The Density Scale

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?

> ANSWER:

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)