United States
Hong KongCompetency 4: Probability, statistics and data interpretation
Competency 4 has seven skills and about 11 of the 35 questions on our split. Only one is about probability. Three are about how the presentation or selection of statistics can lead to inappropriate interpretations, which makes this a statistical-literacy competency more than a calculation one.
Read the seven skills and the balance is not what the name suggests. Probability gets one skill. Misleading data gets two, and misleading choice of statistic gets a third.
The seven skills as the rule states them
1. Analyze data presented in various forms (e.g., histograms, bar graphs, circle graphs, pictographs, line plots, tables) to solve problems. 2. Analyze and evaluate how the presentation of data can lead to different or inappropriate interpretations in the context of a real-world situation. 3. Calculate range, mean, median, and mode of data sets. 4. Interpret the meaning of measures of central tendency (i.e., mean, median, mode) and dispersion (i.e., range, standard deviation) in the context of a real-world situation. 5. Analyze and evaluate how the selection of statistics (e.g., mean, median, mode) can lead to different or inappropriate interpretations in the context of a real-world situation. 6. Solve and interpret real-world problems involving probability using counting procedures, tables, and tree diagrams. 7. Infer and analyze conclusions from sample surveys, experiments, and observational studies.
Section 82, Mathematics, incorporated into Rule 6A-4.0021, F.A.C.
How the seven group up
| Group | Skills | What it is |
|---|---|---|
| Reading data | 1 | Extracting values and solving from a chart or table |
| Computing statistics | 3 | Range, mean, median, mode |
| Interpreting statistics | 4 | What a mean or a range means in context |
| Misleading data and statistics | 2, 5 | How presentation and selection distort |
| Probability | 6 | Counting procedures, tables, tree diagrams |
| Inference from studies | 7 | Surveys, experiments, observational studies |
FLDOE publishes 35 questions for the Mathematics subtest and no split beneath it. We apportion the 35 in proportion to the skills the rule states under each competency. This competency and the algebra competency both have seven skills, so they tie; the 11 and the 12 differ only because the column has to sum to 35.
Only one skill is calculation
Skill 3 asks you to calculate range, mean, median and mode. That is the only skill in the competency whose answer is a number you compute from a list, and a calculator is supplied.
Everything else is judgment. What a statistic means, whether a chart supports a claim, whether a conclusion follows from a study design. That is closer to the Reading subtest than most candidates expect, and it needs a different kind of preparation.
The misleading-data skills are the distinctive ones
Two of the seven skills, using almost identical wording, are about inappropriate interpretation. Skill 2 is about how data is presented; skill 5 is about which statistic gets chosen.
- A truncated vertical axis makes a small change look large
- A circle graph of percentages hides a falling total
- A mean pulled by one outlier misrepresents a typical value
- A median hides the spread entirely
Those four cover most of what an item of this kind can ask, and the last two connect directly to skill 4, which is about interpreting central tendency and dispersion in context.
Skill 7 and study design
"Infer and analyze conclusions from sample surveys, experiments, and observational studies." That names three designs and the difference between them decides what you may conclude.
An experiment can support a causal claim, because the researcher assigns the treatment. An observational study cannot. The groups selected themselves, and whatever made them select themselves may be doing the work. A survey describes only the population it sampled.
That is the same intellectual move as the argument-evaluation skill on the Reading subtest, which is worth knowing if you are preparing both. They are separately registered subtests at USD 32.50 each and the underlying reasoning is shared.
Our read
This competency is undersold by its name and by most study material, which treats it as a short chapter on averages. On our estimate it is about a third of the subtest and only one of its seven skills is arithmetic.
If you are strong at reading and weak at algebra, this is where your marks are. And the estimate is ours, derived from the number of skills the rule states, so treat the 11 as an order of magnitude rather than a count.
Common questions
What is Competency 4 on the FTCE Mathematics subtest?
Knowledge of probability, statistics and data interpretation. Seven skills cover reading data in various forms, calculating range, mean, median and mode, interpreting those measures in context, how presentation and selection mislead, probability, and inference from studies.
How much probability is on the FTCE?
One skill of the seven in this competency, covering real-world problems using counting procedures, tables and tree diagrams. The name of the competency puts probability first, and the rule gives it a seventh of the space.
Does the FTCE test misleading graphs?
Yes, twice. Skill 2 covers how the presentation of data can lead to inappropriate interpretations, and skill 5 covers how the selection of a statistic can do the same. Two of the seven skills in this competency are about distortion rather than computation.
What is the difference between an experiment and an observational study?
In an experiment the researcher assigns the treatment, which supports a causal claim. In an observational study the groups selected themselves, so causation cannot be inferred. Skill 7 names both, along with sample surveys, as sources you must reason from carefully.