Histogram

A histogram is nothing more than a graphical representation, or picture, of a set of data. In that sense, it is like a pie chart. However, while most pie charts show the relative size of various categories of a qualitative variable (e.g., favorite flavor of ice cream), a histogram provides a picture of data that are quantitative in nature (e.g., examinees' earned scores on an examination).

A histogram reveals three things about a set of scores: the place(s) where scores tend to congregate along the score continuum, the degree to which the scores are spread out, and the possibility that the full set of scores can be referred to by a term such as normal or skewed or rectangular. Stated differently, three important questions can be answered (at least in an approximate fashion) by quickly glancing at a histogram:

1.
What is the average score?
2.
How much variability is there among the scores?
3.
What kind of shape does the distribution have?

Example

Figure 1 contains an example of a histogram. This histogram was created to show the published weight of players on a professional football team. In this histogram, the abscissa (i.e., the baseline) corresponds to the variable of interest, player weight, and the ordinate (i.e., the vertical axis, on the left) represents the frequency of the team's players who have a given weight. There are nine bars in this histogram, and the height of each bar indicates how many football players were in the weight interval indicated on the abscissa beneath the bar. Thus, this histogram shows that 3 of the team's players weighed somewhere between 160 and 179 pounds that 11 of the players weighed between 180 and 199 pounds, and so on.

A quick glance at Figure 1 allows us to answer the three questions concerning average, variability, and shape. More players were in the 200- to 219-pound interval than in any other interval, so that interval is the modal interval. The weight intervals, in combination[Page 440] with the heights of the bars, make it clear that there is a great deal of variability among the players' weights. Finally, the shape of the distribution appears to be skewed to the right (i.e., positively skewed).

Figure 1 Example of a Histogram