6.1 Reading & Creating Data Displays: Bar Graphs, Circle Graphs, Dot Plots, Histograms & Box Plots

Why Data Displays Matter on the GED

Data-display questions live inside Quantitative Problem Solving (45% of the test) under assessment target Q.6, "Interpret and create data displays." The GED Testing Service Assessment Guide splits this target into two indicators: Q.6.a (bar graphs and circle graphs, which display categorical data) and Q.6.b (dot plots, histograms, and box plots, which display one-variable numerical data on a number line). Together with Q.6.c (scatter plots and two-variable data, covered in the next section), these questions test whether you can translate between a real-world data set and its visual representation — in both directions.

That "both directions" detail matters because the GED is a computer-delivered test that uses hot-spot and drag-and-drop item types alongside standard multiple choice. A hot-spot item might show you a blank number line and ask you to click where a data point belongs; a drag-and-drop item might ask you to sort values into the correct bars of a histogram. You cannot pass these items by only knowing how to read a finished graph — you also need to know how each display is built.

The Core Terms: Five Displays, Two Data Types

The first distinction to lock in is categorical data (data sorted into named groups, like favorite colors or job titles) versus numerical data (data measured on a scale, like test scores or heights). Bar graphs and circle graphs are for categorical data; dot plots, histograms, and box plots are for numerical data.

Bold key term: a histogram is defined in the GED's own glossary as "a display that expresses frequencies of data in numerical intervals or ranges; similar to a bar graph." That "similar to" is exactly why the GED tests the difference so often — a histogram's bars touch (the data is continuous, like ages 0–10, 11–20, 21–30) while a bar graph's bars have gaps (the categories are separate, like "Blue," "Red," "Green").

Worked Example 1: Circle Graph — Percent to Actual Value

A community center's $40,000 annual budget is shown in a circle graph: Programs 45%, Staff 30%, Facilities 15%, Supplies 10%. How much money goes to Facilities?

The wedge shows a percent of a whole, not a dollar amount. Multiply: 15% × $40,000 = 0.15 × $40,000 = $6,000. A test-taker who selects "15" as the answer (mistaking the percent label for the dollar answer) falls into the most common circle-graph trap on the exam.

Worked Example 2: Histogram vs. Bar Graph Reading

A histogram of quiz scores has bars for the intervals 60–69, 70–79, 80–89, and 90–99, with heights (frequencies) of 3, 8, 10, and 4 students. How many students scored 80 or above?

Add the frequencies for the 80–89 and 90–99 bars: 10 + 4 = 14 students. The trap here is treating each bar as if it represented one exact score (like a bar graph category) rather than a range of scores — you must add whole bins, not read a single bar height as "the answer."

Worked Example 3: Box Plot — Interquartile Range

A box plot of delivery times (minutes) shows: minimum = 12, Q1 = 18, median = 24, Q3 = 32, maximum = 50. What is the interquartile range (IQR)?

IQR = Q3 − Q1 = 32 − 18 = 14 minutes. This is a frequent trap question: some test-takers compute the full range (50 − 12 = 38) instead, because they don't distinguish "range" (max − min, covers 100% of data) from "interquartile range" (Q3 − Q1, covers the middle 50% of data and is not affected by extreme outliers the way the full range is).

Worked Example 4: Dot Plot Counting

A dot plot of the number of pets owned by 15 households shows dots at 0 (4 dots), 1 (5 dots), 2 (3 dots), 3 (2 dots), and 4 (1 dot). How many households own 2 or more pets?

Count dots at 2, 3, and 4: 3 + 2 + 1 = 6 households. Dot plots reward careful, literal counting — the most common error is miscounting a cluster of overlapping dots or including/excluding the boundary value incorrectly.

Common Traps Checklist

• Treating a circle-graph percent as the final answer instead of multiplying by the total.
• Confusing histogram bins (touching, ranges) with bar-graph categories (gapped, discrete labels).
• Computing the full range instead of the interquartile range (or vice versa) on a box plot question.
• Miscounting dots in a dense cluster on a dot plot, or double-counting a value at the edge of an interval.
• Assuming every display type is drawn identically to what you've seen before — always check the axis labels and units before reading values off a graph.

Takeaways: know which display fits categorical versus numerical data, always convert circle-graph percents into real values using the given total, keep histogram bins distinct from bar-graph categories, and remember that a box plot's IQR (not its full range) measures the spread of the middle 50% of the data.