# FREQUENCY DISTRIBUTIONS: AN ILLUSTRATION Stats Assignment Homework Help

FREQUENCY DISTRIBUTIONS: AN ILLUSTRATION

Each year, Fortune magazine publishes a variety of data on the nation’s largest corporations. The data in Tables 3.1 and 3.2 were compiled from that magazine. The numbers in each table are percent returns on investments in the corporations. Thus, for example, an entry of 27 for a corporation means’ that an investor who bought a share of the corporation’s stock at the beginning of the year and sold it at the year’s end would have had a total return of 27 percent on the investment. The total return reflects both the amount paid to the shareholder by the corporation (the dividend) and the change in the price of the stock during the year. A negative entry means a loss.

TABLE 3.1 PERCENT RETURN ON INVESTMENT FOR 212 INDUSTRIAL COR-RATIONS WITH SALES OF \$1 BILLION OR MORE

TABLE 3.2
PERCENT RETURN ON INVESTMENT FOR 248 INDUSTRIAL CORPORATIONS WITH SALES FROM \$328 MILLION UP TO \$1 BILLION

Table 3.1 contains percent returns for “billions” corporations that is corporations having sales of \$1 billion or more. The “hundred millions” corporations in Table 3.2 had sales from \$328 million up to, but not including, \$1 billion. You can get some information from the numbers in Tables 3.1 and 3.2 by “eyeing” them-but not much. For example, the smallest and largest numbers in Table 3.1 are – 30 and 154, respectively. But it is difficult to see how the numbers are distributed in the interval from -30 to 154. And it is impossible to compare how the numbers in the two tables are distributed. You might try computing and comparing the average returns on investment. That would be useful-but it would not provide a comparison of the distributions of the numbers. A numerical frequency distribution is a table which shows how then umbers in a data set (a group of numbers) are distributed in an interva which includes the smallest and largest numbers in the data set. Table 3.3 provides frequency distributions for the two data sets at hand. Percent return classes are shown down the left. A class is a description of a group of similar numbers in a data set. The total number of data values in a class is

TABLE 3.3
PERCENT RETURN FREQUENCY DISTRIBUTIONS “BILLIONS” AND “HUNDRED-MILLIONS” CORPORATIONS

called the class frequency. For example, Table 3. 3 shows a class frequency of 54 fur the 30-49 class of “billions” corporations. Thus, 54 of the 6 billions cor corporations in Table 3.1 have returns of from 30 to 4~cent. Table 3.3 summarizes the masses of data in Tables 3.1 and 3.2. It also reveals the pattern of the data in each table. Note that the “billions” frequencies increase up to a peak of 64, then decline. The frequency pattern-rising to a peak, then declining-is a fairly common pattern. The “hundred-millions” corporations exhibit the same general pattern.

EXERCISE What proportion of all the “billions” and what proportion of all ;:he “hundred-millions” corporations included in Table 3.3 had returns of at least 30 percent?
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