Descriptive and inferential statistics is technique 3.9 of the IIBA Guide to Business Data Analytics. Descriptive statistics summarize the data you have; inferential statistics use a sample to make "informed generalizations" about a population [1]. For the CBDA exam the technique is listed in Analyze Data (Guide, 2.3.6), 16% of the questions [2]. The guide "purposely avoids" the math [1], so the exam tests choices: which measure, which test, which assumption.
Descriptive and inferential statistics at a glance
This technique is the shared language between the analyst, the data scientist and the business. The facts:
| Item | Value |
|---|---|
| Guide section | 3.9, chapter 3 (Techniques) [1] |
| Purpose | Quantify, compare or predict business information [1] |
| Listed in | Section 2.3.6, Select Techniques for Analyze Data (no BABOK reference) (Guide, 2.3.6) |
| Also used in | Exploratory data analysis, steps 2 and 3 (Guide, 3.11) |
| Elements | Descriptive statistics (8 concepts), inferential statistics (3 concepts) [1] |
| Exam | 75 multiple-choice, scenario-based questions in 2 hours; Analyze Data is 16% [2] |
Last verified: November 2026 (exam facts on iiba.org; guide text checked section by section).
What the guide says the technique is
The guide starts from a practical problem: business data is plentiful, and the challenge is how to interpret and use it [1]. The first step is to quantify the data so it can be compared and assessed for trends. Then it is interpreted in the business context [1].
- Descriptive statistics summarize and describe data. The guide's example is the most natural one: to compare sales across quarters, you think of the average [1].
- Inferential statistics infer meaning from summaries of a sample that represents a population. The guide adds that most advanced analytics, machine learning and neural nets use inferential methods "as their first principle" [1].
The generic definition from a university statistics course is the same idea in one line: inferential procedures use data from an observed sample to make a conclusion about a population [7].
Where statistics is used in the CBDA domains
The technique is formally listed only in Analyze Data, but it runs through several tasks:
| Domain, task or technique | What the guide says |
|---|---|
| 2.3.6, Select Techniques for Analyze Data | Used "to understand the underlying data patterns and signals" during exploratory analysis and modelling; descriptive to describe, inferential for predictive and prescriptive modelling, for example a Bayesian inference model (Guide, 2.3.6) |
| 3.11, Exploratory Data Analysis | Step 2 reviews descriptive statistics; step 3 checks inter-dependence with ANOVA, t-test, F-test and chi square (Guide, 3.11) |
| 2.3.2, Prepare Data | Mean or median imputation may be sound statistically but "may conflict with some business rules" (Guide, 2.3.2) |
| 2.3.5, Assess the Analytics and System Approach Taken | Missing variables such as income or education may be confounding variables (Guide, 2.3.5) |
| 2.4.4, Derive Insights from Data | A correlation between ride demand and crime rate is not enough to model on; analysts need "sound statistical judgment" (Guide, 2.4.4) |
For the full task picture, see Analyze Data, Domain 3.
Descriptive statistics: the eight concepts
The guide lists eight foundational concepts [1]. I put each into one row with the point the exam is most likely to touch:
| Concept | What the guide says [1] | Exam angle |
|---|---|---|
| Types of data | Continuous (revenue, age), discrete (items ordered), categorical (department), ordinal (grades A, B, C) | Treating ordinal data as categorical ignores the order: grade A and grade F count the same |
| Organization of data | Structured ("rectangular") vs unstructured | Structured for speed, unstructured for volume and variety |
| Central tendency | Mean, median, mode, quantiles, percentiles | "Mean is susceptible to outliers"; median is often used to impute missing values |
| Deviation | Variance, standard deviation, skewness, kurtosis | Variance is not in the same unit as the mean and can confuse stakeholders |
| Sample measures | Sample statistics estimate population parameters | You do not survey every customer to find service issues |
| Probability basics | Expected value is a weighted mean of outcomes | Optimizing the wrong measure, for example attrition probability instead of expected loss of business |
| Multivariate measures | Covariance and correlation, from -1 to 1 | Highly correlated drivers (ad spend and channels) risk double counting |
| Probability distributions | How likely different values are around the mean | Best shown as visuals |
Two examples from the guide are worth remembering.
The two stocks. Both have the same yearly mean return, but one moves wildly day to day. The mean alone hides the risk, so you need a measure of deviation [1].
The insurer. An insurer expects claims of $2,000, $1,500 and $1,000. The printed example has typos, but the calculation uses probabilities 0.5, 0.3 and 0.2. So the expected claim is 2,000 × 0.5 + 1,500 × 0.3 + 1,000 × 0.2 = 1,000 + 450 + 200 = $1,650 [1]. If you see this on the exam, trust the method, not the typo.
A statistics course says the same about the mean in plain words: means are "easily affected by extreme values", while the median is a resistant measure [6].
Inferential statistics: tests, regression, Bayes
The guide names three inferential concepts [1].
Statistical tests
Sample statistics, such as a sample mean or variance, are used to draw inferences about the population [1]. The guide's margin note gives one line per test, and I compare it with a standard statistics handbook:
| Test | Guide [1] | Statistics reference |
|---|---|---|
| z-test | "Deduces what range an observed sample mean can take"; margin: checks whether a population parameter differs significantly from a hypothesized value | Used when the standard deviation is known [5] |
| t-test | Used instead of the z-test when the number of observations is small | The more typical case: the standard deviation is estimated from the data [5] |
| F-test | Compares population variances to sample variances | Tests whether the variances of two populations are equal [3] |
| Chi-square | Margin: how well a distribution resembles a hypothesized distribution; body: tests variation such as sample variances | Goodness of fit [4]; also a test of whether one variance equals a specified value [25] |
The chi-square test has two standard uses, and the guide mentions both. The margin note describes goodness of fit [1, 4]. The body text says it is "mostly used to test the variation of test statistics such as sample variances" [1], and section 3.12 adds that a chi-square test "may be used to compare variances" (Guide, 3.12). The handbook has a chi-square test for whether one variance equals a specified value [25]. So, for the exam:
- "Does the data follow this distribution?" points to chi-square goodness of fit.
- "Is this variance equal to a target value?" points to chi-square for a variance.
- "Are the variances of two groups equal?" points to the F-test [3].
The guide adds that in finance and healthcare these tests are industry best practice, and analysts need enough knowledge to engage stakeholders there [1].
Regression analysis
Regression predicts the value of a dependent variable from independent variables [1, 8]. The guide is clear about roles. Analysts may use regression to explain the basic principles of complex models to stakeholders. During modelling, data scientists build the model, and analysts verify "the key factors (independent variables)" with business knowledge [1].
Bayesian inference
Bayesian inference applies Bayes theorem to infer population characteristics. The guide notes two practical uses: quick benchmarking of the success rate of predictions, and easy updating when new data arrives [1].
A worked example: did the new courier make delivery faster?
This example is mine and the numbers are invented. An online store pilots a new courier on 400 orders. The research question: is delivery faster, and is it worth the extra fee?
- Types of data. Delivery time in days is continuous. Region is categorical. The customer rating (1 to 5 stars) is ordinal, so I report its distribution and median, not treat it as five unrelated labels.
- Central tendency. The historical mean is 2.8 days, but the median is 2 days. A few remote islands take 10 days or more. The mean is pulled up by the tail, so the median is a better "typical order".
- Deviation. In the pilot, the mean is 2.6 days and the standard deviation 1.2 days.
- Test. The population standard deviation is unknown, so a t-test fits [5]. Standard error = 1.2 / √400 = 0.06. t = (2.6 − 2.8) / 0.06 = −3.33, p ≈ 0.001. The difference is unlikely to be chance. With 400 orders, t and z give almost the same answer; the guide's "small sample" rule is the simple version of the "unknown standard deviation" rule.
- Practical significance. 0.2 days is about 4.8 hours. A p-value says nothing about whether that matters [9].
- Expected value. Late deliveries (over 4 days) fall from 12% to 8%. Each late order costs a $5 voucher. On 20,000 orders a month: 20,000 × 0.12 × $5 = $12,000 before, 20,000 × 0.08 × $5 = $8,000 after. The saving is $4,000. The new courier charges $0.30 more per order: 20,000 × $0.30 = $6,000. Net result: −$2,000 a month.
The test said "faster". The expected value said "not worth it at this price". This is the guide's warning about optimizing the wrong measure, in numbers [1].
Strengths and limitations
The guide lists four strengths and four limitations [1]:
| Strengths [1] | Limitations [1] |
|---|---|
| Statistical methods are embedded in the core business rules of most organizations | Real-world use needs many assumptions, which must be identified and recorded |
| Business decisions become quantitative values for evidence-based decisions | Not all factors can be identified; every prediction carries uncertainty |
| Helps build consensus, "as the quantitative analysis does not change" | When factors are not distinguishable, a subjective assessment may be better |
| Most business metrics are applications of statistics, which helps set analytics goals | Harder to communicate without visuals and stories |
My take on the last limitation: it is the reason the CBDA has a whole domain on reporting. A t-statistic convinces no one in a steering meeting.
What practitioners and data say about statistics at work
Practitioners agree that the simple measures do most of the work, and that they fail in quiet ways.
- Mostly descriptive. In an analytics forum thread about regression, a commenter at a data consulting firm wrote: "Descriptive statistics are 95% of what businesses use." Another replied that you cannot analyse data without some form of stats [11].
- Practical over statistical significance. In another thread about what barely mattered in real work, an analyst wrote: "Stakeholders care about practical significance: is the effect big enough to matter?" [12]
- Simpson's paradox in an A/B test. An engineer on a travel company's experimentation platform describes every segment moving one way while the total moved the other. The cause was a segment with a data problem and very unequal sample sizes [13].
- Averaging averages. A data science practitioner describes stakeholders averaging monthly ARPU figures to get a quarterly ARPU, which ignores the weights: "Sadly, I've seen this happen in real life." [14]
- The average delivery time. A newsletter for analysts describes a 1.9-day average delivery time that almost became a "2-day guarantee", while 25% of orders took longer than 2 days [15].
- Percentiles in operations. A software engineer summarizing a latency talk writes: "You can't average percentiles." [16]
Data on how people read p-values is not comforting. In a study summarized by a business school, about 90% of researchers described data correctly when the p-value was below 0.05, but only about 15% when it was above [10]. The 2016 statement of the American Statistical Association says a p-value does not measure the probability that a hypothesis is true, nor the size of an effect [9].
From the exam side, a business system analyst who passed the CBDA says "almost all the questions will be scenario-based" [23]. Expect the mean and the median inside a story about orders or salaries, not as a definition.
Experts disagree on statistics in business
Practitioners agree on the basics, but not on how much inference a business needs or how to do it.
1. Descriptive is enough vs inference is essential. The forum view above says descriptive statistics cover most business work [11]. A practitioner blog argues that tasks "like testing whether a sales campaign increased revenue" need inference, and so does knowing why correlation does not imply causation [24]. The guide sides with both: descriptive to describe, inferential for predictive and prescriptive work (Guide, 2.3.6).
2. Mean vs percentiles. One school says averages hide the tail and are useless for describing latency [16]. An engineer at a large cloud provider argues the mean still matters, for example for capacity planning, even though "medians and percentiles suck less than the mean" for many tasks [17]. The guide's position is simple: the choice of measure is contextual to the research problem [1].
3. Frequentist vs Bayesian testing. A data scientist at a freight company argues that Bayesian A/B testing "better balances risk and speed" [18]. An analytics team at an online car marketplace moved to Bayesian methods and wanted to show stakeholders the most likely range of the effect; in their words, "a measurement without an error bar is of little use" [19]. Two data scientists at a music streaming company explain why it is not their default, starting from the point that "Bayesian inference for A/B testing is not one thing." [20]
4. What to do with the 0.05 threshold. A large group of researchers proposed moving the default threshold from 0.05 to 0.005 [21]. A 2019 editorial in a statistics journal went further about "statistically significant": "don't say it and don't use it." [22]
My view: for the exam, learn the guide's version. For work, report the effect size and the range next to any p-value, and write down every assumption, as the guide's first limitation asks [1].
How this technique differs from similar ones
| Compared with | Difference in the guide |
|---|---|
| Exploratory Data Analysis (3.11) | EDA is the process; descriptive statistics and tests are tools inside its steps 2 and 3 (Guide, 3.11) |
| Hypothesis Formulation and Testing (3.12) | 3.12 is the full cycle from a business premise to a test; 3.9 provides the tests and measures (Guide, 2.1.7; [1]) |
| Technical Visualizations (3.18) | Used next to statistics during EDA and modelling to see patterns visually (Guide, 2.3.6) |
| Business Visualizations (3.2) | Communicate results; the guide says statistics are hard to communicate without visuals [1] |
The two neighbours I would review next are Exploratory Data Analysis and Hypothesis Formulation and Testing.
Exam traps for statistics
| Scenario | Tempting answer | Guide reading |
|---|---|---|
| Salaries with a few executives | Report the mean | The mean is susceptible to outliers; consider the median [1] |
| Survey grades A to F | Treat as categories | Ordinal data: treating it as categorical ignores the order [1] |
| Small sample, unknown spread | z-test | t-test for few observations [1] |
| Compare variability of two groups | t-test | F-test compares variances [1, 3] |
| Does data follow an expected distribution? | Correlation | Chi-square goodness-of-fit test [1, 4] |
| HR wants to cut attrition | Optimize the probability of leaving | Optimize the expected value of the business loss [1] |
| Two drivers are highly correlated | Add both to the model | Risk of double counting; check correlation between independent variables [1] |
| Who picks the key factors in a regression? | The data scientist alone | The analyst verifies key factors with business knowledge [1] |
For a full set, try the CBDA statistics questions and the deep dive on what a p-value really says.
Check yourself: CBDA practice questions
1. An HR team asks the analytics team to "minimize the probability that employees leave". What does the guide suggest the analyst point out? A) Use a larger sample. B) Focus on the expected value of the loss of business due to attrition. C) Use the mode. D) Run a chi-square test.
Answer: B. The guide uses this example to show how a team can optimize the wrong measure [1].
2. A pilot has 15 observations and the population standard deviation is unknown. Which test fits? A) z-test. B) t-test. C) F-test. D) Chi-square.
Answer: B. The guide uses the t-test instead of the z-test when there are few observations [1]; a standard handbook ties it to an estimated standard deviation [5].
3. Customer satisfaction is recorded as poor, fair, good, excellent. The data scientist encodes it as unordered categories. What is the risk? A) None. B) The order is ignored, so the analysis is not accurate. C) The variance becomes negative. D) The data becomes unstructured.
Answer: B. Treating ordinal data as categorical ignores the order [1].
Conclusion: the gap between the guide and real business statistics
The guide's toolkit matches practice, but real work leans more on descriptive measures and on judging practical significance than the guide's emphasis on tests suggests.
| Area | Guide | Reality | Delta |
|---|---|---|---|
| Descriptive measures | Eight concepts [1] | Most of everyday business analysis [11] | No gap |
| Statistical tests | z, t, F, chi-square [1] | A/B tests, often with Bayesian methods [18, 19] | Added by practice |
| Practical significance | Not named | What stakeholders care about [12] | Under-used |
| Aggregation errors | Not named | Simpson's paradox, averaging averages [13, 14] | Added by practice |
| Communication | Hard without visuals and stories [1] | p-values often misread [10] | No gap |
So, for the exam, know which measure and which test fits which situation. For real work, add one question before every average: what does it hide?
Related topics
- Correlation vs causation on the CBDA exam.
- Full mock exams in the CBDA exam simulator.
FAQ
What is the difference between descriptive and inferential statistics?
Descriptive statistics summarize and describe the data you have, using measures such as the mean, median, variance and correlation. Inferential statistics use a sample to draw conclusions about a larger population, using tests, regression or Bayesian inference. The CBDA guide covers both in technique 3.9.
Which CBDA domain covers descriptive and inferential statistics?
The guide lists the technique in section 2.3.6, Select Techniques for Analyze Data. Analyze Data is Domain 3 and makes up 16% of the CBDA exam. Statistics also appear inside exploratory data analysis and in deriving insights.
When should I use a t-test instead of a z-test?
The guide says to use a t-test when the sample has few observations. Statistics references put it more precisely: use the t-test when the population standard deviation is unknown and estimated from the sample. With large samples the two give almost the same result.
Why is the median sometimes better than the mean?
The mean is sensitive to outliers, so a few extreme values can pull it far from a typical case. The median splits the data in half and resists extreme values. The guide also notes that the median is often used to impute missing values.
Does a business analyst need to calculate statistics for the CBDA?
The guide purposely avoids mathematical complexity. The analyst needs to choose the right measure, recognize which test fits, record assumptions and explain results to stakeholders. Data scientists usually build the models, and analysts verify the key factors with business knowledge.
Sources
- IIBA: Guide to Business Data Analytics, 3.9 Descriptive and Inferential Statistics
- IIBA: Certification in Business Data Analytics (CBDA)
- NIST/SEMATECH e-Handbook: F-test for equality of two variances
- NIST/SEMATECH e-Handbook: Chi-square goodness-of-fit test
- NIST/SEMATECH e-Handbook: Are the data consistent with the assumed process mean?
- Penn State STAT 500: Measures of central tendency
- Penn State STAT 200: Samples and populations
- Penn State STAT 501: Simple linear regression
- ASA statement on statistical significance and p-values (2016)
- Kellogg Insight: Blinded by statistical significance (2015)
- r/analytics: Do you use linear regression much in your work? (2024)
- r/analytics: What barely mattered in the real world?
- Simpson's paradox in A/B testing
- The "average" trap: your analysis might be wrong (2025)
- Averages, medians, percentiles: when each one is the wrong choice (2026)
- Everything you know about latency is wrong (2015)
- Is the mean really useless? (2017)
- The power of Bayesian A/B testing (2018)
- Auto Trader: Moving to a Bayesian A/B world (2024)
- Spotify Engineering: Why Spotify is not using Bayesian A/B testing (2026)
- Benjamin et al.: Redefine statistical significance (2018)
- Retraction Watch: Time to say goodbye to "statistically significant" (2019)
- Techcanvass: IIBA CBDA certification journey (2024)
- Do you need statistics to work in data? Spoiler: it depends (2025)
- NIST/SEMATECH e-Handbook: Chi-square test for the variance