2.1.14 · D5Data Preprocessing & Feature Engineering
Question bank — Exploratory data analysis (EDA) workflow
Some words you will meet a lot below, all built in the parent note:
Two ideas below lean on a formula and on a plot's internal rules, so let us build both from zero before the traps.
A histogram (bars counting values per bin) and a boxplot are two views of the same numbers, shown side by side here so you can see where they agree and where the boxplot's rule can mislead:
And the two classic "low , strong relationship" shapes — the parabola and the V — are worth seeing before you meet them as edge cases:
True or false — justify
A right-skewed distribution has its mean pulled to the right of its median.
True — the long right tail contains large values that drag the average up, while the median (the middle value) barely moves; so signals right skew.
Skewness of exactly guarantees the distribution is symmetric.
False — skewness measures only the third moment ; a distribution can have zero skew yet still be lopsided in a way that cancels out (e.g. two offsetting bumps). Zero skew is necessary for symmetry, not sufficient.
A Pearson correlation of means the two variables are unrelated.
False — it means no linear relationship. A perfect parabola (symmetric around zero) can give while is fully determined by (see figure 3). Always look at the scatterplot.
If two variables both increase over time, they must be causally linked.
False — this is spurious correlation. Both may be driven by a hidden third variable (a confounder) like population growth; correlation never proves causation.
The correlation matrix is always symmetric.
True — because : swapping which variable is and which is does not change how tightly they track each other, so the matrix mirrors across its diagonal.
Removing a column with 60% missing values is always the right move.
False — if the fact of being missing carries signal (MNAR — Missing Not At Random), you may want a "was-missing" flag or careful imputation; blindly dropping can throw away predictive information.
A histogram and a boxplot of the same variable always agree perfectly about skew.
False — they draw the same numbers, so gross skew shows in both, but they emphasize different things: the boxplot compresses each tail into a single whisker plus dots, so it can under-state a long thin tail (few points, short whisker) or over-flag it as many separate outlier dots, while the histogram's bins show the tail's true mass. If they disagree wildly suspect a bug; mild disagreement is just the whisker rule versus binning (figure 2).
Standardizing skewness by dividing by makes it independent of the unit of measurement.
True — measuring income in dollars vs cents scales the cubed deviations and by the same factor, so the ratio is unchanged; that scale-invariance is exactly why we divide.
Spot the error
"Age has 9,876 unique values across 10,000 rows, so it is a very rich, informative feature."
The error: near-unique cardinality means it behaves like an identifier, not a feature — a value seen once teaches a model nothing generalizable. High cardinality on a numeric ID is a red flag, not richness.
"Income and age have , so age causes higher income."
Correlation strength says nothing about direction of causation. describes a linear association; the causal story (experience, seniority, or a lurking variable) needs domain reasoning or an experiment, not the coefficient.
"The mean purchase amount is $250, so a typical customer spends about $250."
If the variable is right-skewed (a few whales), the mean is inflated above the typical value. Report the median for "typical", and cite the mean only alongside spread and skew.
"I computed Pearson between product_category and income."
Pearson needs two numerical variables.
product_category is categorical, so the arithmetic (means, deviations) is meaningless on its labels. Use grouped boxplots or an ANOVA F-test instead."Electronics is 45% of rows and the rest are smaller, so the data is clean and balanced."
45% vs 30/15/10 is imbalance, not balance. For a classification target this skews the model toward the majority class; imbalance is a quality note to flag, not evidence of cleanliness.
"Two predictors have , so together they give the model twice the information."
They are nearly redundant (multicollinearity). They carry almost the same information, which can destabilize regression coefficients rather than double the signal — usually you drop or combine one.
"I filled the missing incomes with so the column is complete now."
Zero is a real value here (it means "no income"), so this silently invents 500 unemployed customers and corrupts the mean, skew, and any correlation. Use a sentinel/flag or a principled imputation, and always record what you did.
Why questions
Why do we do univariate analysis before bivariate analysis?
You cannot correctly read a relationship between two variables until you understand each one's own shape and quirks — a wild outlier or hidden skew in one variable can fake or hide a correlation.
Why divide covariance by to get correlation?
Covariance answers "do they move together?" but its size depends on the units, so it is uncomparable across pairs. Dividing by both standard deviations rescales it onto a fixed ruler, making any two correlations directly comparable.
Why prefer a heatmap over reading a raw correlation table of numbers?
The eye spots colour patterns far faster than it parses a grid of decimals; a heatmap makes clusters of high correlation (multicollinearity) and negative blocks pop out instantly, which is the whole point of exploratory analysis.
Why check data types in the very first inspection step?
A date stored as text (
object) or a number stored as a string will silently break every statistic and plot downstream; catching the mismatch in the first minute saves hours of confused debugging later.Why might a log transform be applied to a right-skewed variable?
The log compresses the stretched large-value tail more than the small values, pulling the distribution toward symmetry so that mean-based methods and linear models behave better.
Why is a regression line drawn on top of a scatterplot, not instead of it?
The line summarizes the linear trend, but only the raw points reveal whether that summary is honest — curvature, fanning spread, or clusters would make the single misleading, and you can only see them in the cloud of points.
Why do we distinguish MCAR, MAR, and MNAR types of missingness?
These stand for Missing Completely At Random (missingness unrelated to anything), Missing At Random (explained by other observed variables), and Missing Not At Random (tied to the hidden value itself). The mechanism decides whether dropping or imputing is safe: MCAR loses only sample size, but MNAR biases every estimate, so you must handle it deliberately rather than ignore it.
Edge cases
A column has exactly one unique value (constant). What does correlation with it give?
Undefined — its standard deviation is , so dividing by is division by zero. A constant column carries no information and should be dropped before analysis.
You have only data points. What is their Pearson correlation?
Always exactly (or undefined if either point repeats a coordinate) — two points define a line, so the "linear fit" is perfect by construction. Correlation is meaningless at such tiny .
Every value in a numeric column is identical except one huge outlier. What happens to mean vs median?
The median stays at the common value (robust), while the mean is dragged toward the outlier — a textbook demonstration of why the median is the robust measure of centre.
A boxplot shows no whiskers and no box — just a flat line. What does that mean?
The variable has (almost) zero spread: nearly all values are equal, so , the median and collapse to one point and . It is effectively constant and near-useless as a feature.
Two variables have a perfect V-shaped relationship (down then up). What does report?
Close to , because the downward and upward halves cancel in the linear measure (figure 3, right panel). This is the classic case where a low hides a strong non-linear dependence — inspect the plot.
A category appears in the training rows but never in a value-count until you refresh the data. What EDA habit catches this?
Re-checking cardinality and value counts after any data reload — silently appearing/vanishing categories signal a pipeline or filtering change that would break encodings downstream.
The income mean equals its median almost exactly. What does that suggest about skew?
Near-symmetry — with mean median the third-moment skew is close to , so the distribution is roughly balanced and no log transform is needed.
Recall Self-check before you move on
Can you, from memory, give one example where but the variables are strongly related? ::: Yes — a symmetric parabola centred at , or a V-shape: strong dependence, zero linear correlation. Which measure of centre do you trust on skewed data, and why? ::: The median — it is unmoved by the extreme tail values that inflate the mean. What do MCAR, MAR and MNAR stand for? ::: Missing Completely At Random, Missing At Random, and Missing Not At Random.
Related deep dives: 2.1.15-Statistical-measuresfor-data-analysis, 2.1.16-Data-visualization-techniques, 2.1.3-Handling-missing-data, 2.1.5-Outlier-detection-and-treatment, 2.2.8-Feature-selection-methods, 3.1.1-Bias-variance-tradeoff.