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### Course: High school statistics>Unit 3

Lesson 2: Distributions in two-way tables

# Marginal and conditional distributions

We investigate distributions using a two-way table and then explain the concept of marginal distribution, both in counts and percentages, to understand the distribution of each variable individually. Finally, we cover conditional distribution, where we look at the relationship between variables and understand how one variable impacts the distribution of another.

## Want to join the conversation?

• i dont understand this at all. i need serious help
• From what I've understood, marginal distribution is the percentage of a certain margin/bucket over the total. Conditional distribution is observing the data following the given condition.
• Why do we need to find Marginal and Conditional Distribution?
• They are both different types of relative frequency and they both have two different functions.
• Is marginal distribution just the percentage of a certain margin or bucket out of the total? For reference, Sal starts talking about marginal distributions at
• Well, basically yes. A marginal distribution is the percentages out of totals, and conditional distribution is the percentages out of some column.

UPD: Marginal distribution is the probability distribution of the sums of rows or columns expressed as percentages out of grand total. Conditional distribution, on the other hand, is the probability distribution of certain values in the table expressed as percentages out of sums (or local totals) of certain rows or columns. So you're basically going one level down here. These row and column totals is what's given in the conditional distribution. Intuitively, when you here the word given, think of it as your new total, out of which you'll calculate the percentage or the probability.

Hope this clears things out!
• So the name "marginal" here, is from being the edge of the table ?
• Yes that would be correct.
• I kind of think of it like, marginal distribution is the distribution of one factor and conditional is two or more factors or circumstances in the data collected in the table.
• at , why do we need to know about the other types of distributions?
• Well, from what I see, you need to know about different types of distributions, to gain more knowledge, so you can build off of that knowledge...
• At the minute , Sal mentioned one of the differences between marginal and conditional distribution in terms of representations. specifically the standard practice for representing conditional distribution is to think in terms of percentage.
Is it safe to say Conditional distribution must be represented in terms of percentages ?
• Yes that is what he says.