Chapter 1:Introduction to

Statistics

LO1 Define statistics and list example applications of statistics in business.

LO2 Define important statistical terms, including population, sample, and parameter, as they relate to descriptive and inferential statistics.

LO3 Explain the difference between variables, measurement, and data.

LO4 Compare the four different levels of data: nominal, ordinal, and ratio.

Learning Objectives

• The gathering, (organizing, summarizing) analyzing, interpreting, and presenting data

• The science of numbers• Branch of mathematics• Course of study or way of thinking• The recording of numerical facts and figures• The recording or registration of a death• Measurement(s) on characteristics associated with objects

(things, elements) included in a sample• Type of distribution being used to analyze data

What is Statistics?

• A survey of 1,007 adults by RBC Capital Markets showed that 37% of adults would be willing to drive 8 to 15 km to save 5 cents on a litre of gas.

• A Deloitte Retail “Green” survey of 1,080 adults revealed that 54% agreed that plastic, non-compostable shopping bags should be banned.

• In a 2008 survey of 14 countries conducted by GlobeScan for the National Geographic Society, Canada ranked 13 out of 14 when it came to environmentally friendly consumption patterns. This was due mostly to Canadian preferences for bigger houses and an established culture of using privately owned cars as opposed to transit.

Applications in Business

• Descriptive Statistics: – Using data gathered on a group to describe or reach conclusions

about that same group and that group alone: The average for your statistics class.

• Inferential Statistics: – Using sample data to reach conclusions or make general

statement(s) about the population from which the sample was taken: The average litres per 100 km based on four cars selected from a parking lot.

Descriptive vs. Inferential Statistics

• Population: – Webster’s Third New International Dictionary defines population as a

collection of persons, objects, or items of interest.

• Census: – When researchers gather data from the whole population for a given

measurement of interest, they call it a census.

• Sample: – A sample is a portion of the whole and, if properly taken, is

representative of the whole.

Population Versus Sample

• Parameter — a descriptive measure (s) of the population with respect to some characteristic of interest.

• Usually values representing the tendency for things to be alike(converge to a norm); and the tendency for things to differ (diverge) from that norm. – Parameters are usually represented by Greek letters

• Statistic — a descriptive measure(s) of the population with respect to some characteristic but using sample data.– Sample statistics are usually represented by Roman letters

Parameter vs. Statistic

Population All The Cars in the Parking Space Of Interest

The Population and Census Data

Identifier Color MPG

RD1 Red 12

RD2 Red 10RD3 Red 13

RD4 Red 10RD5 Red 13BL1 Blue 27BL2 Blue 24

GR1 Green 35GR2 Green 35GY1 Gray 15GY2 Gray 18GY3 Gray 17

• The accuracy of the sample statistic depends on how representative the sample is.

• Is the sample in the next slide representative of the twelve cars in the parking lot?

• There are 2 blue, 2 green, 3 grey, and 5 red cars.

• In the sample there are no blue cars. The sample is biased in terms of consumer choice attributes, green, grey and red.

Representativeness of the Sample

Sample and Sample Data

• Each member of the population may have several characteristics associated with it.

• Cars in a parking lot may have characteristics such colour, speed, design, manufacturer, fuel consumption rates, price, performance ranking by AAA, etc

• The various characteristics are measured using nominal, ordinal, interval or ratio measures.

• The type of statistical analysis that is appropriate depends on the level of data measurement used.

Characteristics

• A variable is a characteristic of any entity being studied that is capable of taking on different values.

• A measurement occurs when a standard process is used to assign numbers to particular attributes or characteristics of a variable.

• Once such measurements are recorded and stored, they can be

denoted as “data.” It can be said that data are recorded measurements. The processes of measuring and data gathering are basic to all that we do in business statistics.

Variables and Data

Hierarchy of Levels of Data

• Nominal. Player number 10. Identifies the player but does not assign a value to the player. “John is an educator” assigns John to a category, coded as 5. This number assigns no value to john.

• Ordinal ranks. The ranking in the Canadian dance skating competition; 1, 2, 3, 4… The order is clear but the difference between the performances cannot be inferred by the numeric values.

• Interval. Measures of temperature have no natural or fixed zero point. Zero is just a reference point.

• Ratio scale measures: height, weight, time, etc. Here zero is not arbitrary. It is fixed. It means the absence of the characteristic.

Examples of Levels of Data Measures

Usage Potential of VariousLevels of Data

• Using numbers or codes to classify or categorize the characteristic or attribute

Nominal Level Data

• Numbers are used to indicate rank or order– Relative magnitude of numbers is meaningful– Differences between numbers are not comparable

• Example: Ranking productivity of employees• Example: Taste test ranking of three brands of soft drink• Example: Positions within an organization where

– 1 used for President– 2 used for Vice President– 3 for Plant Manager– 4 for Department Supervisor– 5 for Employee

Ordinal Level Data

• Coding of Responses on a Questionnaire:• “Faculty and staff should receive preferential treatment for

parking space”.• Rank Your response from 1 (least important) to 5 (most

important)

Ordinal measures require special statistical techniques

Ordinal Data as Indicators of Preference or Degrees of Agreement

Example of Ordinal Measurement Position at the Finish Line

• Distance between consecutive integers (1,2,3,4 or 20o , 21o, and 22o ) are equal.

• Differences between consecutive numbers have meaning• The zero point is a matter of convention or convenience and

not a natural or fixed zero point. Zero is just another point on the scale and does not mean the absence of the phenomenon.• For example, zero degrees Celsius is not the lowest possible

temperature.

• Examples: • Fahrenheit Temperature: zero does not mean the absence of

temperature• Calendar Time, Percentage Change

Interval Level Data

• Characteristics of measure– Relative magnitude of numbers is meaningful– Differences between numbers are comparable– Location of origin, zero, is absolute (natural)– Vertical intercept of unit of measure transform function is zero

• Examples: – Height, Weight, and Volume– Monetary variables: Profit and Loss, Revenues, and Expenses;

unemployment insurance, subsidies– Financial ratios, such as P/E Ratio, Inventory Turnover, and Quick Ratio.

Ratio Level Data

Statistical Techniques

• Parametric statistics require that data be interval or ratio.• If the data are nominal or ordinal, nonparametric

statistics must be used. Nonparametric statistics can also be used to analyze interval or ratio data.

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