Course: Statistics and Probabilities

Following table shows a data set with information on 25 of "shadow" stocks monitored by American Association of Individual Investors. These are common stocks of small companies that are not closely watched by Wall Street analysts.

FIRM	Stock Exchange	Short Name	Market capacity (millions of $)	Price / profit Ratio	Gross Profit Margin (%)
DeWolfe Companies	AMEX	DWL	36.4	8.4	36.7
North Coast Energy	OTC	NCEB	52.5	6.2	59.3
Hansen Natural Corp.	OTC	HANS	41.1	14.6	44.8
MarineMax, Inc.	NYSE	HZO	111.5	7.2	23.8
Nanometrics Incorporated	OTC	NANO	228.6	38.0	53.3
TeamStaff, Inc.	OTC	TSTF	92.1	33.5	4.1
Environment Tectonics	AMEX	ETC	51.1	35.8	35.9
Measurement Specialties	AMEX	MSS	101.8	26.8	37.6
SEMCO Energy, Inc.	NYSE	SEN	193.4	18.7	23.6
Party City Corporation	OTC	PCTY	97.2	15.9	36.4
Embrex, Inc.	OTC	EMBX	136.5	18.9	59.5
Tech/Ops Sevcon, Inc.	AMEX	TO	23.2	20.7	35.7
ARCADIS NV	OTC	ARCAF	173.4	8.8	9.6
Qiao Xing Universal Tele.	OTC	XING	64.3	22.1	30.8
Energy West Incorporated	OTC	EWST	29.1	9.7	16.3
Barnwell Industries, Inc.	AMEX	BRN	27.3	7.4	73.4
Innodata Corporation	OTC	INOD	66.1	11.0	29.6
Medical Action Industries	OTC	MDCI	137.1	26.9	30.6
Instrumentarium Corp.	OTC	INMRY	240.9	3.6	52.1
Petroleum Development	OTC	PETD	95.9	6.1	19.4
Drexler Technology Corp.	OTC	DRXR	233.6	45.6	53.6
Gerber Childrenswear Inc.	NYSE	GCW	126.9	7.9	25.8
Gaiam, Inc.	OTC	GAIA	295.5	68.2	60.7
Artesian Resources Corp.	OTC	ARTNA	62.8	20.5	45.5
York Water Company	OTC	YORW	92.2	22.9	74.2

Based on this table, answer following activities and questions as appropriate:

(a) How many variances are there in this data set?

b) Which variables are qualitative and which are quantitative?

c) For the Stock Exchange variable, show Frequency and Percentage Frequency of AMEX, NYSE and OTC.

d) Construct a bar chart according to table elaborated in c) above.

e) Show Frequency Distribution of Gross Profit Margin using 5 intervals: 0-14.9, 15-29.9, 30-44.9, 45-59.9 and 60-74.9.

f) Construct a histogram with grouped table of point e).

g) What is the most frequent price/earnings ratio according to intervals in e)?