What is Descriptive Statistics?

The Story That Starts Everything

It is 7 am on a Monday. A hospital manager walks into her office and finds a spreadsheet with 50,000 rows — every patient visit from the past year. Name, age, diagnosis, treatment, cost, duration, outcome. Her board meeting starts in one hour and they want to know: how is the hospital performing?

She cannot read 50,000 rows in an hour. She cannot hand the spreadsheet to the board. What she needs is a way to compress 50,000 data points into a handful of meaningful numbers — numbers that tell the story of the data without showing every detail.

That is exactly what Descriptive Statistics does.

What is Descriptive Statistics?

Descriptive statistics is the branch of statistics that organises, summarises, and describes a dataset using numbers and charts. It does not make predictions. It does not test hypotheses. It simply answers one question: What does this data look like?

The Four Types of Data

Before you can choose which descriptive statistic to calculate, you must know what type of data you are working with. The wrong statistic on the wrong data type produces meaningless results.

All data falls into one of four types, arranged in a hierarchy from least to most informative:

Data Types — Real Examples Side by Side

Another way to remember it — the thermometer test

Population vs Sample — The Most Important Distinction

Every dataset you will ever work with is either a population or a sample. Getting this wrong leads to the wrong formulas, the wrong conclusions, and sometimes catastrophically bad decisions.

Story — the hospital again

The hospital manager has data on every patient visit last year — all 50,000. That is the population for the question "how did we perform last year?" She has every data point. She uses population formulas (divide by N).

But now she wants to know: do patients in general — across the entire NHS — prefer morning or evening appointments? She cannot collect data from every NHS patient. So she surveys 800 patients from her hospital. That 800 is a sample. She uses sample formulas (divide by n−1) and her conclusions come with uncertainty — they might not perfectly reflect all NHS patients.

Population vs Sample — More Real-World Examples

Python — Identifying Data Types and Basics

Loading and inspecting data types

import pandas as pd
import numpy as np

# Create a realistic hospital dataset
data = {
    'patient_id':    [1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008],
    'blood_type':    ['A', 'O', 'B', 'AB', 'O', 'A', 'O', 'B'],          # Nominal
    'pain_level':    [3, 7, 5, 2, 8, 4, 6, 1],                           # Ordinal (1–10 scale)
    'temperature_c': [37.1, 38.4, 36.9, 39.2, 37.8, 36.5, 38.1, 37.3],  # Interval
    'weight_kg':     [72, 85, 61, 93, 78, 55, 88, 70],                    # Ratio
    'stay_days':     [2, 5, 1, 8, 3, 1, 4, 2],                           # Ratio
}

df = pd.DataFrame(data)
print(df.dtypes)
print("\n", df.head())

Descriptive stats for each data type

import pandas as pd
from scipy import stats

data = {
    'blood_type':    ['A','O','B','AB','O','A','O','B','A','O'],
    'pain_level':    [3, 7, 5, 2, 8, 4, 6, 1, 5, 7],
    'temperature_c': [37.1, 38.4, 36.9, 39.2, 37.8, 36.5, 38.1, 37.3, 37.0, 38.9],
    'weight_kg':     [72, 85, 61, 93, 78, 55, 88, 70, 66, 82],
}
df = pd.DataFrame(data)

# ── Nominal: blood_type — only mode and frequency make sense ──
print("=== Nominal: Blood Type ===")
print(df['blood_type'].value_counts())
print(f"Mode: {df['blood_type'].mode()[0]}")

# ── Ordinal: pain_level — mode and median are appropriate ──
print("\n=== Ordinal: Pain Level ===")
print(f"Mode:   {df['pain_level'].mode()[0]}")
print(f"Median: {df['pain_level'].median()}")

# ── Interval/Ratio: temperature and weight — full stats ──
print("\n=== Ratio: Weight (kg) ===")
print(f"Mean:    {df['weight_kg'].mean():.1f} kg")
print(f"Median:  {df['weight_kg'].median():.1f} kg")
print(f"Std Dev: {df['weight_kg'].std():.1f} kg")  # sample std (ddof=1)
print(f"Min:     {df['weight_kg'].min()} kg