IAI Actuarial Core Principles · Business Management

Using data, company functions, people skills, influence and clear communication: formula sheet

Full chapter guide

Key formulas

Completeness rate: Completeness = (number of records with the field filled ÷ total records) × 100%; A simple way to quantify missing data for one field. It says nothing about whether the filled values are correct.
Error rate from a sample: Error rate = (records found wrong in sample ÷ sample size) × 100%; Only an estimate for the whole dataset. It is reliable only if the sample is chosen without bias.
Quality dimensions checklist: Completeness, Accuracy, Consistency, Timeliness, Relevance, Validity; Use these as a memory list for any data quality question. Add source and sample size where relevant.
Data classification: Structured / semi-structured / unstructured; internal / external; Classify any dataset on both scales before judging it.
Mean: x̄ = Σx ÷ n; Sum of the values divided by the number of values. Sensitive to outliers.
Median: Middle value of the ordered data (average of the two middle values if n is even); Better than the mean for skewed data such as claim amounts.
Sample standard deviation: s = √[ Σ(x − x̄)² ÷ (n − 1) ]; Measures spread around the mean. Uses n − 1 for a sample.
Coefficient of variation: CV = s ÷ x̄; Compares spread between data sets with different means. Meaningful only when the mean is positive.
Percentage change: (New − Old) ÷ Old × 100%; Always state the base. A rise from 2% to 3% is a 1 percentage point rise but a 50% relative rise.
Approximate 95% confidence interval for a mean: x̄ ± 1.96 × s ÷ √n; A rough guide for a reasonably large sample. It reflects sampling error only, not bias.
Tuckman's team development stages: Forming → Storming → Norming → Performing (→ Adjourning); Teams can move back a stage when members or tasks change. Say what a leader should do at each stage.
Thomas-Kilmann conflict styles: Competing | Collaborating | Compromising | Avoiding | Accommodating; Two dimensions: assertiveness and co-operativeness. Collaborating is high on both. Choose the style to fit the situation.
Maslow's hierarchy of needs: Physiological → Safety → Social → Esteem → Self-actualisation; Lower needs must be reasonably met before higher ones motivate. Use it to explain what motivates a person.
Herzberg's two-factor theory: Hygiene factors (prevent dissatisfaction) vs Motivators (create satisfaction); Pay and conditions are hygiene factors. Achievement, recognition and responsibility are motivators.
Leadership styles: Autocratic | Democratic | Laissez-faire | Situational; Match the style to the task, team experience and time available.
Power-interest grid: high power, high interest: Manage closely; Key decision makers. Involve them early and often, and seek their active support.
Power-interest grid: high power, low interest: Keep satisfied; They can block you but may not follow detail. Give short, relevant updates and avoid surprises.
Power-interest grid: low power, high interest: Keep informed; They can be supporters or sources of useful feedback. Communicate regularly.
Power-interest grid: low power, low interest: Monitor; Minimal effort, but review as their position may change.
Influence cycle: Identify → Analyse → Plan → Engage → Review; A simple memory aid for the stakeholder management process. It is a framework, not a fixed IAI formula.
Communication process: Sender → message (encoded) → medium → receiver (decoded) → feedback; Barriers can arise at any stage. Feedback closes the loop and checks understanding.
Planning checklist for any advice: Audience + Purpose + Message + Medium + Structure; Use this to plan a report, presentation or conversation and to structure an exam answer.
Typical report structure: Summary → Background → Findings → Assumptions and limitations → Recommendations → Appendices; A guide, not a fixed rule. Put the conclusion first for non-technical readers.
Core content of advice: Conclusion + Key assumptions + Uncertainty + Limitations + Next steps; Leaving out assumptions or uncertainty is a professional risk, not only a style issue.

Quick revision

Data can be classified by type, such as numerical or categorical, and by source, such as internal or external.
Check data quality for accuracy, completeness, consistency, relevance and timeliness before using it.
State the limits of the data and how they affect the conclusion.
Choose a presentation method to suit the audience and the message, not just what looks neat.
Company functions depend on each other, so a decision in one area affects the others.
Teams work better with clear roles, shared goals and open discussion.
Leadership style should fit the situation and the people involved.
Identify stakeholders and think about their interests and their power to affect the outcome.
Tailor your message to what the reader already knows and needs to decide.
Lead with the recommendation, then give reasons, risks and next steps.
Avoid unexplained jargon when writing for non-actuaries.
In case studies, tie every point to the facts given.

Common mistakes

Listing the quality dimensions without applying them to the case. Fix: For each dimension, link it to a specific fact in the scenario and say what problem it could cause there.
Treating unstructured data as useless because it is hard to count. Fix: Explain that unstructured data, such as complaints, can reveal causes and customer views that numbers miss, and say how it can be coded or summarised.
Quoting only the mean for skewed data. Fix: Check the shape first. For skewed data give the median and a spread, and explain why.
Choosing a chart because it looks good, not because it fits the message. Fix: Match the chart to the purpose: line for trend, bar for categories, histogram for distribution, scatter for relationships.
Listing functions and their duties without any link between them. Fix: For every function you name, add what it gives to or needs from another function.
Treating the actuarial function as only a calculation team. Fix: Describe the actuary as an adviser to management, who also explains results and limits to other functions.
Listing theories without applying them to the case. Fix: Use each model only to explain a fact from the case, and then give an action.
Saying one leadership style is always best. Fix: Say it depends on task urgency, team skill and risk. Give a situation where another style would suit better.
Listing stakeholders without saying what they want. Fix: For every stakeholder, write their goal or concern in one short phrase, taken from the case.
Placing every stakeholder in 'manage closely'. Fix: Judge power and interest separately. Show that you can prioritise limited time.

Exam tips

Always tie each point to a fact in the case. Generic lists score low in written parts.
Learn the quality dimensions as a list and apply at least three of them to the data in the question.
For MCQs, watch the exact wording: structured means fixed fields, unstructured means no fixed format, and internal or external depends on who holds the data.
Always add what you would do about a limitation, not only that it exists.
End with a clear view on how far the decision maker can rely on the data.
In written and case-study questions, always link the analysis to the decision. Marks go to the recommendation, not just the calculation.
Name the bias specifically, such as survivorship or confirmation, and say how it would change the result.
When asked for a chart, give the type, what goes on each axis, and why it suits the message and audience.