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I am studying an introductory course in statistics, Essentials of Statistics. The author mentioned that histograms are used to represent the frequency distribution of a continuous data. Then directly, he explained how to detect if there is skewness in the data using histograms. Later he highlighted some other types of plots and graphs including the bar chart.

What is missing for me: What are the graphs that represent quantitative discrete data? If using a bar chart, then is it possible to use bar chart to detect the skewness in a quantitative discrete data?

Alexis
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Nizar
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  • It’s fine; histogram away with quantitative discrete data. Depending on the range of values, you might find it easy to do the binning better than the software default, however. – Dave Oct 10 '20 at 14:07
  • I think it's important to differentiate between 1) the method that is used to determine the representation of the property/feature/characteristic of the data you're analyzing and 2) the way that representation is displayed. For example, no one stops you to display a histogram as a - please don't do this - pie chart. To answer your question: The [skewness](https://en.wikipedia.org/wiki/Skewness) of a random variable describes the degree of asymmetry about the mean value. As a consequence, the bar plot of the corresponding histogram will have a trend towards the left or right side. – applesoup Nov 18 '21 at 21:35

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Does the author specify which definition of skewness is being used? There are several and normally do not rely on looking at histograms.

I am guessing that the author is proposing a (vague) definition of skewness that you could apply to discrete quantitative variables. You could plot an histogram for this and proceed as if you were dealing with a continuous variable.

Guilherme Costa
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You also use a histogram to represent discrete data, including quantities like counts. A histogram is a visual representation of the frequency or probability (for values of a discrete variable or probability density (for values of a continuous variable).

A bar chart, on the other hand, is a graph relating two different variables (e.g. $x$ is number of oranges eaten per capita per year, and $y$ is country). So you do not really use a bar chart to represent the distribution of a single variable.

Alexis
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  • In my opinion, it doesn't make sense to compare "histogram" and "bar graph". The histogram is a general way to find some representation of discrete data. While it has become common practice to display that representation in the form of line or bar graphs, plotting is not part of determining the "histogram". A bar graph as I see it is just a way to visualize some discrete, i.e. categorial, data by means of bars of different lengths. – applesoup Nov 18 '21 at 21:27
  • @applesoup I think I agree: one is a one-variable graph, the other a two (or more) variable graph. – Alexis Nov 18 '21 at 21:56