Choosing the right chart is a core skill in statistics because a graph can make a pattern clear or hide it completely. The best chart depends on what you want to show, such as comparison, distribution, relationship, composition, or change over time. It also depends on the type of data you have, including categorical, numerical, paired, or time-ordered values.
A good chart helps the viewer answer one main question quickly and accurately.
A chart-selection decision guide starts by identifying the purpose of the display, then matches that purpose to the structure of the data. Bar charts compare categories, histograms show the shape of numerical data, scatterplots show relationships between two numerical variables, and line charts show trends across time. Pie charts and stacked bars can show composition, but they work best when there are only a few parts and the totals are meaningful.
Clear labels, consistent scales, and honest axes are just as important as the chart type itself.
Key Facts
- Comparison across categories: use a bar chart or dot plot.
- Distribution of one numerical variable: use a histogram, box plot, or density plot.
- Relationship between two numerical variables: use a scatterplot and consider r for correlation.
- Trend over time: use a line chart with time on the horizontal axis.
- Composition of a whole: use a pie chart, stacked bar chart, or 100% stacked bar chart when parts sum to 100%.
- Mean = sum of values / number of values, and it is often shown with error bars or a reference line.
Vocabulary
- Categorical data
- Data that place observations into groups or labels, such as species, grade level, or favorite color.
- Numerical data
- Data measured with numbers where arithmetic operations are meaningful, such as height, time, or temperature.
- Distribution
- The overall pattern of values in a dataset, including its center, spread, shape, and unusual values.
- Correlation
- A measure of how strongly two numerical variables move together in a roughly linear pattern.
- Time series
- A dataset in which measurements are recorded in time order, such as daily temperature or monthly sales.
Common Mistakes to Avoid
- Using a pie chart for too many categories is misleading because small differences become hard to compare accurately.
- Using a line chart for unordered categories is wrong because connected points imply a continuous sequence or trend.
- Starting a bar chart axis far above zero can exaggerate differences because bar length represents magnitude.
- Using a scatterplot for one numerical variable is not appropriate because scatterplots require paired values from two variables.
Practice Questions
- 1 A school records the number of students in each club: Robotics 24, Drama 18, Art 30, Music 27, and Debate 15. Which chart should be used to compare club sizes, and why?
- 2 A scientist measures the resting heart rates of 80 students and wants to show the shape, center, and spread of the values. Which chart should be used, and what would each bin in the chart represent?
- 3 A city tracks average monthly temperature for 5 years and also records monthly electricity use. Which chart would best show the temperature trend over time, and which chart would best investigate whether hotter months are related to higher electricity use?