Question

2. Summarizing interval data - Frequency distributions and histograms

The Dow Jones Industrial Average (DJIA) is a stock index of 30 of the leading companies in the main industries of the United States. It is the second-oldest continuing U.S. market index (after the Dow Jones Transportation Average).

Companies in the DJIA are classified into 10 industries according to the Industry Classification Benchmark (ICB), a classification system developed by Dow Jones & Company and the FTSE Group. Although the DJIA was originally meant to describe the industrial component of the U.S. market, today the modifier “Industrial” in its name is mainly historical. As Table 1 shows, many of its companies have little to do with heavy industry. Table 1, located in the following DJIA Table dropdown menu, shows the companies’ names, ICB classifications, and market capitalizations.

DJIA Table

Table 1

No.	Company	Industry	Capitalization
			(Billions of dollars)
1	International Business Machines Corp.	Technology	129.9
2	Chevron Corp.	Oil and Gas	86.1
3	Exxon Mobil Corp.	Oil and Gas	81.5
4	Caterpillar Inc.	Industrials	70.9
5	3M Co.	Industrials	68.9
6	Boeing Co.	Industrials	68.1
7	Johnson & Johnson	Health Care	67.8
8	United Technologies Corp.	Industrials	64.1
9	Procter & Gamble Co.	Consumer Goods	63.7
10	McDonald’s Corp.	Consumer Services	60.4
11	Wal-Mart Stores Inc.	Consumer Services	57.9
12	Coca-Cola Co.	Consumer Goods	50.0
13	E.I. DuPont de Nemours & Co.	Basic Material	44.2
14	Hewlett-Packard Co.	Technology	43.4
15	American Express Co.	Financials	42.2
16	JPMorgan Chase & Co.	Financials	40.0
17	Merck & Co. Inc.	Health Care	37.7
18	Verizon Communications Inc.	Telecommunications	35.5
19	Alcoa Inc.	Basic Material	33.8
20	AT&T Inc.	Telecommunications	32.1
21	Walt Disney Co.	Consumer Services	30.9
22	General Electric Co.	Industrials	28.0
23	Bank of America Corp.	Financials	27.5
24	Microsoft Corp.	Technology	25.9
25	American International Group Inc.	Financials	25.1
26	Home Depot Inc.	Consumer Services	23.4
27	Intel Corp.	Technology	22.1
28	Citigroup Inc.	Financials	19.4
29	Pfizer Inc.	Health Care	18.3
30	General Motors Corp.	Consumer Goods	13.2
		Total	1,412.0

Table 2 divides the range of the market capitalization of the DJIA companies into six intervals and gives some of their frequencies and relative frequencies. Based on the information provided in Table 1, use the dropdown menus to fill in the rest of Table 2.

Table 2
Market Capitalization	Frequency	Relative Frequency
(Billions of dollars)
110 to 130	1	0.03
90 to 110	0	0.00
70 to 90	3	0.10
50 to 70
30 to 50	10	0.33
10 to 30
Total	30	1.0

On the following graph, create a relative frequency histogram of the companies’ market capitalizations based on the distribution in Table 1 by using the blue rectangles (drag the circle symbols to increase or decrease the size) to draw each individual bar of the histogram. (Hint: Do not place a rectangle when the frequency of the class is zero.)

10305070901101301.000.800.600.400.200RELATIVE FREQUENCYMARKET CAPITALIZATION (Billions of dollars)

The relative frequency distribution of the market capitalizations is   .

Answer 1

Solution :

From the table 1, the frequency table is,

Make Capitalization (Billions of dollars )	Frequency	Relative frequency (Rounded to two decimal places )
10 to 30	9	0.3 = 0.30
30 to 50	10	0.333333 = 0.33
50 to 70	7	0.233333 = 0.23
70 to 90	3	0.1 = 0.10
90 to 110	0	0
110 to 130	1	0.033333 = 0.03
Total	30	1

Here, the relative frequency can be calculated using the below formula:

Relative frequency = Frequency / Total frequency

From the above table, the frequency values are obtained from the table 1.

Use Excel to construct the histogram :

From the histogram, the relative frequency distribution of the market Capitalizations is Positively skewed.

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