Histograms don't need a vertical scale
A vertical scale is often provided to help finding %s of areas
In a histogram the height of a block represents CROWDING -- % per horizontal unit
DENSITY SCALE = % / hor.unit
with the DENSITY SCALE, areas come out in %s
AREA (%) = WIDTH (hor.unit) * HEIGHT ( % / hor.unit )
Notice that hor.unit's cancel out.
Find the HEIGHT of a block with
HEIGHT = (AREA %) / (WIDTH hor.unit)
Consider the following example:A histogram of wages for part-time employees is shown below with the heights of the blocks (in the density scale) marked in parenthesis. Nobody earned more than $1,000 a month. The block from $200 to $500 is missing.
How tall should the missing block be?
The heights of the blocks are given in the DENSITY SCALE of % per $100. Hence, the areas of the blocks come out in %s.
The areas of the first two blocks are then: 10% and 20% resp.
The area of the last block is:
5 ($100) * 5(%/$100) = 25 %
The 3 blocks together give (10+20+25)% = 55 %
The missing block must have an area of (100% - 55%) = 45%
The HEIGHT of the missing block is then:
HEIGHT = 45% / (3 $100) = 15 (%/$100)