How to tell which distribution your data has
We covered a family of distributions. But in real work nobody labels the data "this is log-normal". You have to recognize the shape yourself — it decides which measures and methods are even allowed. Let's assemble a practical checklist for "reading" a distribution.
PDF — density: the height itself is not a probability; the probability of an interval = the area under the curve over it. Total area = 1.
A symmetric "bell": most values crowd near the center, thinning toward the edges. μ sets where the center stands, σ how widely values fan out (σ stretches the bell wider and lower, μ slides it along the axis). Appears wherever a quantity is the sum of many small independent random influences — heights, measurement errors, part deviations. Press "pour" — the real sample\'s histogram approaches the theoretical density.
Step one — always draw a histogram (and a box plot). One glance answers the essentials: one hump or several? Symmetric or tailed? Any outliers? Train your eye right here: switch shapes in the widget's list (uniform, normal, exponential, log-normal, power law) and press "pour" each time — the yellow histogram of a real sample settles onto the theoretical curve, and each shape's silhouette sticks in memory.
An analyst's reflex: opened a new column — drew a histogram and a box plot, and only then computed anything. It catches skew, outliers, bimodality and tells you whether the mean can be trusted at all.
You rarely need the distribution's exact name; what matters is answering three questions — is it symmetric, is the tail heavy, is it one group. The answers drive the choice of measures (mean vs median) and tests (t-test vs non-parametrics).
Service response time almost always has a heavy tail — which is why engineers go straight to percentiles, not the mean. Recognized the shape → picked the right metric.
Bimodal distributions are everywhere in product data: "time to purchase" is often two-humped (impulse vs deliberate buys), and analyzing them as one whole is a mistake.