Confirm the frequency distribution table

[chwala]

Homework Statement

The question below is from a textbook, the data given is continous and the frequency table indicated is having a class interval which is discrete.

Relevant Equations

statistics

I feel this is not correct, from my understanding of data, discrete data will always have a corresponding discrete frequency table and continuous data will always have a corresponding continuous frequency table. The class interval ought to be $0≤x<5$, $5≤x<10$... i need clarity on this...
if someone was to indicate that the discrete class interval is correct, then where would we place $5$? on which class interval?

 

[FactChecker]

Good catch. I think that your point is valid whether the distribution is discrete or continuous. The height values of 5, 10, 15, and 20 should only be in one of the height categories and not in the adjoining one.

 

[chwala]

In my understanding if we have data that has only discrete values then we shall have a discrete frequency table, but if you have $100$ items in a data pool, where $99$ are discrete values and only $1$ value is continuous then, the frequency table would be continuous because of this $1$ value, is this correct? It all depends on the data given...and not on the subject. Height is presumed to be continuous but if i was looking at a data pool of height values that are all discrete, then i shall consider the data as discrete data. Discrete data is a subset of continuous data in this context.

 

[FactChecker]

Whether the underlying distribution is continuous or discrete, you only have a sample of 40. The histogram is the same either way. Suppose the underlying distribution is continuous and you had a huge number of data points. Then, you could increase the number of cells and it would start to have the shape of a continuous distribution. You would still need to keep the number of cells small enough so that the numbers could be large enough in highly likely cells to form the shape.

 

[chwala]

Whether the underlying distribution is continuous or discrete, you only have a sample of 40. The histogram is the same either way. Suppose the underlying distribution is continuous and you had a huge number of data points. Then, you could increase the number of cells and it would start to have the shape of a continuous distribution. You would still need to keep the number of cells small enough so that the numbers could be large enough in highly likely cells to form the shape.

my point is that if data is discrete then we shall have either a discrete frequency table/continous frequency table i.e either a bar or histogram to be specific and if data is continuous then we shall have only a continuous frequency table- histogram.
in the problem above, the data is continuous and it was being put in a discrete frequency of which i felt is not correct. That is the specific point that i wanted clarified...

 

[chwala]

Whether the underlying distribution is continuous or discrete, you only have a sample of 40. The histogram is the same either way. Suppose the underlying distribution is continuous and you had a huge number of data points. Then, you could increase the number of cells and it would start to have the shape of a continuous distribution. You would still need to keep the number of cells small enough so that the numbers could be large enough in highly likely cells to form the shape.

i think you are not addressing my question or rather my concern to be specific...and neither am i disputing your statement. Please check my concern again and i thank you for yourinput, cheers...

 

[FactChecker]

I don't understand what you are referring to when you talk about a difference between a discrete table versus a continuous table. I only know one type of histogram for a set of data. Can you describe or show me one of each?

 

[chwala]

Discrete data cannot be plotted on a histogram...only continuous data. Are you implying that my understanding is wrong on this??discrete data can only be plotted on a bar graph and furthermore a bar graph is not a histogram.

 

[FactChecker]

Discrete data cannot be plotted on a histogram...only continuous data. Are you implying that my understanding is wrong on this??discrete data can only be plotted on a bar graph and furthermore a bar graph is not a histogram.

If I understand you correctly, I disagree. (see https://en.wikipedia.org/wiki/Histogram )

 

[chwala]

I don't understand what you are referring to when you talk about a difference between a discrete table versus a continuous table. I only know one type of histogram for a set of data. Can you describe or show me one of each?

an example of discrete data is the binomal distribution of a fair coin that is tossed eg 3 times, it follows that if $x$ is a discrete variable that denotes Heads then, bin$(3,0.5)$=

X=xi	0​	1​	2​	3​
P(X=xi)	0.125​	0.375​	0.375​	0.125​

plotting this on a bar graph yields,
there is discontinuity between $0$ and $1$... whereas in continuous data, for eg height or the reference that you have given on wikipedia, we may not have discontinuity because all values on the real number line system are captured on the graph i.e including decimals...unless my understanding has all been wrong, then you may correct me.

 

[chwala]

I think i may be right, ...that is what i learned in my undergraduate, i hope my professors were correct. Awaiting your response.

 

[FactChecker]

I see. I don't think that there is an authoritative body that enforces particular definitions of the terms "bar chart" versus "histogram", but here is how I use the terms:
A bar chart shows the number of samples in different, disjoint, categories. The categories may or may not be defined using ordered numerical data. If they are not, then they can be put in any order.
A histogram is a bar chart where the categories are defined using ordered numerical data. The bars must be ordered from smaller to larger numerically-defined categories.
I think that the distinction between discrete versus continuous variables can get very blurred and is not a good way to distinguish between bar charts and histograms. Consider the population of the United States over time. It is a discrete variable since there are no half-people. But we would graph it as a continuous variable.
Other people may use the terms differently, but I don't know if you can assume or count on any particular definition unless you state your particular definitions.

 

[chwala]

Difference Between Histogram and Bar Graph
April 30, 2016 By Surbhi S 8 Comments

The fundamental difference between histogram and bar graph will help you to identify the two easily is that there are gaps between bars in a bar graph but in the histogram, the bars are adjacent to each other.

After the collection and verification of data, it needs to be compiled and displayed in such a way that it highlights the essential features clearly to the users. The statistical analysis can only be performed if it is properly presented. There are three modes of presentation of data i.e. textual presentation, tabular presentation, and diagrammatic presentation. The diagrammatic representation of data is one of the best and attractive way of presenting data as it caters both educated and uneducated section of the society.
Bar Graph and Histogram are the two ways to display data in the form of a diagram. As they both use bars to display data, people find it difficult to differentiate the two.
Content: Histogram vs Bar Graph

1. Comparison Chart
2. Definition
3. Key Differences
4. Conclusion

Comparison Chart

BASIS FOR COMPARISON	HISTOGRAM	BAR GRAPH
Meaning	Histogram refers to a graphical representation, that displays data by way of bars to show the frequency of numerical data.	Bar graph is a pictorial representation of data that uses bars to compare different categories of data.
Indicates	Distribution of non-discrete variables	Comparison of discrete variables
Presents	Quantitative data	Categorical data
Spaces	Bars touch each other, hence there are no spaces between bars	Bars do not touch each other, hence there are spaces between bars.
Elements	Elements are grouped together, so that they are considered as ranges.	Elements are taken as individual entities.
Can bars be reordered?	No	Yes
Width of bars	Need not to be same	Same

Key Differences Between Histogram and Bar graph
The differences between histogram and bar graph can be drawn clearly on the following grounds:

1. Histogram refers to a graphical representation; that displays data by way of bars to show the frequency of numerical data. A bar graph is a pictorial representation of data that uses bars to compare different categories of data.
2. A histogram represents the frequency distribution of continuous variables. Conversely, a bar graph is a diagrammatic comparison of discrete variables.
3. Histogram presents numerical data whereas bar graph shows categorical data.
4. The histogram is drawn in such a way that there is no gap between the bars. On the other hand, there is proper spacing between bars in a bar graph that indicates discontinuity.
5. Items of the histogram are numbers, which are categorised together, to represent ranges of data. As opposed to the bar graph, items are considered as individual entities.
6. In the case of a bar graph, it is quite common to rearrange the blocks, from highest to lowest. But with histogram, this cannot be done, as they are shown in the sequences of classes.
7. The width of rectangular blocks in a histogram may or may not be same while the width of the bars in a bar graph is always same.

 

[chwala]

I see. I don't think that there is an authoritative body that enforces particular definitions of the terms "bar chart" versus "histogram", but here is how I use the terms:
A bar chart shows the number of samples in different, disjoint, categories. The categories may or may not be defined using ordered numerical data. If they are not, then they can be put in any order.
A histogram is a bar chart where the categories are defined using ordered numerical data. The bars must be ordered from smaller to larger numerically-defined categories.
I think that the distinction between discrete versus continuous variables can get very blurred and is not a good way to distinguish between bar charts and histograms. Consider the population of the United States over time. It is a discrete variable since there are no half-people. But we would graph it as a continuous variable.
Other people may use the terms differently, but I don't know if you can assume or count on any particular definition unless you state your particular definitions.

cheers, i appreciate your perspective... in my post $5$ i indicated that discrete data (like in your case the population of United States may be represented as a continuous data,...no dispute on that. My only concern with the original problem was on the set of data (which is continous) being represented/described by a discrete frequency table.

 

[FactChecker]

I see what you are saying. That may be the generally agreed-upon use of the terms. I am not sure. I will keep that possibility in mind if I have to use the terms.

 

[pai535]

cheers, i appreciate your perspective... in my post $5$ i indicated that discrete data (like in your case the population of United States may be represented as a continuous data,...no dispute on that. My only concern with the original problem was on the set of data (which is continous) being represented/described by a discrete frequency table.

In my perspective, in reality it is not even possible to say that a data set is "continuous" - because there is an infinite number of real numbers between all two data in a data set.

A histogram represents the frequency distribution of continuous variables. Conversely, a bar graph is a diagrammatic comparison of discrete variables.

I think the meaning of "continuous" here is that if you have a probability distribution function, then the Independent Variable in this function should be continuous, like in your question, the height is continuous because it can take any positive value. However, in a data set data would never be continuous. A data set is only a sample of all possible data, so definitely it can be written in a discrete frequency table. Actually this is an attempt for us to make a histogram from only a limited number of data.