Ratio

A ratio compares two quantities of the same kind.

"For every 2 boys, there are 3 girls." Ratio = 2 : 3

Just a comparison - no units needed
Both numbers must be in the same unit

Rate

A rate compares two quantities of different kinds (different units).

"A car travels 60 km in 1 hour." Rate = 60 km/hour

Always has units (km/h, price per kg, words per minute)
A unit rate means the second quantity is 1 (e.g., "per hour", "per person")

Proportion

A proportion says that two ratios are equal to each other.

"2 : 3 = 4 : 6" → This is a proportion.

It's an equation between two ratios
Used to find an unknown value when things scale up or down
Example: "If 2 pens cost ₹10, how much do 6 pens cost?" → You set up a proportion.

Quick Memory Table

Concept	What it compares	Example
Ratio	Same type of things	2 apples : 5 oranges
Rate	Different types of things	₹50 per kg
Proportion	Two ratios that are equal	1:2 = 3:6

One-line summary:

Ratio = comparing two similar things
Rate = comparing two different things (with units)
Proportion = two ratios that are equal to each other

Give me according to community medicine

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I have all the content from Park's. Here is the full answer as per community medicine:

Rate, Ratio, and Proportion in Community Medicine

(As per Park's Textbook of Preventive and Social Medicine)

These are the three basic tools used in epidemiology to measure and express the frequency of disease in a population.

1. RATE

A rate measures the occurrence of an event (disease or death) in a defined population over a given time period. It is a statement of risk.

"500 deaths from motor vehicle accidents in City A in 2010" is just a count. To compare City A with City B, you need a rate."

Formula:

Death Rate = (Number of deaths in one year / Mid-year population) × 1000

4 essential elements of a rate:

Element	Example
Numerator	Number of deaths
Denominator	Mid-year population
Time specification	Per year (calendar year)
Multiplier	×1000, ×10,000, ×100,000

Types of rates:

Crude rates - actual observed rates (e.g., crude birth rate, crude death rate); also called unstandardized rates
Specific rates - rates for a specific cause (e.g., TB death rate) or specific group (e.g., age/sex group)
Standardized rates - adjusted by direct or indirect method (e.g., age-sex standardized rates) to allow fair comparison

2. RATIO

A ratio expresses the relation in size between two quantities. The key point is: the numerator is NOT part of the denominator - they are two separate groups being compared.

Formula:

x : y or x/y

Examples:

WBC : RBC = 1 : 600 (for every 1 white cell, there are 600 red cells)
Number of children with scabies / Number of children with malnutrition
Doctor-population ratio
Sex ratio
Child-woman ratio

3. PROPORTION

A proportion is a special type of ratio where the numerator IS included in the denominator (i.e., the numerator is a part of the whole). It is usually expressed as a percentage (%).

Formula:

Number of children with scabies / Total number of children in the village × 100

Example: If 30 out of 200 children have scabies:

Proportion = 30/200 × 100 = 15%

Quick Comparison Table

Feature	Rate	Ratio	Proportion
Definition	Occurrence of event in population over time	Relation between two quantities	Part of a whole
Numerator in denominator?	Yes (usually)	No	Yes
Time element	Always present	May or may not be	Not essential
Expression	Per 1000 / 10,000 / 100,000	x : y	Percentage (%)
Community medicine example	Infant mortality rate	Doctor : population ratio	% of diseased in a community

Key Memory Trick

Rate = risk over time (always has a time factor)
Ratio = two separate groups compared (numerator is NOT part of denominator)
Proportion = part divided by whole (numerator IS part of denominator), shown as %

- Park's Textbook of Preventive and Social Medicine, Epidemiology section

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