United States
Hong KongReading tables, charts and graphs
Skill 1 lists the forms by name: histograms, bar graphs, circle graphs, pictographs, line plots and tables. Skill 2 asks how presentation can mislead. Read the title, the axes and the units before any value, because that is where the second skill is tested.
The rule names six forms of data display in one bracket. Unusually specific, for a competency statement. It is a list worth taking literally, because it is the state telling you what a data item on this subtest can look like.
The six, and what each is for
| Form | Shows | Watch for |
|---|---|---|
| Bar graph | Comparison between categories | A vertical axis that does not start at zero |
| Histogram | Distribution across intervals | Unequal interval widths |
| Circle graph | Parts of a whole | Percentages that hide a changing total |
| Pictograph | Counts using repeated symbols | What one symbol represents |
| Line plot | Frequency of individual values | Stacked marks, not a line |
| Table | Exact values | Row and column totals, and what is missing |
A histogram is not a bar graph. Bars in a histogram touch, because the horizontal axis is continuous; categories in a bar graph are separate, so the bars have gaps between them. An item can turn on that one distinction and ask you to compute nothing at all.
The order to read in
- Title. What is this about?
- Axis labels. What is being measured on each?
- Units and scale. Thousands? Percentages? Where does the axis start?
- Legend, if there is one
- Only then, the values
Twenty seconds. It prevents the whole class of error this competency was built to catch, and a subtest running at 2.86 minutes a question on our division of the published figures has plenty of room for it.
How presentation misleads
Skill 2 exists for this and it is the most distinctive thing in the Mathematics competencies.
- A truncated axis. Start the vertical axis at 20 and a rise from 22 to 24 looks enormous
- Inconsistent intervals. Bars covering different widths cannot be compared by height
- Percentages without a base. A share can rise while the number falls
- A pictograph where the symbol is scaled by area rather than count, which exaggerates
The percentage case is worth rehearsing. It is the least visual of the four and the most common in real reporting: if a circle graph shows a category rising from 20 percent to 30 percent, you cannot say the number rose unless you also know what happened to the total behind it.
A circle graph shows that one program grew from 20 percent of a district budget to 30 percent over two years. Which conclusion is supported?
- The program received more money in the second year
- The program took a larger share of the budget in the second year
- The district budget grew
- Other programs received less money in the second year
Tables
Tables give exact values, which makes them the friendliest form, and they carry their own traps. Check whether a total row is present and whether the columns actually add to it. Check what is missing: a table showing four schools in a district with more than four schools supports nothing about the district.
That scope check is the same one the Reading subtest asks for under its own diverse-formats skill, and reading graphics and data in a passage covers the reading version.
Where these questions sit
Skills 1 and 2 are two of the seven in Competency 4, which is about 11 of the 35 questions on our split. That split is our arithmetic on the number of skills the rule states, not a published weighting, and this competency ties with algebra on skill count.
Our view: these are the most winnable questions on the Mathematics subtest for a candidate who reads well. The arithmetic is trivial. The reasoning is what the Reading subtest rewards. If algebra frightens you, this is where you make the marks back.
Common questions
What chart types are on the FTCE math subtest?
The rule names six in one skill: histograms, bar graphs, circle graphs, pictographs, line plots and tables. That list is unusually specific for a competency statement and it is worth treating as the actual scope of the skill.
What is the difference between a histogram and a bar graph?
A histogram shows a distribution across continuous intervals, so its bars touch. A bar graph compares separate categories, so its bars have gaps. An item can turn on that distinction without asking you to compute anything.
How can an accurate graph still mislead?
A vertical axis that does not start at zero exaggerates small changes. Unequal intervals make bar heights incomparable. Percentages without a stated total let a share rise while the underlying number falls. The rule devotes a whole skill to this.
What should I check first on a chart?
The title, then the axis labels, then the units and where the scale starts, then the legend, and only then the values. Twenty seconds of that prevents almost every error the misleading-presentation skill is designed to catch.