Why is "using counts of a frequency table as data" for a histogram a "mistake"? The textbook, The Practice of Statistics, states the following as a "common mistake" when making histograms:

Don't use counts (in a frequency table) or percents (in a relative frequency table) as data. Below is a frequency table displaying the lengths of the first 100 words in a journal article.

And it gives the following as an example:


I don't understand how this is a mistake. Isn't a histogram supposed to show frequency?
 A: The example table shows how many times each length was observed. For example: length 1 was observed once, length 2 was observed 15 times, etc.
The typical purpose of a histogram here would be to show how often each length is observed. If you simply plotted the numbers in the table with length on the x axis and count on the y axis, it would be a proper histogram. Or, you could define a set of bins (each corresponding to a range of lengths). Then, for each bin, plot the number of times you observe a length that falls inside it (given by adding up the counts for lengths in each bin).
Instead, the "common mistake" example plot is the result of taking the "count" row of the table, treating it as a raw list of values, and calculating a histogram from this list. What the plot actually represents is the number of lengths that have been observed a certain number of times. Confusingly, the x axis (labeled "value") represents the value of the "count" entry in the table. And, the y axis (labeled "count") represents the number of times this value occurs.
