The height of a rectangle in a histogram shows:

A histogram represents grouped, continuous frequency data as a set of adjacent rectangles, one for each class interval, drawn with no gaps between them. Two different features of each rectangle carry two different pieces of information: the rectangle's width, measured along the horizontal axis between the class limits, shows the size of that class interval, while — for the standard case of equal-width classes used in a basic frequency histogram — the rectangle's height is drawn proportional to the frequency, i.e., the number of observations that fall in that class.

Height is a vertical measurement of the bar; it is not a position on the horizontal axis and not the size of the interval along that axis. Applying this to the question, height corresponds to how many data points the class contains, so the height of a rectangle in a histogram shows the frequency of the class.

This can be cross-checked from the axes themselves: a histogram has exactly two axes — the horizontal axis carries every class-boundary quantity (the lower limit, the upper limit, and therefore the class width, which is just the distance between them), while the vertical axis carries the count of observations, i.e., frequency. Height is a measurement along the vertical axis, so it cannot be showing a horizontal-axis quantity like width or a limit; it can only be showing frequency. (Since every class here has the same width, the area of each rectangle — width × height — is also directly proportional to its height, so comparing rectangle areas gives the same ranking as comparing heights; this is exactly why an equal-width histogram is read off by height rather than needing an area calculation.)

• width of the class — the size of the interval, read along the horizontal axis as the distance between the class limits; this is a horizontal measurement, not the bar's height.

• upper limit of the class — a single boundary value marking where one class interval ends on the horizontal axis; a position, not a height.

• lower limit of the class — a single boundary value marking where a class interval begins on the horizontal axis; also a position, not a height.

So the height of a rectangle in a histogram shows the frequency of the class.