Univariate EDA in R: Every Variable Deserves Individual Attention Before Modelling

Univariate EDA is the practice of examining one variable at a time — its distribution shape, central tendency, spread, outliers, and missing values — before you combine variables or fit a model. Skip this step and you risk feeding garbage into an algorithm that won't complain until it's too late.

What does a single variable look like before you touch it?

Before you build a model, ask a simpler question: what does each column actually contain? A quick summary reveals the range, typical values, and immediate red flags — like a minimum of -999 that screams "missing data in disguise." Let's start with the airquality dataset, which tracks daily air measurements in New York across the summer of 1973.

Right away you can see that Ozone has 37 missing values and Solar.R has 7. Ozone ranges from 1 to 168 — that's a massive spread — and its mean (42.1) is well above its median (31.5), which hints at right-skewness. You already know three things worth investigating, and you haven't drawn a single chart yet.

Now let's check the data types, because the analysis strategy depends on whether a variable is numeric, integer, or factor.

Ozone, Solar.R, Temp, Month, and Day are integers. Wind is numeric (has decimals). Month and Day are technically numeric but represent calendar values — you'd treat them differently than continuous measurements. This distinction matters: you wouldn't compute skewness for Month.

How do you visualize the distribution of a numeric variable?

Numbers alone can't tell you whether a variable is bell-shaped, has two peaks, or trails off to the right. You need a picture. The histogram is the workhorse of univariate visualization — it chops the range into bins and counts how many observations fall in each.

The histogram reveals a strongly right-skewed distribution. Most days have ozone below 50 ppb, but a handful of extreme days push past 100. This shape is typical of environmental measurements and suggests that the mean is being pulled up by those high values.

A density plot gives you a smoother view of the same information. Think of it as a histogram with infinitely narrow bins — it traces the underlying curve.

The density confirms one clear peak around 20 ppb with a long right tail. There's no second peak, so we're dealing with a unimodal distribution — just a skewed one.

Figure 2: Common distribution shapes you will encounter during univariate analysis.

You can also overlay a density curve onto a histogram for the best of both worlds. The trick is to set freq = FALSE in the histogram so the y-axis shows density instead of counts.

What do skewness and kurtosis actually tell you?

You've seen the histogram, but how do you quantify "how skewed is this?" That's what skewness and kurtosis do — they put a number on the shape.

Skewness measures asymmetry. A perfectly symmetric distribution (like the normal) has skewness = 0. Positive skewness means the right tail is longer (values trail off to the right). Negative skewness means the left tail is longer.

Kurtosis measures tail heaviness. Higher kurtosis means more extreme values (fatter tails). The normal distribution has a kurtosis of 3, so "excess kurtosis" (kurtosis minus 3) tells you how much heavier or lighter the tails are compared to normal.

Let's compute both for Ozone using base R.

A skewness of 1.21 confirms the right-skew we saw in the histogram. The excess kurtosis of 0.84 tells us the tails are slightly heavier than a normal distribution — consistent with those high ozone days pulling the distribution rightward.

Here's a quick reference for interpreting these numbers:

How do you spot and handle outliers?

Outliers aren't automatically "bad data." A temperature of 115°F in Phoenix is extreme but real. A temperature of 999°F is a data entry error. Your job during EDA is to find them — what you do about them depends on domain knowledge.

The boxplot is the classic outlier detector. It draws a box from the 25th to 75th percentile (the IQR), with whiskers extending to 1.5 × IQR beyond each edge. Anything past the whiskers gets flagged as an outlier.

Three values — 115, 135, and 168 — sit above the upper whisker. These are the highest ozone days in the dataset. Are they errors? Probably not — ozone can spike during heat waves. But they could distort a linear model.

Let's identify these outliers programmatically using the IQR rule so you can apply this to any variable.

The lower bound is negative (impossible for ozone), so there are no low-end outliers. Two values exceed the upper bound of 131.1 ppb. Notice that the boxplot flagged 115 as an outlier too — boxplot uses a slightly different calculation internally. The IQR method is more transparent and reproducible.

One safe alternative to deletion is winsorizing — capping outliers at the whisker boundaries rather than removing them.

Capping brought the maximum down from 168 to 131 and barely moved the mean (42.1 → 41.6). That's the beauty of winsorizing — it reduces the influence of extremes without throwing away data points.

How much missing data is too much?

Missing data is the silent problem in most datasets. A variable with 5% missing is easy to handle — impute with the median and move on. A variable with 60% missing might need to be dropped entirely, because any imputation would be more guess than data.

Let's count the damage across all columns.

Ozone has 24.2% missing — that's significant but workable. Solar.R has 4.6% — easy to impute. The other four columns are complete. A visual makes the pattern even clearer.

The dashed lines mark common thresholds: below 5% is "impute and forget," 5-20% is "impute carefully," and above 20% starts raising questions about whether the variable is reliable enough to use.

When should you transform a variable (and which transformation)?

A skewed variable can distort model coefficients, inflate variance, and violate the normality assumptions that many statistical tests rely on. Transformations "compress" the long tail and pull the distribution closer to symmetric.

The two most common transformations are log (for strong right skew) and square root (for moderate right skew). Let's see how they work on Ozone.

The log transform dramatically reduces the right skew. Let's confirm with numbers.

The log transform brought skewness from 1.21 all the way to -0.06 — nearly perfectly symmetric. The sqrt transform improved it to 0.46, which is acceptable but not as good. For Ozone, log is the clear winner.

A Q-Q plot gives you one more visual check. If the points follow the diagonal line, the data is approximately normal.

The original Q-Q plot shows the characteristic upward curve of right-skewed data — points peel away from the line at the high end. After the log transform, the points hug the line much more closely. This variable is now ready for methods that assume normality.

How do you analyze a categorical variable?

Not every variable is numeric. Factor and character columns need a different toolkit: frequency tables and bar charts instead of histograms and density plots. The key questions are: how many levels exist, are the categories balanced, and do any levels need merging?

Let's treat mtcars$cyl (number of cylinders: 4, 6, or 8) as a categorical variable.

Eight-cylinder cars make up 44% of the dataset, four-cylinder cars 34%, and six-cylinder cars 22%. No single level dominates overwhelmingly, so this variable should have predictive value.

A bar plot makes the comparison visual.

The distribution is reasonably balanced. If one level had contained 95% of observations (imagine 30 out of 32 cars being 4-cylinder), that variable would provide almost no predictive signal and you might consider dropping it or merging levels.

Practice Exercises

Exercise 1: Full Univariate Profile of mpg

Create a complete univariate profile of mtcars$mpg: compute mean, median, standard deviation, skewness, and outlier count (using the IQR rule). Then create a histogram and a boxplot side by side. Summarize your findings in a comment.

Exercise 2: Reusable Univariate Profile Function

Write a function my_profile(x) that takes a numeric vector and prints: the mean, median, standard deviation, skewness, number of outliers (IQR rule), and missing percentage. Then apply it to every numeric column of airquality using sapply().

Exercise 3: Outlier Detection + Transformation Assessment

For iris$Sepal.Width: detect outliers with the IQR rule, apply a log transform, compare Q-Q plots before and after, and state whether the transformation improved normality.

Putting It All Together

Let's walk through a complete univariate analysis on airquality$Ozone — the full workflow from raw data to a modelling-ready recommendation.

Figure 1: The univariate EDA workflow: one variable at a time, from raw data to modelling-ready.

That's the complete univariate story for one variable. In a real project, you'd run this analysis (or the my_profile() function from Exercise 2) on every column before touching any modelling code.

Summary

Figure 3: Decision flow: what to do when you find outliers, skewness, or missing data.

The key takeaway: every variable you plan to use in a model deserves five minutes of individual attention. Check the shape, count the NAs, look for outliers, and decide whether a transformation helps. These five minutes can save you hours of debugging a model that "isn't working" because the inputs were never inspected.

References

1. Tukey, J.W. — Exploratory Data Analysis. Addison-Wesley (1977). The foundational text on EDA philosophy and methods.
2. Wickham, H. & Grolemund, G. — R for Data Science, 2nd Edition. O'Reilly (2023). Chapter 11: Exploratory Data Analysis. Link
3. R Core Team — ?summary, ?hist, ?boxplot built-in documentation. Link
4. NIST/SEMATECH — e-Handbook of Statistical Methods: Exploratory Data Analysis. Link
5. Kabacoff, R. — Modern Data Visualization with R. Chapter 4: Univariate Graphs. Link
6. Penn State STAT 500 — Lesson 1: Summarizing Data. Link
7. R Documentation — airquality dataset. Link

Continue Learning

1. Exploratory Data Analysis in R — the full 7-step EDA framework including bivariate and multivariate analysis
2. Descriptive Statistics in R — deeper dive into summary statistics, skimr, and reporting formats
3. Distribution Charts with ggplot2 — advanced histogram, density, and ridgeline plots with ggplot2