Mila asked 80 of her colleagues the age of their cars. The results are shown in the table. Mila’s attempt to draw a histogram for the information is also shown. Make two criticisms about Mila’s histogram.
A histogram is a graph of frequency density and class width. Almost immediately, we see Mila has used the height of the bar to represent the frequency. However, on a histogram, the frequency density will be the height of the bar. The area of the bar should be the frequency. Our first criticism can be that the vertical axis should show frequency density and not just frequency.
Next, we need to consider her class widths. She goes from zero to two, from two to four, and then from four to five. From there, she jumps from five to 10 and from 10 to 15. This means that Mila is using an inconsistent scale. Criticism two: the scale on the horizontal axis should be linear so each square represents the same amount.
If you notice the distance from five to 10, the width of that large box is five. But here the distance from two to four is only two, making the width of this box only two. That’s an inconsistent scale.