Exploratory Data Analysis and Visualization

Introduction and Context

Exploratory Data Analysis (EDA) is the systematic examination of data before formal modelling, hypothesis testing, or operational deployment. It combines statistical summaries, visual representations, domain knowledge, and critical questioning to reveal structure, identify data-quality problems, detect unusual observations, and formulate plausible explanations. Visualization is not merely a presentation activity; it is an analytical instrument through which patterns become visible and assumptions become testable.

In postgraduate data analytics, EDA should be understood as an iterative reasoning process. An analyst moves between questions, data transformations, numerical summaries, visual displays, and domain interpretation. The objective is not to produce attractive charts, but to improve the quality of decisions and models. A dashboard may show that sales declined, whereas EDA may reveal that the decline is concentrated in one region, follows a change in product availability, and is accompanied by increased returns. These distinctions have different managerial consequences.

EDA is especially important because real-world data are rarely clean, independent, complete, or neutrally collected. Missing values may be systematic, measurements may be duplicated, categories may be inconsistently coded, and apparent relationships may be caused by time, exposure, or confounding variables. Consequently, every descriptive result should be interpreted in relation to how the data were generated.

Learning Objectives

After completing this chapter, the reader should be able to:

1. Explain the purpose, scope, and iterative nature of EDA.

2. Select and interpret appropriate numerical summaries for different data types and distributions.

3. Use visual methods to examine distributions, relationships, time patterns, and anomalies.

4. Distinguish association from causation and recognize common sources of misleading interpretation.

5. Design dashboards and analytical narratives for executive decision-making.

6. Communicate uncertainty, data limitations, and ethical risks responsibly.

7. Apply a structured EDA workflow to a practical business or engineering problem.

1. Foundations of Exploratory Data Analysis

1.1 Data structures and analytical questions

An EDA begins by clarifying the unit of analysis: a customer, transaction, machine reading, patient, employee, or time interval. Confusing rows with entities is a common source of error. For example, a customer-transaction table contains repeated observations per customer; calculating the average customer income directly from such a table can overweight frequent purchasers.

Variables can be classified as:

• Numerical: quantities on which arithmetic operations are meaningful, such as revenue, temperature, or latency.
• Nominal categorical: labels without an intrinsic order, such as region or payment method.
• Ordinal categorical: ordered categories, such as low, medium, and high risk.
• Temporal: dates, timestamps, durations, or recurring periods.
• Identifier variables: keys used to distinguish records, normally not meaningful predictors by themselves.
• Spatial variables: coordinates, locations, or geographic regions.

The analytical question determines the appropriate summary. “What is typical?” requires a measure of central tendency. “How variable is performance?” requires dispersion. “Which groups differ?” requires comparative summaries and uncertainty assessment. “What changed over time?” requires a temporal display with a suitable time scale.

1.2 EDA and confirmatory analysis

EDA differs from confirmatory analysis, although the two are complementary. Exploratory work generates hypotheses and exposes data problems; confirmatory work evaluates pre-specified hypotheses using appropriate inferential procedures. If an analyst repeatedly searches many variables and groups until a striking pattern appears, the pattern may reflect multiple comparisons rather than a stable finding. Exploratory findings should therefore be labelled as exploratory and, when important, tested on new data or through a clearly specified confirmatory analysis.

A useful EDA cycle is:

1. Define the decision and population of interest.

2. Audit data provenance, granularity, quality, and privacy constraints.

3. Inspect individual variables and their distributions.

4. Examine relationships, groups, and time or spatial structure.

5. Investigate anomalies and missingness.

6. Transform or derive variables only with documented justification.

7. Communicate findings, uncertainty, and limitations.

8. Validate important conclusions using alternative views, samples, or data sources.

This cycle is not strictly linear. A visualization may reveal an error that requires returning to the data audit.

2. Numerical Summaries

2.1 Measures of location

For observations \(x_1,x_2,\ldots,x_n\), the arithmetic mean is

\[

\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_i.

\]

The mean uses every observation and is useful for approximately symmetric distributions without extreme values. It is sensitive to outliers and therefore may not represent a typical observation in a skewed distribution.

The median is the middle ordered observation; for an even number of observations it is commonly the average of the two central observations. It is resistant to extreme values and is often preferable for income, response time, property prices, and other right-skewed variables.

The mode is the most frequently occurring value or category. It is particularly useful for categorical data, for which a mean is generally meaningless. For ordinal data, the median and selected quantiles can be informative, but numerical coding should not automatically imply equal distances between categories.

2.2 Measures of dispersion and position

The range is the difference between the maximum and minimum. It is easy to calculate but depends entirely on two observations. The sample variance is

\[

s^2=\frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})^2,

\]

and the sample standard deviation is \(s=\sqrt{s^2}\). The denominator \(n-1\) is used when estimating population variance from a random sample under standard sampling assumptions. Standard deviation is expressed in the same units as the observations, whereas variance is in squared units.

The interquartile range is

\[

IQR=Q_3-Q_1,

\]

where \(Q_1\) and \(Q_3\) are the first and third quartiles. It measures the spread of the central 50% and is resistant to outliers. A common exploratory rule flags values below \(Q_1-1.5IQR\) or above \(Q_3+1.5IQR\) as potential outliers. This is a screening convention, not a universal error criterion; valid extreme observations can occur beyond these limits.

Percentiles locate observations relative to an ordered dataset. The 90th percentile of response time, for example, is more operationally meaningful than the average when service-level commitments concern the slowest ten percent of requests. Different software packages use different interpolation conventions, so reproducible work should document the method.

The coefficient of variation is

\[

CV=\frac{s}{\bar{x}},

\]

usually reported as a percentage when the mean is positive and meaningfully above zero. It allows relative variability comparisons across positive variables with different units, but is inappropriate when the mean is zero, near zero, or when the variable can take meaningful negative values.

2.3 Shape of distributions

A distribution may be symmetric, right-skewed, left-skewed, heavy-tailed, multimodal, or bounded. Skewness affects the relationship between mean and median: in a right-skewed distribution, the mean is often greater than the median, although this is not a mathematical rule for every dataset. Multimodality may indicate subpopulations, operational regimes, or data combination problems.

Histograms and density plots display distributional shape, but their appearance depends on bin width or smoothing bandwidth. Analysts should examine several reasonable settings and compare with quantile summaries. A box plot efficiently compares groups, while a violin plot combines a density shape with summary information; however, density estimates can be misleading for very small samples.

2.4 Grouped summaries

Grouped means, medians, counts, and quantiles can reveal differences between regions, products, or time periods. Counts should be accompanied by denominators. Ten failures in a group of 100 is not equivalent to ten failures in a group of 10,000. Rates, such as failures per 1,000 operating hours, should use an exposure measure appropriate to the process.

Aggregation can conceal important variation. A monthly average may hide daily peaks; a global average may hide regional deterioration. Analysts should move between multiple levels of aggregation and explicitly state the denominator and time window.

3. Visual Methods for Discovery

3.1 Principles of effective analytical visualization

A good analytical chart makes comparisons easy, represents quantities faithfully, and minimizes unnecessary cognitive load. Position along a common scale is usually easier to compare than area, angle, or colour intensity. Bar charts are therefore often preferable to pie charts for comparing categories. A zero baseline is important for bar lengths unless a truncated scale is clearly justified and labelled; line charts for rates or indices may use a non-zero axis when the context is unambiguous.

Visual design should include an informative title, units, source, time period, definitions, and annotations for material events. Colour should encode a meaningful variable rather than decorate the display. Accessible palettes should support readers with colour-vision deficiencies, and patterns or direct labels should supplement colour where necessary.

3.2 Univariate displays

For numerical variables, use histograms, empirical cumulative distribution functions, box plots, and density plots. An empirical cumulative distribution function shows the proportion of observations less than or equal to each value and is useful for comparing service-level performance. For categorical variables, use sorted bars with counts or percentages. A high-cardinality category should generally be grouped carefully or examined through a focused subset rather than displayed as an unreadable chart.

3.3 Bivariate and multivariate displays

Scatterplots show relationships between two numerical variables. Transparency, jitter, or hexagonal binning can reduce overplotting when many observations overlap. A fitted trend line may summarize association but should not be interpreted as proof of causation. A correlation coefficient can be useful for linear association but may miss nonlinear patterns and can be distorted by outliers.

For categorical versus numerical variables, grouped box plots, interval plots, strip plots, and beeswarm displays show both distribution and group differences. For two categorical variables, contingency tables, proportion bars, and heat maps can be useful. Heat maps require a clear legend and should distinguish counts from normalized proportions.

For multivariate analysis, small multiples often outperform a single crowded chart. Faceting by region or product can reveal whether a relationship is consistent across groups. Parallel coordinates, pair plots, and interactive filtering can be helpful for advanced exploration, but complexity must be controlled. Three-dimensional charts often impair precise comparison and should be used only when they add analytical value.

3.4 Time-series visualization

Time-series charts must preserve temporal order and should identify the observation frequency, time zone, and missing periods. Analysts should distinguish level, trend, seasonality, cycles, and irregular variation. Rolling averages can expose trend, but they smooth peaks and troughs and should not replace the original series. A moving average of window length \(k\), for example, is commonly written as

\[

MA_t=\frac{1}{k}\sum_{j=0}^{k-1}x_{t-j},

\]

where \(x_t\) is the observation at time \(t\), and the window contains the current and preceding \(k-1\) observations. This formula assumes equally spaced observations and a meaningful arithmetic average. It should not be applied blindly to irregular timestamps or rates with changing exposure.

A dual-axis chart can create false visual relationships because the scales may be independently manipulated. Separate aligned panels are generally safer. Cumulative charts should state whether they represent cumulative totals, cumulative averages, or cumulative rates.

3.5 Geographic displays

Maps are valuable when location is analytically meaningful, but they can mislead when large geographic areas receive disproportionate visual attention. Choropleth maps should normally display rates or standardized values rather than raw counts when population or exposure differs across areas. Classification thresholds, projection, missing areas, and spatial dependence should be documented. A map that suggests a regional pattern does not by itself establish a geographic cause.

4. Relationships, Anomalies, and Uncertainty

4.1 Association is not causation

Two variables may be associated because one causes the other, because of reverse causality, because both are influenced by a confounder, or because the pattern is coincidental. A classic aggregation problem occurs when a relationship within groups differs from the relationship after groups are combined; this is often called Simpson’s paradox. Analysts should therefore stratify important comparisons, consider plausible causal structures, and avoid causal language unless the design supports it.

Correlation is not automatically evidence of a useful predictive relationship. A time trend can produce high correlation between unrelated variables, and restricted ranges can conceal relationships. Scatterplots, residual displays, subgroup analysis, and domain knowledge are essential companions to correlation statistics.

4.2 Detecting and evaluating anomalies

An anomaly is an observation that differs substantially from an expected pattern. It may be a data-entry error, sensor malfunction, fraud signal, rare but valid event, or change in the underlying process. Detection methods include robust rules based on the IQR, standardized scores, control charts, nearest-neighbour distances, isolation methods, and domain-specific thresholds.

An anomaly should not be deleted merely because it is inconvenient. The analyst should ask: Is the record valid? Does it represent the target population? Is the unusualness conditional on time, group, or exposure? Would removal alter a decision? Possible treatments include correction from a trusted source, retaining with an indicator, winsorizing for a specific sensitivity analysis, or excluding under a documented rule. Every treatment must be recorded because it affects reproducibility and model risk.

4.3 Missing data

Missingness is itself informative. Common conceptual mechanisms are:

• MCAR: missing completely at random; missingness is unrelated to observed and unobserved values.
• MAR: missing at random conditional on observed variables.
• MNAR: missingness depends on unobserved or missing values, even after conditioning on observed data.

These labels concern a data-generating mechanism, not simply the percentage missing. Visualize missingness by variable, time, group, and record. Complete-case analysis can introduce bias when missingness is systematic. Imputation, missing-indicator methods, or model-based approaches may be appropriate, but the choice should reflect the estimand, mechanism, and uncertainty. Imputed values should not be presented as directly observed facts.

4.4 Communicating uncertainty

Descriptive analysis should communicate uncertainty where sampling, measurement, or estimation uncertainty matters. A confidence interval describes a procedure’s long-run coverage under stated assumptions; it is not, strictly speaking, the probability that a fixed parameter lies in one computed interval. Prediction intervals address the likely range of a future observation and are generally wider than confidence intervals for a mean.

For dashboards, uncertainty may be expressed through interval bands, ranges, scenario values, data-quality flags, or explicit confidence labels. Suppressing uncertainty to make a metric look decisive can produce overconfident decisions. When the data cover the entire operational population rather than a sample, sampling uncertainty may be less relevant, but measurement error, future uncertainty, and changing process conditions remain important.

5. Dashboard Design and Analytical Narratives

5.1 From chart to decision system

A dashboard is an information system, not a collection of charts. Its design should begin with decisions, users, actions, and refresh requirements. Executives often need a concise view of strategic outcomes, drivers, risks, and exceptions; operational users may require detailed filters and near-real-time monitoring. The same metric can be appropriate for one audience and misleading for another.

A useful dashboard hierarchy is:

1. Context: reporting period, population, and definitions.

2. Outcome indicators: key results compared with target or prior period.

3. Drivers: factors associated with movement in the outcome.

4. Exceptions: locations, products, or processes requiring attention.

5. Detail and action: drill-down, owner, threshold, and recommended next step.

Every key performance indicator should have a formal definition, numerator, denominator, inclusion rules, time window, data owner, refresh time, and target. Metrics that appear similar may have different denominators; “conversion rate” must specify whether the denominator is visitors, sessions, leads, or eligible customers.

5.2 Narrative principles

An analytical narrative connects evidence to a decision without overstating certainty. A practical structure is: what happened, where and when it happened, what appears to explain it, how certain the interpretation is, and what action should follow. Annotations should identify product launches, policy changes, outages, or other events that affect interpretation.

Narratives should distinguish observation from inference. “Response time increased by 18% after the deployment” is descriptive; “the deployment caused the increase” is causal and requires stronger evidence. Good narratives also state what is not known and propose a verification step.

5.3 Interactivity and governance

Filters, drill-downs, and tooltips can support exploration, but excessive interactivity can hide the analytical frame and enable selective reporting. Default views should be meaningful, filter states should be visible, and exported charts should retain titles, units, and source information. Version control, metric dictionaries, access controls, audit logs, and retention rules are essential for governed analytics.

6. Worked Example: Service Operations EDA

A software provider monitors API response times for 120,000 requests during one week. The management question is whether a recent deployment created a service-quality problem and where corrective action should focus.

Data audit

Each row represents one request, with timestamp, endpoint, region, response time in milliseconds, status code, deployment indicator, and request size. Duplicate request identifiers are checked. Timestamps are converted to a common time zone, and response times below zero are rejected as impossible. The analyst verifies that failed requests are not absent from the response-time table, because excluding failures would create survivorship bias.

Univariate exploration

The mean response time is 246 ms, while the median is 131 ms and the 95th percentile is 812 ms. The difference between mean and median indicates right skew, and the percentile reveals a long slow tail that the mean alone conceals. A histogram on a logarithmic horizontal scale and an empirical cumulative distribution provide complementary views. Because response time is positive and heavily skewed, the median and upper percentiles are emphasized in the executive dashboard.

Temporal and group exploration

A time-series plot shows that the 95th percentile rose sharply approximately 20 minutes after deployment, while the median changed only modestly. Faceted plots show that the increase is concentrated in the payments endpoint and the European region. A rate chart shows that error frequency also increased for that endpoint. Counts and denominators are displayed because the European region handles a different request volume from other regions.

Anomaly investigation

The largest response times are not automatically removed. Logs show that many are legitimate requests involving unusually large payloads. After stratifying by request size, a separate cluster of extreme values appears for a single server group. Infrastructure records reveal a connection-pool configuration error affecting that group. This demonstrates why anomaly detection should lead to investigation rather than mechanical deletion.

Interpretation and action

The evidence supports an operational hypothesis: the deployment is associated with a post-deployment increase in tail latency, concentrated in a specific endpoint, region, and server group. It does not alone prove that the deployment caused every increase. Engineers roll back the configuration, then compare post-remediation percentiles with the pre-deployment baseline. The dashboard presents median, 95th percentile, error rate, request volume, deployment markers, and a data-quality note. Management receives a clear action: correct the configuration and establish a deployment guardrail based on tail latency, not only the mean.

Learning points

The example illustrates five principles: define the unit of analysis; use distributional summaries rather than one average; segment by meaningful operational dimensions; investigate anomalies in context; and translate findings into a monitored decision and verification plan.

7. Implementation Practices and Tools

EDA may be performed with SQL, spreadsheets, Python, R, statistical packages, or business-intelligence platforms. The tool is less important than reproducibility and analytical discipline. A robust workflow separates raw data from transformed data, stores code and query versions, records assumptions, and produces repeatable outputs. Exploratory notebooks are useful, but production dashboards should use tested pipelines and governed metric definitions.

Automated data-quality checks can monitor schema changes, row counts, duplicate rates, missingness, range violations, freshness, and distribution drift. However, automated checks cannot replace domain review. A valid business event may look like a data error, while a systematic error may pass simple range checks.

AI-assisted chart generation and natural-language summaries can accelerate exploration, but they introduce risks of fabricated explanations, inappropriate chart selection, leakage of confidential information, and untraceable transformations. Human review, source citations, access controls, prompt and output logging where appropriate, and validation against authoritative data are required. AI should assist interpretation, not silently determine business conclusions.

8. Limitations, Ethics, and Governance

EDA can reinforce existing bias when historical data reflect unequal access, discriminatory processes, or uneven measurement. A dashboard showing lower service use in a group may reflect barriers rather than lower need. Analysts should inspect coverage, missingness, measurement invariance, and subgroup performance. Sensitive attributes should be handled according to legal and organizational requirements, with purpose limitation and minimum necessary access.

Privacy risks arise from granular records, small-cell reporting, re-identification, and unnecessary retention. Suppress or aggregate small groups where disclosure risk is material, and document lawful purpose and access rights. Fairness cannot be inferred from visual similarity alone; relevant fairness criteria depend on the decision context and may conflict.

Other limitations include selection bias, measurement error, temporal drift, ecological fallacy, aggregation bias, overplotting, and researcher degrees of freedom. A visually compelling pattern may be unstable under a different time window or subgroup definition. Sensitivity analysis, holdout validation, preregistered follow-up tests where feasible, and consultation with domain experts improve reliability.

9. Best-Practice Checklist

Before publishing an EDA result or dashboard, verify that:

• the population, unit of analysis, and time window are explicit;
• variable definitions, units, and denominators are documented;
• missing values, duplicates, exclusions, and transformations are reported;
• distributions and subgroup differences have been examined;
• unusual observations have been investigated rather than automatically removed;
• charts use honest scales, accessible colours, and clear labels;
• association is not described as causation without suitable evidence;
• uncertainty and data-quality limitations are visible;
• important results have been checked through alternative views or data;
• privacy, fairness, access, auditability, and retention requirements are satisfied;
• the dashboard identifies an owner, refresh time, and decision or action supported.

Contemporary Developments

Modern EDA increasingly includes streaming data, automated anomaly detection, interactive semantic layers, and observability platforms. High-frequency systems require attention to event time, late-arriving data, windowing, and concept drift. Responsible analytics is also moving toward data contracts, lineage graphs, reproducible analytical assets, and model cards or metric documentation. These developments improve scale and governance but do not eliminate the need for statistical reasoning. Automation can find deviations; it cannot independently decide whether a deviation is erroneous, important, fair to act upon, or causally meaningful.

Chapter Summary

Exploratory Data Analysis is an iterative process for understanding data quality, distributions, relationships, anomalies, and decision relevance before formal modelling or action. Numerical summaries should be chosen according to variable type, distribution, and purpose: means are sensitive to extremes, medians and IQRs are more robust, and percentiles often express operational risk effectively. Visualizations reveal shape, subgroup differences, temporal behaviour, and potential anomalies, but their design must preserve quantitative comparisons and disclose context.

Reliable EDA distinguishes association from causation, investigates missingness and unusual observations, and communicates uncertainty. Dashboards should be designed around decisions, clearly defined metrics, appropriate denominators, accessible displays, and governed data pipelines. In professional settings, ethical practice requires attention to privacy, fairness, coverage, measurement bias, and responsible use of AI. The central principle is that EDA is not a preliminary decoration around analytics; it is disciplined evidence-building that connects data to defensible decisions.

Key Terms

Exploratory Data Analysis: Iterative examination of data to discover structure, quality problems, patterns, and hypotheses.

Unit of analysis: Entity or event represented by one analytical observation.

Mean: Arithmetic average of numerical observations.

Median: Middle value of an ordered dataset.

Quantile: Value dividing ordered data at a specified proportion.

Interquartile range: Difference between the third and first quartiles.

Skewness: Asymmetry in a distribution.

Outlier: Observation unusually distant from the prevailing pattern.

Anomaly: Observation or event inconsistent with an expected process pattern.

Missingness: Absence of a recorded value.

MCAR: Missing completely at random.

MAR: Missing at random conditional on observed information.

MNAR: Missing not at random because missingness depends on unobserved information.

Confounder: Variable related to both an apparent explanatory factor and an outcome.

Overplotting: Visual overlap that obscures individual observations.

Small multiples: Repeated comparable charts split by groups or conditions.

Dashboard: Governed visual interface presenting metrics and evidence for decisions.

Denominator: Reference population or exposure used to calculate a rate or proportion.

Confidence interval: Interval produced by a procedure intended to cover a parameter at a stated long-run frequency.

Data provenance: Record of data origin, transformations, ownership, and lineage.

Review Questions

Short Answer Questions

1. Why can the median be more appropriate than the mean for response-time data?

2. What is the purpose of identifying the unit of analysis before summarizing data?

3. Define overplotting and state one method for reducing it.

4. Why should an analyst avoid automatically deleting an outlier?

5. What information should accompany a key performance indicator?

Long Answer Questions

1. Explain the iterative EDA workflow from data audit through communication and validation.

2. Compare histograms, box plots, density plots, and empirical cumulative distribution functions, including their limitations.

3. Discuss how missing-data mechanisms affect EDA and subsequent decisions.

4. Explain why association does not establish causation, using confounding or aggregation as part of your discussion.

5. Design a dashboard for an executive audience and justify its metrics, visual hierarchy, uncertainty displays, and governance controls.

Analytical / Application Questions

1. A product has a mean delivery time of 5.8 days, a median of 3.1 days, and a 95th percentile of 17 days. What does this suggest about the distribution, and which measures should be emphasized in an executive service dashboard?

2. A regional map shows that the largest region has the greatest number of equipment failures. Describe the additional data and visualization steps needed before concluding that it has the worst reliability.

3. After a software release, average revenue per user rises while the number of active users falls. Propose an EDA plan to determine whether the change reflects a genuine improvement, a population-composition effect, a measurement issue, or a causal release effect.

Multiple Choice Questions with Answers

Question 1

Which measure is generally most resistant to extreme observations?

A. Arithmetic mean

B. Median

C. Range

D. Variance

Correct Answer: B. Median

Question 2

For a positive, highly right-skewed response-time variable, which summary is typically especially useful for service-level reporting?

A. Median and upper percentiles

B. Mode only

C. Minimum only

D. Variance without units

Correct Answer: A. Median and upper percentiles

Question 3

What does the IQR measure?

A. The distance between the minimum and maximum

B. The spread of the central 50% of observations

C. The average squared deviation from the mean

D. The most frequent category

Correct Answer: B. The spread of the central 50% of observations

Question 4

Why should rates often be used instead of raw counts when comparing regions of different sizes?

A. Rates remove all uncertainty

B. Rates account for different denominators or exposure levels

C. Counts cannot be visualized

D. Rates always prove causation

Correct Answer: B. Rates account for different denominators or exposure levels

Question 5

Which statement about an observation beyond 1.5 IQR from a quartile is correct?

A. It is certainly a data-entry error

B. It must be deleted before analysis

C. It is a potential outlier requiring investigation

D. It proves the distribution is normal

Correct Answer: C. It is a potential outlier requiring investigation

Question 6

Which display is most directly suited to examining the relationship between two numerical variables?

A. Scatterplot

B. Pie chart

C. Single categorical bar chart

D. Choropleth map

Correct Answer: A. Scatterplot

Question 7

What is a major risk of interpreting a strong correlation between two trending time series?

A. The variables must have different units

B. The relationship may be spurious due to common time trends

C. Correlation cannot be calculated for numerical data

D. The sample necessarily contains no outliers

Correct Answer: B. The relationship may be spurious due to common time trends

Question 8

Which missingness mechanism means that missingness depends on unobserved or missing information even after considering observed variables?

A. MCAR

B. MAR

C. MNAR

D. Random sampling

Correct Answer: C. MNAR

Question 9

Which dashboard practice best supports responsible executive interpretation?

A. Hide definitions to reduce visual clutter

B. Use independent dual axes for every comparison

C. Display metric definitions, denominators, time period, and data-quality notes

D. Remove all uncertainty indicators

Correct Answer: C. Display metric definitions, denominators, time period, and data-quality notes

Question 10

A moving average with window length 4 is calculated for equally spaced observations 10, 14, 18, and 22. What is the average for that window?

A. 14

B. 15

C. 16

D. 18

Correct Answer: C. 16