Discrete data vs continous data in statistics

[chwala]

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.

 

[chwala]

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.

 

[FactChecker]

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]

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?

 

[chwala]

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.

 

[chwala]

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...

 

[haruspex]

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.

 

[chwala]

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 $2$?

 

[haruspex]

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.

 

[chwala]

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.