An exhibit answer becomes useful when it changes what you would investigate or recommend. This practice set asks you to make that move, rather than describe everything in the chart.
For each exercise, identify the measure and denominator, calculate the comparison that matters, then say your finding aloud. Aim for a clear headline followed by enough evidence to support it. All figures below are illustrative.
1. The overall rate falls while both groups improve
A support manager is considering replacing a system after its resolution rate falls.
| Group | Earlier enquiries | Earlier resolution | Current enquiries | Current resolution |
|---|---|---|---|---|
| Routine | 800 | 90% | 400 | 95% |
| Complex | 200 | 50% | 600 | 60% |
Your task: Calculate the overall rates and explain where to investigate next.
Earlier resolutions are 720 + 100 = 820 out of 1,000, or 82%. Current resolutions are 380 + 360 = 740, or 74%. Both groups improve, but the complex share rises from 20% to 60%.
A useful answer is: “The overall rate falls eight points because the workload shifts towards complex enquiries, despite improvement within both groups. I would investigate why complex demand increased before replacing the system.”
To quantify the effects, apply current rates to the old mix: 80% × 95% + 20% × 60% = 88%. Within-group improvement adds six points; the new mix removes 14, producing the net eight-point fall.
To make this operational, calculate the hours required for each type of support request before adding them together. Penn State's aggregation examples explain why the group and overall patterns can move in opposite directions.
Quick Exhibit Drill
A pizza chain's average profit per order fell by more than a pound this year, and the board blames kitchen cost control.
| Channel | Order share, last year → this year | Profit per order, last year → this year |
|---|---|---|
| Dine-in | 80% → 40% | £5.00 → £5.50 |
| Delivery | 20% → 60% | £1.00 → £1.50 |
At last year's order mix, what would this year's average profit per order be?
2. The cumulative line rises, but acquisition slows
A programme reports these cumulative gross sign-ups, starting from zero before month one:
| Month end | Cumulative sign-ups |
|---|---|
| 1 | 50 |
| 2 | 90 |
| 3 | 120 |
| 4 | 140 |
Your task: Decide whether acquisition is accelerating and identify what this chart cannot tell you about the active customer base.
Monthly additions are 50, 40, 30 and 20. Acquisition is slowing. Cumulative sign-ups continue rising because every month's positive additions are added to the previous total.
Your answer should say: “Monthly additions fell from 50 to 20 even though cumulative sign-ups reached 140. I would inspect prospect volume and conversion, and request cancellations separately to understand active membership.”
If you called the programme's 140 sign-ups “140 active members”, you introduced a measure the table does not contain. Before recommending more acquisition spending, add cancellations, acquisition cost and the year-end active-membership target.
Calculate the change that reveals the answer you need, instead of relying on the raw chart's direction.
3. The pilot headline uses only completed work
A pilot assigned 300 tasks. By the review cutoff, 240 were finished and 216 were accepted. The sponsor presents “90% acceptance” as the reason to roll out.
Your task: Calculate completion, conditional acceptance and accepted delivery across the assigned workload.
Completion is 80%. Acceptance among finished tasks is 90%. Accepted delivery is 72% of assigned tasks: 216 ÷ 300.
There are 60 unfinished and 24 rejected tasks, leaving 84 without accepted output by the cutoff.
A useful answer is: “Finished outputs show 90% acceptance, but the workflow delivers accepted results for 72% of assigned tasks. I would investigate the 60 unfinished tasks and cost the fallback work before deciding to scale.”
Do not collapse every unfinished task into the same cause. Intake problems, access failures, processing delays and manual handoffs call for different actions. Cost each proposed fix against the tasks it can actually help complete.
4. The cheapest route fails a requirement
A client requires at least 95% acceptance and 95th-percentile response time at or below five seconds.
| Route | Cost/request | Acceptance | 95th-percentile response time |
|---|---|---|---|
| A | £0.03 | 93% | 2 seconds |
| B | £0.05 | 96% | 4 seconds |
| C | £0.08 | 98% | 7 seconds |
Your task: Choose the base route and explain which option deserves further cost-reduction work.
B is the only qualifying route. A misses acceptance; C misses response time. Start with B, then investigate whether A can meet the acceptance requirement for a well-defined subset of work or after a specific improvement.
A weighted score that lets low cost compensate for failed acceptance changes the client's decision rule. Apply the requirements before ranking qualifying choices.
Routing different tasks to different providers may change the overall cost, but averaging two percentile values does not produce a combined percentile. Check tail performance separately from the average.
Quick Exhibit Drill
An online pharmacy is choosing a warehouse shift plan for a care-home contract with strict service terms.
- Minimum picking accuracy
- 99.5%
- Maximum dispatch time
- 4 hours
- Analyst's recommendation
- Day crew, cheaper and more accurate than two shifts
| Plan | Cost per order | Picking accuracy | Dispatch time |
|---|---|---|---|
| Night crew | £1.20 | 99.1% | 3 hours |
| Two shifts | £1.60 | 99.7% | 3.5 hours |
| Day crew | £1.40 | 99.8% | 6 hours |
What is the main problem with the analyst's recommendation?
Choose another example by the mistake you made
The next exercise should test the behaviour you want to change.
| If your answer did this | Next practice task |
|---|---|
| Described higher sales without explaining lower profit | Reconcile the revenue and cost changes that explain the profit movement. |
| Used a daily average to dismiss a busy-period queue | Calculate arrivals and service capacity during the peak period. |
| Treated a changed customer mix as deteriorating retention everywhere | Reconstruct retention from the size and renewal rate of each cohort. |
| Recommended an investment from an observed association without testing the mechanism | Separate the proposed mechanism from changes in product mix or maintenance. |
Each example develops a different decision. Do not memorise one sentence and apply it mechanically to every chart.
Review what you said, not only what you calculated
After each attempt, listen for three things. Did the main finding arrive early? Did one or two relevant numbers support it? Did the next action follow from the evidence?
If the arithmetic was correct but you spent a minute touring the table, repeat only the explanation. If the explanation sounded confident but used the wrong denominator, rebuild the calculation before polishing the wording.
Carry the full sequence into an unfamiliar case: understand the exhibit, identify the comparison and explain its implication. Doing that without the worked answer is the test of transfer.
Frequently asked questions
Reading what the chart really shows
Do I need to describe everything in a chart?
No. Lead with a clear headline, support it with one or two relevant numbers, then say what you would do next. Touring every row of a table wastes time and buries the finding. Before speaking, identify the measure and its denominator and calculate the comparison that matters, so your headline rests on evidence.
How can an overall rate fall when every group improves?
Through a mix shift. In the support example, routine enquiries resolve far better than complex ones, and the mix moved from mostly routine to mostly complex. Both groups improved, from 90% to 95% and from 50% to 60%, yet the overall rate fell from 82% to 74% because more enquiries now come from the harder group.
Does a falling resolution rate justify replacing the support system?
Not on this evidence. Because both routine and complex resolution rates improved, performance appears better within each group. The overall decline comes from the changing enquiry mix. A more useful next step is to investigate why complex enquiries rose from 200 to 600, and whether that demand can be reduced or handled differently.
Does a rising cumulative sign-up line mean growth is accelerating?
No. A cumulative line rises whenever any sign-ups occur. Subtract each month's total from the previous one: new sign-ups were 50, 40, 30 and then 20, so acquisition slowed every month. Convert cumulative figures into period additions before judging momentum, otherwise a steadily rising line can hide a clear deceleration.
What can a cumulative sign-up chart not tell me?
It cannot tell you how many customers are still active. The figures are gross sign-ups, so cancellations and lapsed users are not deducted. The 140 cumulative sign-ups could therefore represent fewer active customers. Ask for cancellations or active customer counts before drawing conclusions about the size or health of the programme.
Pilots and client requirements
Is a 90% acceptance rate a good reason to roll out a pilot?
Not by itself. That 90% is acceptance among finished tasks only. Of 300 assigned tasks, 240 were finished, so completion was 80%, and 216 were accepted, meaning accepted delivery was 72% of the assigned workload. Judge the rollout on what the pilot delivered against everything it was asked to do.
What should I investigate next after recalculating the pilot results?
Look at the tasks the headline left out: 60 unfinished by the cutoff and 24 finished but not accepted. Ask why work was unfinished, whether it would have completed later, and what caused the rejections. Those answers show whether the shortfall is a timing issue or a deeper problem that a rollout would amplify.
Should I recommend the cheapest option in a chart?
Only if it meets the client's requirements. Here the client needs at least 95% acceptance and a 95th-percentile response time of five seconds or less. Route A costs £0.03 per request but achieves only 93% acceptance, so it fails. Screen options against hard requirements first, then compare cost among those that pass.
Which route should the client choose, and why not the best performer?
Among the routes shown, Route B is the cheapest that meets both requirements, at £0.05 with 96% acceptance and a four-second response time. Route C has the highest acceptance at 98% but takes seven seconds, breaching the response-time limit while also costing more. Exceeding one requirement does not compensate for failing another.
Choosing and reviewing your practice
How do I decide which chart exercise to practise next?
Choose it by the mistake you made. If you described higher sales without explaining lower profit, practise reconciling the revenue and cost changes behind the profit movement. The aim is to target the behaviour you want to change, rather than working through examples in order or repeating ones you already handle well.
What if I dismissed a queue problem because the daily average looked fine?
Practise calculating arrivals and service capacity during the busy period itself. A daily average spreads peak demand across quiet hours, so it can make a real queue look manageable. Comparing arrivals with capacity at the busiest time shows whether customers will actually wait, which is the evidence a service decision needs.
How should I review my answer after each attempt?
Listen for three things. Did the main finding arrive early? Did one or two relevant numbers support it? Did the next action follow from the evidence? Reviewing what you said, not only what you calculated, reveals whether a correct analysis would actually come across clearly to an interviewer.
My maths was right but my answer rambled. What should I repeat?
Repeat only the explanation. If the arithmetic was correct but you spent a minute touring the table, practise delivering the headline and supporting numbers more directly. The reverse needs a different fix: if you sounded confident but used the wrong denominator, rebuild the calculation before polishing the wording, because fluent delivery cannot rescue a wrong number.