Purpose and function of data analysis: formula sheet

Key formulas

Classification by measurement

Data → Categorical (nominal, ordinal) or Numerical (discrete, continuous)

Ask: is arithmetic meaningful? If not, it is categorical. Ordered categories are ordinal.

Classification by time structure

Cross-sectional = many units, one time; Time series = one unit, many times; Longitudinal = many units, many times

Say which dimension varies. Longitudinal is also called panel data.

Classification by source

Primary = collected for this purpose; Secondary = collected by others or for another purpose

Internal company records reused for a new purpose are secondary in the sense of being collected for another purpose.

Big data characteristics

Volume, Velocity, Variety, Veracity

Some texts add further Vs. Learn these four and be ready to explain each.

Missing data: mean imputation

x̂ᵢ = x̄ = (Σ xⱼ) ÷ n, summed over the n observed values

Keeps the mean unchanged but understates variance. Use only with a few missing values.

Outlier rule of thumb (IQR)

Flag x if x < Q₁ − 1.5 × IQR or x > Q₃ + 1.5 × IQR, where IQR = Q₃ − Q₁

This is a screening rule, not proof of an error. Investigate before removing.

Outlier screen (standard deviations)

z = (x − x̄) ÷ s; investigate if |z| is large, for example above 3

The mean and s are themselves affected by the outlier. The cut-off 3 is a convention.

Reconciliation check

Difference = total from dataset − control total from accounts

A non-zero difference signals missing, duplicated or wrong records.

Quick revision

• Data analysis turns raw data into information that supports a stated decision or question.
• Always state the aim first; the aim drives the data needed and the method used.
• The process runs from defining the objective through collecting, cleaning, analysing and interpreting to communicating results.
• Primary data is collected by you for this purpose; secondary data already exists and was collected for another purpose.
• Discrete data takes countable values; continuous data can take any value in a range.
• Cross-sectional data is taken at one point in time; longitudinal data follows the same units over time.
• Check data for missing values, duplicates, outliers, errors and inconsistent definitions before analysing.
• Cleaning choices must be recorded and justified, and their effect on results should be considered.
• Data protection, confidentiality and fair use matter, especially with personal health or financial data.
• Descriptive analysis summarises the data you have; inferential analysis draws conclusions about a wider population; predictive analysis forecasts new or future outcomes.
• Always state your assumptions and the limits of the data in your conclusion.

Common mistakes

• Treating description and inference as the same thing. Fix: Ask whether the statement is only about the data in hand (description) or about a wider population (inference).
• Giving generic answers with no insurance or finance context. Fix: Tie each aim to a concrete example, such as claim frequency, mortality or reserves.
• Jumping straight to modelling and skipping the objective. Fix: Always start your answer with the objective and the decision that depends on the analysis.
• Listing the stages with no link to the scenario. Fix: For every stage, add one specific action using the data and context in the question.
• Calling numeric codes numerical data Fix: Ask whether arithmetic means anything. If the average of the codes is meaningless, the data is categorical.
• Confusing time series with longitudinal data Fix: Time series tracks one quantity or unit. Longitudinal tracks many units over time. Check how many units there are.
• Deleting every outlier automatically. Fix: Investigate first. Genuine large claims are real risk and should be kept or modelled separately.
• Saying mean imputation is harmless. Fix: State that it understates variance and can distort relationships between variables.
• Calling any use of a sample inferential. Fix: Ask whether a conclusion is drawn about the wider population with uncertainty. If you only report the sample mean, it is descriptive.
• Treating prediction and inference as the same thing. Fix: Inference focuses on parameters and uncertainty about them. Prediction focuses on accuracy for new observations. The same model can serve either aim.

Exam tips

• Start answers with the aim in a single sentence, then give examples. This secures marks quickly.
• Always use the context in the question. Generic lists score less than applied points.
• For 'discuss' questions, mention data quality and uncertainty as limits of any analysis.
• In multiple-choice questions, check whether the scenario talks about the sample only or the wider population.
• Link analysis to a decision at the end, such as pricing, reserving or risk management.
• Tie each stage to the scenario. Generic lists score less than specific actions.
• Allocate words to the stage the question stresses, such as cleaning or communication.
• Mention the iterative loop in at least one sentence.