Welcome to a lesson
on discrete and continuous variables.
One quick way to check to see if a single variable
is continuous or discrete is to ask yourself
if the values of the variable are measured or counted.
If a variable is continuous,
it is measured and can take on any value
over a particular interval.
If a variable is discrete,
it is counted and can only take on certain values
over a particular interval.
And because it is counted,
normally the values would have to be whole numbers,
but this is not always the case.
Let's look at the examples below.
For the examples of continuous variables,
we have gallons of gas,
height of a tree,
volume of water in a pool,
weight of a bag of tomatoes.
All of these are measured,
and therefore they are examples of continuous variables.
Also notice how these variables can take on
any value over a particular interval
which is another reason why they are continuous variables.
For the examples of discrete variables,
we have number of family members,
amount of money in a bank account,
number of soda cans purchased,
number of marbles in a bag.
All of these are counted,
which is the reason why they are discrete variables.
Also notice how they can only take on certain values
over a particular interval.
For example, the number of family members,
number of soda cans,
and number of marbles can only be whole numbers.
While the amount of money in a bank account
can only be dollars and cents.
This is another reason why these are discrete variables.
Let's look at some more examples.
We are asked to determine if the following set of data
is discrete or continuous.
Again if it's discrete,
it is counted.
If it's continuous, it's measured.
Number one we have
the number of books on the shelves in the library.
We would need to count the number of books
on the shelves in the library,
and therefore this is discrete data.
Also this data can only take on certain values
over a particular interval
because the number of books can only be whole numbers.
Number two we have the height of your classmates.
We measure height, this is continuous data.
Also the height of your classmates
can take on any particular length
over a particular interval,
which is another reason why this is continuous data.
Number three is a little bit tricky.
It's the age of a person.
We may be thinking we count the age of a person in years,
but age is really a measurement of time,
and therefore, the age of a person is continuous data.
The age of a person can take on any value
over a particular interval.
For example someone can be 25 years, 11 months,
two weeks, four days, 21 hours,
six minutes, three seconds, and so on old,
and therefore the age of a person is continuous data.
Number four we have the weights of bananas.
Weight is measured, this is continuous data.
The weights of bananas can take on any value
over a particular interval.
Number five, the number of heads when flipping a coin.
We count the number of heads,
and therefore this is discrete data.
The number of heads can only take on whole number values
over a particular interval,
which is another reason why this is discrete.
Number six we have the volume of water
in a swimming pool.
We measure volume, and therefore this is continuous.
Number seven, the number of ants in an ant colony.
We count the number of ants.
This is discrete.
And number eight, the speed of a bicycle.
We measure speed,
and therefore this is continuous.
Again the speed of a bicycle can take on any value
over a particular interval,
and therefore this is continuous data.
I hope you found this helpful.