Practice Data Visualization in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Data visualization is the use of graphs, charts, and other visual representations to communicate patterns, trends, and relationships in data.

A picture is worth a thousand numbers. Graphs reveal patterns we'd miss in tables.

Showing a random 20 of 50 problems.

Example 1

medium
A pie chart shows 4 slices: 25%, 25%, 25%, 25%. What is the angle of each slice?

Example 2

medium
A pie chart shows 20 slices representing 20 countries' market shares. Explain why this is a poor choice and suggest a better visualization.

Example 3

easy
To show the relationship between two numeric variables, which chart is best?

Example 4

hard
A histogram has bin widths of 55 for ages 00-5050. There are 1010 bins and bin heights 2,5,9,14,10,8,6,3,2,12, 5, 9, 14, 10, 8, 6, 3, 2, 1. How many people total?

Example 5

challenge
A bar chart with a y-axis from 100 to 104 shows bars of 101 and 103. The visual heights (above 100) suggest 103 is three times 101. What is the true ratio, and what is the distortion?

Example 6

easy
A bar chart's y-axis starts at 80 instead of 0, making a small difference look huge. What is this called?

Example 7

hard
Scatter plots of test score vs hours studied show a 'random cloud' with no pattern. What does this say about the relationship?

Example 8

medium
A histogram of test scores has a long tail extending to the right. What does this 'right-skew' mean?

Example 9

medium
You want to show the share of total revenue from 6 product lines that adds up to 100%. Bar or pie?

Example 10

hard
A line chart's yy-axis runs from 9898 to 102102. Bars at 9999 and 101101 make the difference look huge. What is the actual ratio of 101101 to 9999, and what's the distortion factor?

Example 11

challenge
A 'stacked area chart' over time shows category shares of total. What is its main strength vs. a multi-line chart, and what's a weakness?

Example 12

hard
A time series of monthly sales shows both a long-term trend and seasonal fluctuations. Design the ideal visualization strategy, including which chart type to use and how to highlight both patterns.

Example 13

challenge
A dataset has 6 categories with shares 40%, 25%, 15%, 10%, 7%, 3%. Converting to pie-slice angles, what is the angle (in degrees) of the 15% slice?

Example 14

medium
A pie chart has slices of 120°, 90°, 60°, and 90°. What percentage is the smallest slice?

Example 15

medium
To compare the distribution of salaries across 4 departments at a glance, which chart works well?

Example 16

easy
A bar chart shows favorite sports of 5 categories. Which axis usually holds the categories?

Example 17

medium
You want to show how total revenue splits into product categories AND how the total changes over 5 years. Which chart fits?

Example 18

medium
You want to compare salary distributions in 5 departments. Which chart compares distributions side-by-side?

Example 19

easy
You have two columns: 'hours studied' and 'test score' for 30 students. Which chart shows their relationship?

Example 20

medium
A histogram of test scores is strongly right-skewed. What does the long right tail tell you?
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