History

Descriptive statistics have an extensive history developed through many disciplines. Basic forms of statistics have been used since the beginning of civilization. Historians posit the ancient use of statistical measures, specifically mean, median, mode. The ancient leaders used these measures to understand their empires in terms of population, geographical area, wealth and taxation, and military power (Kraus, 1994; Jones, 1953; Missiakoulis, 2010).

By the 17th century, Political Arithmetic was introduced by William Petty as a way to document all natural, social, and political components of a state with numbers in order to have a sound basis for decisions and, thus, avoid political controversies (1672) (Stochastikon Encyclopedia, 2014). During the same timeframe, John Graunt and Jacob Bernoulli Pascal were studying vital statistics of populations. Graunt had worked with Petty for a few years, and was an accomplished statistician. He was the first statistician to become a member of the Royal Society of London. While Bernoulli’s

Descriptive Statistics and Visualizing Data 109 greatest contributions are in calculus, geometry, and algebra, he started his career with demographic analysis. In this timeframe, the first weekly data collections on baptisms, marriages, and deaths were produced in London and France, followed by the first published demographic study on bills of mortality by Jacob Graunt. With centuries of development, descriptive statistics are now widely used across a variety of fields. We would guess that half of the quantitative planning articles include descriptive statistics, often as a precursor to inferential statistics (see Tables 7.1a and 7.1b). Qualitative planning articles also often include summary statistics on their subjects.

Tables 7.1a Quantitative Study With Descriptive Statistics Followed by Inferential Statistics (Ewing & Rong, 2008)

Household Variables	2001 RECS	2000 Census	1998 and 2002 AHS
Household Variables	Mean (SD)	Mean (SD)	Mean (SD)
Primary energy use per household (in thousands of BTUs)	95,415 (58,093)	NA	NA
House size (square feet)	2,097 (1,410)	NA	1,689 (1,098)
House type
Single-family detached	60.5%	60.7%	65.5%
Single-family attached	10.4%	7.6%	12.4%
Multi-family	29.1%	31.7%	22.1%
Year built
1939 or earlier	30.1%	14.3%	10.7%
1940 to 1959	20.7%	23.4%	18.9%
1960 to 1979	23.9%	32.5%	36.4%
1980 to 2000	25.3%	29.7%	34.0%
Household composition
Number of children	0.51 (0.93)	0.71 (EH)	0.71 (1.10)
Number of adults	2.11 (1.07)	1.95 (0.91)	1.92 (0.83)
Household income
less than S30.000	38.7%	30.5%	28.4%
$30,000 to $49,999	24.7%	21.5%	20.8%
$50,000 to $74,999	20.7%	19.8%	19.4%
$75,000 or more	15.9%	28.2%	31.4%
Race/Ethnicity of the householder
White	70.7%	69.0%	71.3%
Black	12.8%	12.7%	10.4%
Hispanic	10.9%	12.3%	11.5%
Asian	3.5%	4.1%	5.2%
Other	2.1%	1.9%	1.6%
Country variables
County sprawl index	NA	107 (28)	110 (21)
Residential construction costs	NA	0.982 (0.145)	0.992 (0.130)
Total population in the MSAs	NA	4,388,905 (5,696,873)	4,048,688 (4,136,994)

Sources: E1A (2004), Ewing et al. (2003), and U.S. Bureau of the Census (1998, 2002, 2004).

MSA = metropolitan statistical area; NA = not applicable; SD = standard deviation.

Table 7. lb Relationship Between Delivered Residential Energy Use in the United States, House Size and Type, and Other Control Variables (With Coefficients, t-Ratios, and Significance Levels)

	Heating		Cooling		Others
	Coefficient	p-Value	Coefficient	p-lTz/wc	Coefficient	p-Value
House size (square feet)	0.00015	<0.001	0.00012	<0.001	0.00006	<0.001
House type
Mobile home	0.086	0.020	0060	0.185	-0.025	0.333
Single family attached	-0.037	0.243	-0.115	0.008	-0.105	<0.001
Multi-family	-0.431	<0.001	-0.230	<0.001	-0.366	<0.001
Year built
1940 to 1959	-0.194	<0.001	-0.032	0.353	0.033	0.107
1960 to 1979	-0.355	<0.001	-0.025	0.465	0036	0.064
1980 to 2000	-0.456	<0.001	-0.049	0.157	0.044	0.037
Household income
S30.000 to $49,999	0.017	0.491	0.043	0.147	0.080	<0.001
S50.000 to $74,999	0.021 0.142	0.450	0.131	<0.001	0.131	<0.001
S75.000 or more		<0.001	0.169	<0.001	0.233	<0.001
Race/Ethnicitv of the hou:	seholder
Black	0.283	<0.001	0.166	<0.001	0.117	<0.001
Hispanic	-0.117	0.002	-0.230	<0.001	-0.078	0.001
Asian	-0.162	0.003	-0.350	<0.001	-0.225	<0.001
Other	-0.007	0.918	-0.117	0.161	-0.149	0.001
Household composition
Number ot children	0.016	0.449	0.137	<0.001	0.285	<0.001
Number of adults	-0.002	0.916	0.210	<0.001	0.184	<0 001
/„(energy price)	-1.006	<0.001	-0.571	<0.001	-0.403	<0 001
($ per thousand BTL’s)
HDDs	0 00020	<0.001	NA	NA	NA	NA
CDDs	NA	NA	0.00054	<0.001	NA	NA
R²	0.7293		0.7072		0.5531
Number of households	4,666		3,464		4,822

Source: EIA (2004)

Notes: Dependent variables arc the natural logarithms of delivered residential energy use for heating, cooling, and other uses, respectively, per household per year (in thousands of BTUs). Reference dummies included single-family detached housing, houses built before 1940, households with an annual income of less than $30,000, and white householders. Other controls for heating/cooling energy use models were the age of the heating/cooling equipment variable (dummies as less or more than ten years old), the programmability of the thermostat of the heating/cooling equipment variable (dummies as yes or no), and the building insulation variable (dummies as well or poorly insulated), plus whether the cooling equipment was central or not and whether there was someone at home all day on a typical weekday (dummies as yes or no).

In—natural log; NA—not applicable.

Mechanics

This section will break down the mechanics of descriptive statistics by the five measures discussed previously. It will also cover visual representation of data using graphs. While computer programs have curbed the need to be highly familiar with the mathematical steps required to conduct such operations, it is however of utmost

Descriptive Statistics and Visualizing Data 111 importance that one should understand the concepts behind each of these mathematical operations.