Descriptive Statistics: Center, Spread, and Shape

Before a single test, look at the data. Descriptive statistics summarise a column in three questions: where's the center, how spread out is it, and what shape is it?

Note

Averages hide as much as they reveal. The same mean can describe a tight, symmetric column or a wildly skewed one — the summary you choose matters.

Center

Mean: the average — sensitive to outliers and skew
Median: the middle value — robust, the right choice for skewed data
Mode: the most common value — useful for categories

When mean and median drift apart — as in the chart above — the distribution is skewed, and the median is usually the honest summary.

Spread

Range: max minus min — simple but fragile
Standard deviation: typical distance from the mean
IQR: the middle 50% — resistant to outliers, pairs with the median

Shape

Skew: a long tail on one side pulls the mean toward it
Outliers: extreme values that distort mean and standard deviation
Modality: one peak, or several hidden groups?

Watch out

Reporting only a mean and standard deviation on skewed data is misleading. Show the median and IQR, or a histogram, so the shape is visible.

Descriptive Stats in the SKARI Data Editor

SKARI's Data Editor and column profiling summarise every column at a glance: center, spread, missing values, and distribution shape — before you run anything.

Mean, median, mode, standard deviation and IQR per column
Distribution preview and missing-value counts
Outlier and skew flags to guide your next step

Takeaway

You see the shape of your data first — so you pick the right summary and the right test.

Frequently Asked Questions

Mean or median?

Median for skewed data or when outliers are present; mean for roughly symmetric data.

Standard deviation or IQR?

Standard deviation pairs with the mean for symmetric data; IQR pairs with the median for skewed data.

Why look at shape at all?

Shape decides which summary and which test are valid — skew and outliers break methods that assume normality.

Conclusion

Descriptive statistics are the first, essential look at your data. Match the summary to the shape, and you avoid being fooled by an average before you've even started.

Takeaway

Describe before you test — the summary you choose sets up everything that follows.

The Normal Distribution

The shape most methods assume

Outlier Detection

Handle the extremes that skew summaries

Hypothesis Testing Basics

From describing to testing