Data ScienceBeginner12 min readUpdated March 2025

Descriptive Statistics

Descriptive statistics summarize a dataset with a few meaningful numbers. Learn measures of center, spread and shape, and when each one is the right choice.

Measures of Central Tendency

These describe the "typical" value:

Mean — The arithmetic average. Sensitive to outliers.
Median — The middle value. Robust to outliers; good for skewed data like income.
Mode — The most frequent value. Useful for categorical data.

Measures of Spread

Spread tells you how much values vary around the center:

Range — Max minus min.
Variance and standard deviation — Average squared / typical distance from the mean.
Interquartile range (IQR) — Q3 minus Q1; the spread of the middle 50%.

Computing Statistics

A single outlier can pull the mean far from the median — a good reason to look at both:

python

import numpy as np
from scipy import stats

salaries = np.array([48, 52, 50, 55, 53, 51, 49, 400])  # in thousands

print("mean   :", salaries.mean())            # 94.75
print("median :", np.median(salaries))        # 51.5
print("std    :", salaries.std(ddof=1).round(2))

q1, q3 = np.percentile(salaries, [25, 75])
iqr = q3 - q1
outliers = salaries[(salaries < q1 - 1.5 * iqr) | (salaries > q3 + 1.5 * iqr)]
print("outliers:", outliers)                  # [400]

print("skew   :", stats.skew(salaries).round(2))

Shape: Skewness and Kurtosis

Skewness measures asymmetry (right-skewed data has a long tail of large values). Kurtosis measures how heavy the tails are. Both guide whether a transformation or a robust statistic is appropriate.

Key Takeaways

Use the median for skewed data or data with outliers.
Standard deviation and IQR quantify spread.
The 1.5 x IQR rule is a quick outlier check.
Report center and spread together, never one alone.

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