These plots expose relationship shape and unusual observations that summary numbers can hide.
A correlation of 0.7 does not tell you whether the points cluster around one straight line, split into two groups, or are driven by one unusual observation. Graphs reveal structures that summary statistics conceal.
A scatterplot displays each observation for two variables. A boxplot compresses one variable into its median, quartiles, whiskers, and potential outliers.
Key question
How can we read a two-variable relationship and a one-variable distribution safely from graphs?
What does a scatterplot show?
Check the axes
Different ranges, units, or transformations can make the same relationship look very different.
What does a boxplot compress?
| Element | Meaning |
|---|---|
| Bottom of box | Q1 |
| Line inside box | Median, Q2 |
| Top of box | Q3 |
| Box length | IQR=Q3−Q1 |
| Whiskers | usually the farthest values within 1.5×IQR |
| Points beyond whiskers | potential outliers |
Boxplots are useful for quickly comparing centers and spreads across groups, but they hide the exact point distribution and the number of peaks.
How should outliers be handled?
If a point beyond the whiskers is a data-entry error, it should be corrected. If it is a rare but valid case, it may contain important information. Before excluding it, inspect the raw data, the measurement process, and its effect on the analysis.
| Point characteristic in regression | Possible meaning |
|---|---|
| Far in the y direction | large-residual outlier |
| Far in the x direction | high-leverage observation |
| Substantially changes the fitted result | influential observation |
When should both plots be used?
Scatterplots by group
An overall positive relationship may weaken or reverse after separating the data into groups. Use color or panels to check subgroup patterns.
Use a scatterplot to inspect the two-variable relationship, then grouped boxplots to compare the outcome's median, IQR, and potential outliers across groups.
Caution
Overlapping boxes or whiskers do not prove that two groups are statistically identical. These plots support exploration; formal inference requires a separate analysis.
Change the relationship and outlier
First change the direction of the relationship and inspect the scatterplot pattern. Then move the final observation sharply and compare how the correlation and boxplot outlier flag respond.
Correlation
0.91
Potential outliers
0
Scatterplot
Boxplot
What to notice
One observation can alter both the apparent relationship in a scatterplot and the outlier display in a boxplot, but the two plots emphasize different information.