# Discrete data vs continous data in statistics

• chwala
But it's possible to have a mixture.No, in summary, the terms "discrete" and "continuous" are often used to describe data, but it is possible for a dataset to have a mixture of both discrete and continuous values. It is important to consider the context and how the data is being treated when determining whether it is discrete or continuous.
chwala
Gold Member
Homework Statement
Indepth understanding of the two terms; discrete and continous data
Relevant Equations
statistics
I would like to seek your take on the two terms; discrete and continuous in this context,
In my understanding, when we look at height of individuals (in cms), this measure in general or in definition implies continuous data. If we are to look at specific math problem that involves height of say ##5## people given in cm as ##[140, 159, 165, 170, 178]## then in this context the values given are in this case; discrete. Where discrete in this case being a subset of continuous data. Would that be correct?
On the other hand, if the heights of ##5## people (in cms) are given as ##[145.7, 178, 189, 190,156]##, then in this particular context, the data given is continous.

Now, considering data in a grouped frequency table, the data given would be discrete or continuous depending on the class interval given, for instance, if the class interval is given as ##1-10, 11-20, 21-30##...then the data would be discrete, as there is discontinuity between ##10## and ##11##...
if the data given had a class interval given as,## 1≤x<10, 10≤x<19, 19≤x<28##...then in this case, the data given would be continous. I would appreciate your input on this.

You are talking about a data sample from a continuous variable. How they are treated, graphed, put in a frequency table, etc., does not change that.

chwala
FactChecker said:
You are talking about a data sample from a continuous variable. How they are treated, graphed, put in a frequency table, etc., does not change that.
interesting, in my understanding, discrete data would be shown/presented on a bar chart whereas continuous data would be presented on a histogram...dependant on the class interval...this is in response to post ##2##.

in regards to post ##1##, you're implying that as long as we are dealing with height, then the data would always be treated as continous regardless of the data given? What if the data only consists of a total of "the" ##5## individuals, why are we considering this to be a sample?

Last edited:
am also trying to read on google on the definition of the two...they're saying height is a measured quantity and is therefore continuous whereas discrete quantities can only be counted.

64

Discrete data can only take particular values. There may potentially be an infinite number of those values, but each is distinct and there's no grey area in between. Discrete data can be numeric -- like numbers of apples -- but it can also be categorical -- like red or blue, or male or female, or good or bad.
Continuous data are not restricted to defined separate values, but can occupy any value over a continuous range. Between any two continuous data values, there may be an infinite number of others. Continuous data are always essentially numeric.
It sometimes makes sense to treat discrete data as continuous and the other way around:
• For example, something like height is continuous, but often we don't really care too much about tiny differences and instead group heights into a number of discrete bins -- i.e. only measuring centimetres --.
• Conversely, if we're counting large amounts of some discrete entity
-- i.e. grains of rice, or termites, or pennies in the economy -- we may choose not to think of 2,000,006 and 2,000,008 as crucially
different values but instead as nearby points on an approximate
continuum.
It can also sometimes be useful to treat numeric data as categorical, eg: underweight, normal, obese. This is usually just another kind of binning.
It seldom makes sense to consider categorical data as continuous...

Note:
The above is not my analysis but rather copied from internet.
i just looked/copied the above from internet search...i think it is now clear to me ie post ##1## the heights of the ##5## people is regarded as continous, where continuous implies both discrete and non discrete values...whereas discrete data can only take integer values...

Last edited:
chwala said:
64

Discrete data can only take particular values. There may potentially be an infinite number of those values, but each is distinct and there's no grey area in between. Discrete data can be numeric -- like numbers of apples -- but it can also be categorical -- like red or blue, or male or female, or good or bad.
Continuous data are not restricted to defined separate values, but can occupy any value over a continuous range. Between any two continuous data values, there may be an infinite number of others. Continuous data are always essentially numeric.
It sometimes makes sense to treat discrete data as continuous and the other way around:
• For example, something like height is continuous, but often we don't really care too much about tiny differences and instead group heights into a number of discrete bins -- i.e. only measuring centimetres --.
• Conversely, if we're counting large amounts of some discrete entity
-- i.e. grains of rice, or termites, or pennies in the economy -- we may choose not to think of 2,000,006 and 2,000,008 as crucially
different values but instead as nearby points on an approximate
continuum.
It can also sometimes be useful to treat numeric data as categorical, eg: underweight, normal, obese. This is usually just another kind of binning.
It seldom makes sense to consider categorical data as continuous...

Note:
The above is not my analysis but rather copied from internet.
i just looked/copied the above from internet search...i think it is now clear to me ie post ##1## the heights of the ##5## people is regarded as continous, where continuous implies both discrete and non discrete values...whereas discrete data can only take integer values...
Just to note that not every dataset falls neatly into either bucket. In principle, the range could have both disjoint continuous ranges and isolated points.

SammyS and chwala
haruspex said:
Just to note that not every dataset falls neatly into either bucket. In principle, the range could have both disjoint continuous ranges and isolated points.
This is in regards to post ##2##?

chwala said:
This is in regards to post ##2##?
No, in relation to the terminology "discrete" and "continuous". They tend to be used as though those are the only two possibilities.

haruspex said:
No, in relation to the terminology "discrete" and "continuous". They tend to be used as though those are the only two possibilities.
Thanks haruspex, I've taken note of that.

## 1. What is the difference between discrete data and continuous data in statistics?

Discrete data refers to data that can only take on specific values and cannot be broken down into smaller units, such as the number of students in a class or the number of red cars in a parking lot. Continuous data, on the other hand, can take on any value within a certain range and can be broken down into smaller units, such as height or weight.

## 2. How are discrete and continuous data represented in statistical analysis?

Discrete data is typically represented using bar graphs or pie charts, while continuous data is often represented using histograms or line graphs. This is because discrete data can only take on specific values, while continuous data can take on any value within a range.

## 3. Can discrete and continuous data be used interchangeably in statistical analysis?

No, discrete and continuous data cannot be used interchangeably in statistical analysis. They require different types of statistical tests and methods to analyze and interpret the data accurately. Using the wrong type of data can lead to incorrect conclusions and results.

## 4. What are some examples of discrete data and continuous data?

Examples of discrete data include the number of siblings a person has, the number of books in a library, and the number of pets in a household. Examples of continuous data include temperature, time, and height.

## 5. How do you determine if a dataset contains discrete or continuous data?

To determine if a dataset contains discrete or continuous data, you can look at the type of values that are being measured. If the values can only take on specific, whole numbers, then it is most likely discrete data. If the values can take on any value within a range, then it is most likely continuous data.

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