A. Frequency Distributions

In 2012 there were 92 people whose net worth was 10 billion dollars or more. The following table lists their values in billions of dollars.

Net Worth of People Worth over 10 Billion in 2012
(in billions of dollars)
15.9 44.0 25.3 11.9 15.3 13.0 12.0 10.0 12.1 12.4 12.0 18.3 25.0
12.5 23.1 24.0 11.2 12.5 12.4 10.0 16.0 15.9 13.2 10.3 25.0 14.2
11.5 18.0 13.4 18.0 41.0 14.0 17.4 25.4 18.7 11.0 12.4 13.8 10.7
10.6 18.7 23.7 10.2 10.0 10.4 11.2 14.0 11.3 12.2 18.1 13.5 15.9
61.0 20.0 10.0 11.9 10.9 15.7 13.8 26.0 17.8 16.5 37.5 18.0 14.4
14.5 12.5 22.3 17.6 69.0 11.0 10.0 18.4 36.0 23.3 20.7 24.9 14.2
12.0 13.0 17.5 13.8 10.8 17.5 17.8 22.0 13.8 19.0 25.5 30.0 16.0
10.2

When looking at this table, you may have tried to find the largest value or the smallest value and you may have gotten a vague sense of the distribution of values, but probably not much more. Raw data like this can be fairly difficult to interpret and answering a question like "are more of the values near 10 billion or near 60 billion?" can be a challenge.

In an attempt to make data more user-friendly, it can be arranged into a frequency distribution. With a frequency distribution, trends in the data become more evident. A frequency distribution groups data into classes, which are usually the same size, and then the number of data values falling in each class is listed. A frequency distribution is usually represented as a table or a graph.

Net Worth
(in billions of dollars)		TallyFrequencyPercent of Total
10 - 20
 |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |
71
77%
20 - 30
 |||| |||| ||||
15
16%
30 - 40
 ||
2
2%
40 - 50
 ||
2
2%
50 - 60
0
0%
60 - 70
 ||
2
2%

Frequency distributions can show the frequency of each class, the percent each class represents of the total, or both. Notice that the percentages do not add to 100 (they add to 99). This is due to rounding to the nearest percent.

Using tally marks isn't necessary, but they help avoid the risk of missing values as the data is sorted.

Using the frequency distribution table on the previous page, you can clearly see that most of the people worth over 10 billion are worth less than 20 billion.

A more visual way to represent a frequency distribution is to use a histogram. This type of graph separates and represents data in equal-size intervals (classes) using adjacent rectangles. The lack of space between rectangles shows there is no gap between the intervals. Looking at a histogram for the billionaire data allows you to see quickly that most of the billionaires are worth between 10 and 20 billion dollars.