Welcome to NRICH.

 
Histogram vs bar graph
By Anonymous on Wednesday, January 19, 2000 - 10:34 am:

I am a member of a team of teachers engaged in preparing materials for use in several schools. Within our team there is a difference of opinion regarding the correct usage of the term "histogram". My rule of thumb definition has been - a bar graph constructed so that the area of each bar is proportional to the frequency, BUT there is a body of opinion that this is not sufficient and that the vertical scale must represent frequency density.
My main query is: what is the correct description of a bar graph which covers the range of a continuous variable and has frequency plotted along vertical axis?
Is there a definitive, accepted, definition?
I would really appreciate, not only some opinions, but also, if possible, the origins of the term and some quotable sources (for whichever definition)
Thank you for your help,
T

By Graham Lee (P1021) on Thursday, January 20, 2000 - 10:44 pm:

In my A-Level Stats course (just running off to get the textbook), a bar chart can be used for qualitative classes (e.g. Red, Blue, Green) or discrete quantitative classes (e.g. shoe size), whereas a histogram can be used for continuous variables. In a bar chart, the bars are of equal width (and should be spaced), and the height of the bar represents the frequency.
In a histogram, the area should be proportional to the frequency, so that the x-axis represents the continuous variable, and the height represents a constant multiplied by the freq. den.

In "Introducing Statistics" by Upton and Cook:
1.6 Bar Charts p6
"The lengths of the rows on a tally chart or of a stem-and-leaf diagram provide an instant picture of the data. This picture is neatened using bars whose lengths are proportional to the numbers of observations of each outcome (i.e. the frequencies). In the resulting diagram, known as a bar chart, the bars may be either horizontal[...] or vertical."
1.12 Histograms p13
"Bar charts are not appropriate for data with grouped frequencies for ranges of values. A histogram is a diagram using rectangles to represent frequency. It differs from the bar chart in that the rectangles may have different widths, but the key feature is that, for each rectangle:
are is proportional to class frequency
When all the class widths are equal, histograms are easy to construct, since then not only is area proportional to frequency, but height is proportional to frequency."

Hope this helps,

GL.