Practical comparisons and worked calculations, connected to charts you can inspect and edit. Every numerical teaching example is fictional and labelled.
Use a histogram to group individual numeric observations into intervals. Use a bar graph to compare values attached to named categories. The distinction is the meaning of the data, not simply whether the bars touch.
A box plot summarizes centre and spread with quartiles and whiskers. A histogram displays counts across numeric intervals. Choose a box plot for compact group comparisons and a histogram when distribution shape is central to the question.
A stacked dot plot keeps each observation visible at its exact numeric value. A histogram groups observations into intervals. Dot plots suit small datasets where repeats matter; histograms provide a compact view of larger distributions.
Use a scatter plot to inspect the relationship between paired numeric variables. Use a line graph when connecting observations expresses a meaningful progression, such as time or distance. A connection is an additional claim about order.
Bar graphs emphasize amounts compared from a common baseline. Line graphs emphasize movement across an ordered scale. For a time series either can be useful, but the geometry highlights a different aspect of the same observations.
A pie chart represents nonnegative parts of one meaningful whole. A bar graph compares amounts using aligned lengths and can also show parts. Choose bars when exact comparisons, many categories, negative values or multiple series matter.
The mean is the sum divided by the number of observations. The median is the middle position in the sorted data. They answer different questions about centre and can differ substantially when a sample has a long tail.
Standard deviation describes variation among observations. Standard error describes the sampling variability of an estimator. For an independent identically distributed sample with finite variance, the estimated standard error of the mean is sample SD divided by √n.
Bin width sets how much numeric range each histogram bar covers. Narrow bins preserve local detail; wider bins combine it. Choose a width tied to the question, then check nearby reasonable settings without changing the underlying observations.
Quartiles divide ordered data into positions, but finite-sample algorithms can differ. ChartsAI offers R type 7 linear interpolation and medians of halves excluding an odd sample’s middle observation. State the method when reproducing a box plot.
For 1.5 × IQR box plots, an observation is flagged when it falls below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. Fences are calculated cutoffs; whiskers end on actual observations inside them.
An ordinary least-squares line with an intercept minimizes the sum of squared vertical residuals. Its slope is the centred cross-product sum divided by the centred X-square sum. It is a model summary of pairs, not a line joining them.
Pearson r measures the direction and strength of a linear association between paired numeric variables. It divides the centred cross-product sum by the square root of the two centred sums of squares. It is undefined when either variable is constant.
A scatter plot can show association without establishing that changing one variable causes the other to change. A causal claim needs evidence about the data-generating process, plausible alternatives and the comparison being made.
A relative frequency histogram divides each interval count by the total number of observations. In ChartsAI its vertical axis displays that fraction as a percentage. The interval boundaries remain the same as in the count version.
A frequency table lists how often values or groups occur. An exact-value table preserves repeat counts for each distinct value; a grouped table combines observations into intervals. A cumulative column adds frequencies in a meaningful order.
A graph can use correct numbers while encouraging an unsupported interpretation. Check the baseline, denominator, order, missing observations and definition of the measure before trusting the visual story.
A truncated axis starts above the natural zero reference. It can help reveal small positional changes in a line or scatter plot, but it distorts the visible length ratios of bars that represent amounts.
On a logarithmic axis, equal distances represent equal ratios. On a linear axis, equal distances represent equal differences. Ordinary real-valued log scales require positive values; zero and negative observations cannot be placed on them directly.
Radar charts can summarize a profile across several dimensions, but their shapes depend on axis scales and order. Use them cautiously for broad patterns, and use aligned bars or a table when precise dimension-by-dimension comparison is the main task.
Start with the question you want a reader to answer. A distribution question needs different input and geometry from a comparison between categories or an association between two measurements. These guides explain those choices with explicit arithmetic and point to working examples. They also identify what the current tools support, including the limits of fitted lines, quartile summaries and transformed percentages.
Browse the chart examples, download attributed public datasets, or open a free maker. Preserve the source, units and relevant calculation convention when adapting any example.