knowledge of basic statistical techniques

What is Statistics?

Chapter 1

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The purpose of this course is to develop your knowledge of basic statistical techniques and methods and how to apply them to develop the business and personal intelligence that will help you make decisions.

Learning Objectives

LO1-1 Explain why knowledge of statistics is important

LO1-2 Define statistics and provide an example of how statistics is applied

LO1-3 Differentiate between descriptive and inferential statistics

LO1-4 Classify variables as qualitative or quantitative, and discrete or continuous

LO1-5 Distinguish between nominal, ordinal, interval, and ratio levels of measurement

LO1-6 List the values associated with the practice of statistics

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Why Study Statistics

Data are collected everywhere and require statistical knowledge to make the information useful

Statistics is used to make valid comparisons and to predict the outcomes of decisions

Statistical knowledge is useful in any career

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Study statistics and learn some basic techniques and applications that can be used everyday. The graphic shows the amount of data generated every minute (www.domo .com). A good working knowledge of statistics is useful for summarizing and organizing data to provide information that is useful and supportive of decision making.

data are collected everywhere and require statistical knowledge to make the information useful,

statistical techniques are used to make professional and personal decisions, and

no matter what your career, you will need a knowledge of statistics to understand the world and to be conversant in your career.

What is Meant by Statistics

What is statistics?

It’s more than presenting numerical facts

Example: The inflation rate for the calendar year was 0.7%. By applying statistics we could compare this year’s inflation rate to past observations of inflation. Is it higher, lower, or about the same? Is there a trend of increasing or decreasing inflation? Is there a relationship between interest rates and government bonds?

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STATISTICS The science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions.

Statistics is about collecting and processing information to create a conversation, to stimulate additional questions, and to provide a basis for making decisions. Chart 1-1 shows using statistics to analyze the distribution and market share of Frito-Lay products compared to the rest of the snack chip markets.

Types of Statistics

There are two types of statistics, descriptive and inferential

Descriptive statistics can be used to organize data into a meaningful form

You can summarize data and provide information that is easy to understand

Example: There are a total of 46,837 miles of interstate highways in the U.S. The interstate system represents 1% of the nation’s roads, but carries more than 20% of the traffic. Texas has the most interstate highways and Alaska doesn’t have any.

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DESCRIPTIVE STATISTICS Methods of organizing, summarizing, and presenting data in an informative way.

The type of statistics depends on the questions asked and the type of data available. Unorganized data is of little value as is, but descriptive statistics can be used to summarize the data and provide information that is easy to understand. Statistical methods and techniques to generate descriptive statistics are presented in chapters 2 and 4. Chapter 3 discusses statistical measures to summarize the characteristics of a distribution.

Types of Statistics (2 of 3)

Inferential statistics can be used to estimate properties of a population

You can make decisions based on a limited set of data

Example: In 2015, a sample of U.S. Internal Revenue Service tax preparation volunteers were tested with three standard tax returns. The sample indicated that tax returns were completed with a 49% accuracy rate. In other words, there were errors on about half of the returns.

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INFERENTIAL STATISTICS The methods used to estimate a property of a population on the basis of a sample.

When it is not practical to study an entire population, use surveys and sampling to estimate the characteristic under consideration. Inferential statistics is used widely in business, agriculture, politics, and government.

Types of Statistics (3 of 3)

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POPULATION The entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest.

SAMPLE A portion or part of the population of interest.

You can save time and money by collecting a sample to estimate the population parameter.

Types of Variables

There are two basic types of variables

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QUALITATIVE VARIABLE An object or individual is observed and recorded as a non-numeric characteristic or attribute.

Examples: gender, state of birth, eye color

QUANTITATIVE VARIABLE A variable that is reported numerically.

Examples: balance in your checking account, the life of a car battery, the number of people employed by a company

There are two basic types of variables, qualitative (non-numeric) and quantitative (numeric). When working with qualitative variables, we simply count the number of observations for each category. Then the percent for each category can be determined. Qualitative variables are often summarized in charts and bar graphs.

Types of Variables (2 of 2)

Quantitative variables can be discrete or continuous

Discrete variables are typically the result of counting

Values have “gaps” between the values

Examples: the number of bedrooms in a house (1, 2, 3, 4, etc.), the number of students in a statistics course (326, 421, etc.)

Continuous variables are usually the result of measuring something

Can assume any value within a specific range

Examples: Duration of flights from Orlando to San Diego (5.25 hours), grade point average (3.258)

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There are two types of quantitative variables and they are usually reported numerically.

Types of Variables Summary

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Chart 1-2 summarizes the two basic types of variables.

Levels of Measurement

There are four levels of measurement

Nominal, ordinal, interval, and ratio

The level of measurement determines the type of statistical analysis that can be performed

Nominal is the lowest level of measurement

Examples: classifying M&M candies by color, identifying students at a football game by gender

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NOMINAL LEVEL OF MEASUREMENT Data recorded at the nominal level of measurement is represented as labels or names. They have no order. They can only be classified and counted.

Data can be classified according to levels of measurement, and the level of measurement will determine how the data should be summarized and presented. The nominal level of measurement does not permit any mathematical operation that has any valid interpretation even if numbers are assigned to the labels or names.

Levels of Measurement (2 of 4)

The next level of measurement is the ordinal level

The rankings are known but not the magnitude of differences between groups

Examples: the list of top ten states for best business climate, student ratings of professors

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ORDINAL LEVEL OF MEASUREMENT Data recorded at the ordinal level of measurement is based on a relative ranking or rating of items based on a defined attribute or qualitative variable. Variables based on this level of measurement are only ranked and counted.

A qualitative variable or attribute is either ranked or rated on a relative scale such as rating a professor as superior, good, average, poor, or inferior. Notice, there is no way to determine the magnitude of the difference between superior and good or any other ranking.

Levels of Measurement (3 of 4)

The next level of measurement is the interval level

This data has all the characteristics of ordinal level data, plus the differences between the values are meaningful

There is no natural 0 point

Examples: the Fahrenheit temperature scale, dress sizes

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INTERVAL LEVEL OF MEASUREMENT For data recorded at the interval level of measurement, the interval or the distance between values is meaningful. The interval level of measurement is based on a scale with a known unit of measurement.

An example of interval level measurement is temperature; temperatures can be ranked and the differences between the values is meaningful. Additionally, a zero does not represent the absence of the condition; in this example of temperature, a zero just means it is really cold.

Levels of Measurement (4 of 4)

The highest level of measurement is the ratio level

The data has all the characteristics of the interval scale and ratios between numbers are meaningful

The 0 point represents the absence of the characteristic

Examples: wages, changes in stock prices, and height

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RATIO LEVEL OF MEASUREMENT Data recorded at the ratio level of measurement are based on a scale with a known unit of measurement and a meaningful interpretation of zero on the scale.

Almost all quantitative variables are ratio level; the zero point and ratios between two numbers is meaningful at this level. Money is an example of ratio level measurement. If you have no money, you have zero dollars and a wage of $50 per hour is twice as much as a wage of $25 per hour.

Levels of Measurement Summary

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Chart 1-3 summarizes the 4 levels of measurement. Statistical methods to analyze nominal level data are covered in chapter 15 and methods used for ordinal-level data are discussed in chapter 16. Methods of analyzing interval or ratio level data are presented in chapters 9-14.

Ethics and Statistics

Practice statistics with integrity and honesty when collecting, organizing, summarizing, analyzing, and interpreting numerical information

Maintain an independent and principled point of view when analyzing and reporting findings and results

Question reports that are based on data that

does not fairly represent the population

does not include all relevant statistics

introduces bias in an attempt to mislead or misrepresent

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Basic Business Analytics

Business Analytics is used to process and analyze data and information to support a story or narrative of a company

Using computer software to summarize, organize, analyze, and present the findings of statistical analysis is essential

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Business analytics is used to process and analyze data and information to support a story or narrative of a company’s business, such as “what makes us profitable,” or “how will our customers respond to a change in marketing”?

The example shows the application of Excel to perform a statistical summary. It refers to sales information from the Applewood Auto Group, a multi-location car sales and service company.

Minitab will also be used to illustrate applications.

Chapter 1 Practice Problems

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Question 1

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What is the level of measurement for each of the following variables?

Student IQ ratings

Distance students travel to class

The jersey numbers of a sorority soccer team

A student’s state of birth

A student’s academic class – that is, freshman, sophomore, junior, or senior

Number of hours students study per week

LO1-5

Question 13

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For each of the following, determine whether the variable is continuous or discrete, quantitative or qualitative, and level of measurement

Salary

Gender

Sales volume of MP3 players

Soft drink preference

Temperature

SAT scores

Student rank in class

Rating of a finance professor

Number of home video screens

LO1-4,5

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