived ratios to decide each table claim without confusing totals and rates.

2. Derive the deciding relationship

   North, West and South qualify with rates 2, 3 and 2. Only West has rate 3; equality at North and South does not qualify. East's revenue and job count are equal.

   North, West and South qualify with rates 2, 3 and 2. Only West has rate 3; equality at North and South does not qualify. East's revenue and job count are equal.

3. Check the information boundary

   Distinguish a ratio of totals from a mean of ratios

   Suppose one site completes ten jobs at two revenue units per job and another completes thirty jobs at four units per job. The unweighted mean of their rates is three. Their combined rate is total revenue divided by total jobs: (20+120)/(10+30)=3.5. The larger site contributes more jobs, so its rate receives more weight. Neither number is inherently wrong; they answer different questions. Look for wording such as 'average across sites' versus 'revenue per job across all sites.' A shortcut that averages displayed percentages can fail whenever their bases differ. Reconstruct the numerator and denominator whenever the requested combined quantity is unclear.

4. Compare competing responses

   North, West and South qualify with rates 2, 3 and 2. Only West has rate 3; equality at North and South does not qualify. East's revenue and job count are equal.

   North, West and South qualify with rates 2, 3 and 2. Only West has rate 3; equality at North and South does not qualify. East's revenue and job count are equal.

5. Select and verify the complete response

   At least three sites earn at least two revenue units per job.: Yes; Exactly one site earns strictly more than two revenue units per job.: Yes; No site has a revenue-per-job value of one.: No

   North, West and South qualify with rates 2, 3 and 2. Only West has rate 3; equality at North and South does not qualify. East's revenue and job count are equal.

6. Verify the target under the original conditions

   At least three sites earn at least two revenue units per job.: Yes; Exactly one site earns strictly more than two revenue units per job.: Yes; No site has a revenue-per-job value of one.: No

   Use columns, units, filters and derived ratios to decide each table claim without confusing totals and rates. North, West and South qualify with rates 2, 3 and 2. Only West has rate 3; equality at North and South does not qualify. East's revenue and job count are equal.

15. Complete the final evidence check

1. Read the target and its restrictions

   Warehouse picks, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

   Warehouse picks: Warehouse picks, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred. Site, Jobs, Revenue, Hours; North, 28, 56, 4; East, 38, 38, 2; West, 48, 144, 5; South, 66, 132, 3

   Use columns, units, filters and derived ratios to decide each table claim without confusing totals and rates.

2. Derive the deciding relationship

   North, West and South qualify with rates 2, 3 and 2. Only West has rate 3; equality at North and South does not qualify. East's revenue and job count are equal.

   North, West and South qualify with rates 2, 3 and 2. Only West has rate 3; equality at North and South does not qualify. East's revenue and job count are equal.

3. Your turn: work this step out. Its working is at the end of the packet.

   Check the information boundary

16. Guided practice

Answer every part using the supplied sources. All parts must be correct.

Deliveries

Deliveries, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

Deliveries, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

17. Guided practice

Answer every part using the supplied sources. All parts must be correct.

Repair orders

Repair orders, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

Repair orders, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

18. Practice

Answer every part using the supplied sources. All parts must be correct.

Support tickets

Support tickets, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

Support tickets, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

19. Practice

Answer every part using the supplied sources. All parts must be correct.

Training seats

Training seats, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

Training seats, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

20. Practice

Answer every part using the supplied sources. All parts must be correct.

Parts inspected

Parts inspected, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

Parts inspected, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

21. Practice

Answer every part using the supplied sources. All parts must be correct.

Subscriptions

Subscriptions, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

Subscriptions, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

22. Practice

Answer every part using the supplied sources. All parts must be correct.

Appointments

Appointments, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

Appointments, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

23. Practice

Answer every part using the supplied sources. All parts must be correct.

Warehouse picks

Warehouse picks, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

Warehouse picks, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

24. Practice

Answer every part using the supplied sources. All parts must be correct.

Reservations

Reservations, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

Reservations, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

25. Practice

Answer every part using the supplied sources. All parts must be correct.

Deliveries

Deliveries, audit 2. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

Deliveries, audit 2. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

26. Somewhere new

Answer every part using the supplied sources. All parts must be correct.

Library loans

Library loans, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

Library loans, audit 1. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

27. Lesson test

Answer three reserved questions without hints. These cases are separate from lesson practice.

28. Test question

Answer every part using the supplied sources. All parts must be correct.

Library loans

Library loans, audit 2. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

Library loans, audit 2. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

29. Test question

Answer every part using the supplied sources. All parts must be correct.

Support tickets

Support tickets, audit 2. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

Support tickets, audit 2. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

30. Test question

Answer every part using the supplied sources. All parts must be correct.

Repair orders

Repair orders, audit 2. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

Repair orders, audit 2. Counts refer to completed jobs in one week. Revenue is in hundreds of credits; hours are paid staff hours. No other jobs occurred.

31. What you can do now

After a study gap, recover the method without notes, then solve a different case. Identify the exact condition that decides the answer before comparing feedback.

Working for the steps left to you

15. Complete the final evidence check, step 3