TSI Math Study Guide
Data Interpretation
Data can be presented in tables, graphs, and other visual displays. On the TSI, you may need to identify the type of data being collected, choose an appropriate graph, read information from a display, compare datasets, and recognize patterns such as trends, clusters, and outliers.
Categorical and quantitative data
Before choosing or interpreting a graph, determine what type of data you have.
Categorical
Places individuals or objects into groups. The categories describe qualities, not measurements.
Usually compared with a bar graph.
Quantitative
Numerical measurements or counts.
Can be analyzed with mean, median, range, and standard deviation.
The distinction matters because different graphs suit different types of data.
Choosing an appropriate graph
Bar graph — compare categories
Which extracurricular activity students prefer. Categories, not numerical intervals — so a histogram wouldn’t be appropriate. Bars have gaps.
Histogram — distribution of numerical data
Test scores grouped into intervals. The bars touch because the intervals form a continuous scale.
Box plot — center and spread
Summarizes a dataset with five values: minimum, Q1, median, Q3, maximum. Especially useful for comparing two or more datasets.
Scatterplot — relationship between two variables
Each point is one observation, such as hours studied vs. test score. Shows trends and relationships.
Reading tables carefully
| Time | Customers |
|---|---|
| 9–11 a.m. | 35 |
| 11 a.m.–1 p.m. | 52 |
| 1–3 p.m. | 48 |
| 3–5 p.m. | 65 |
Which period had the most customers?
3–5 p.m., with 65.
How many visited during the first two periods combined?
35 + 52 = 87
When reading a table
Pay attention to both the row or column labels and the units.
Interpreting histograms
Ages of participants in a program.
Which interval has the most participants?
20–24, with a frequency of 18.
How many participants in total?
5 + 12 + 18 + 9 + 4 = 48
Values are grouped, so you usually can’t determine individual data values. If 18 people are in the 20–24 group, you don’t know how many are 20, 21, 22, 23, or 24. Don’t claim more precision than the graph provides.
Interpreting box plots
The box is the middle 50% of the data, so about half the values fall between 18 and 30.
Comparing box plots
Both classes have the same median, 80. But the boxes differ in width:
The middle half of Class B’s scores is more spread out. A higher median means a higher center; a wider box means greater spread in the middle 50%.
Scatterplots and trends
Positive association
Points rise from left to right. As hours studied increase, scores tend to increase — an overall trend, not a guarantee for every student.
Negative association
Points fall from left to right. As a car’s age increases, its resale value tends to decrease.
No clear association
No obvious upward or downward pattern.
Strength of an association
Stronger
Points lie close to a clear line.
Weaker
Same direction, but the points are widely scattered.
Lines of best fit
Outliers
An outlier lies noticeably far from the rest of the data — here, one point well below an otherwise clear upward trend.
Outliers can affect:
Don’t assume an outlier is a mistake. It may be a legitimate unusual observation.
Association does not prove causation
A scatterplot can show that two variables are associated, but not that one causes the other. If people who exercise more tend to report higher energy, that’s an association — the graph alone doesn’t prove exercise is the reason. Other factors could be involved.
The principle
Association does not necessarily imply causation. Avoid conclusions that go beyond the evidence shown.
TSI strategy: read the labels before the data
Then read the question carefully.
Asks for a trend
Look at the overall pattern, not one point.
Asks for an exact value
Locate the right point, bar, row, or column.
Asks you to compare datasets
Consider both center and spread.
This prevents one of the easiest data-analysis mistakes: performing the right calculation on the wrong values.
Bar graph
compare categories
Histogram
distribution of numerical data
Box plot
center and spread
Scatterplot
relationship between two variables
Don’t just read individual values. Ask what the display tells you about the overall dataset.