Topic 1: Organizing Information Pictorially Using Charts and Graphs

 

Pie Charts are useful when we want to show what percentage of the whole each category represents.

To construct a pie chart from raw (unprocessed) data, we need to find what percentage of the whole each category represents.

Drawing a pie chart by hand provides a deeper understanding of this type of graphs, and helps build our intuition on determining whether a computer-generated chart is correct.

Example 1.5:

The total population of the U.S. was estimated to be 293,655,404 on July 1, 2004.

The number of people in each of six age groups is given below.
(Source: U. S. Census Bureau, www.census.gov)

Age Range

19 Yrs and Younger

20 to 39 Yrs

40 to 59 Yrs

60 to 79 Yrs

80 to 99 Yrs

100 Yrs and Older

Population

 81,551,798 82,055,558 81,164,640 38,463,652 10,358,920 60,836

First, make a table that shows the percentage of population in each age group:

Age Range

19 Yrs and Younger

20 to 39 Yrs

40 to 59 Yrs

60 to 79 Yrs

80 to 99 Yrs

100 Yrs and Older

Population

            

Next, convert the percentages in the table above to fractions with a common denomiator. It's easiest to sub-divide the "pie" if the denominator is a power of 2:

Age Range

19 Yrs and Younger

20 to 39 Yrs

40 to 59 Yrs

60 to 79 Yrs

80 to 99 Yrs

100 Yrs and Older

Population

            

Finally, fill in the pie chart using the fractions above:

Example 1.9:

Data from the 1990 census show that the populations of Alabama and California were 4,040,583 and 29,760,021, respectively.

(a) According to the 2000 census the population of Alabama in 2000 was 4,447,100. Verify that the percent change in Alabama's population from 1990 to 2000 is 10.1 percent.

The change in population is 4,447,100 - 4,040,583 = 406,517. The percentage of 1990 population that this represents is:
406,517 / 4,040,583 = 0.1006, which is approx. 10.1 percent.

(b) Use the information given in the first table of Example 1.8 to find the population of California in 2000.

From the table, we have California with a 13.8 percent increase in population from 1990 to 2000.
So, 0.138 = change in population / 29,760,021, which gives an approx. change in population of 4,106,883. This then gives a 2000 population of 4,106,883 + 29,760,021 = 33,866,904.