Business 212: Business Statistics Ch 1. Introduction to Business Statistics

business statistics

a specialty area of statistics which are applied in the business setting

descriptive statistics

used to describe the total group of numbers

infernal statistics

infers relationships from the population of numbers

mean

the average number

mode

the most frequent number

median

the middle number

ratios

numbers representing relationships

sample size (sampling)

the number of people to ask

statistical model (modeling)

a representation of what will probably happen

probablity

the likelihood of something happening

just-in-time

reduces waste by organizing good delivered as needed, based on accurately forecasted demand

Six Sigma

a term used in business to describe a process that results in no more than 3.4 defects out of a million

control chart

a statistical graph that shows process changes over time

Why would a statistical model be used?

1. To report last month's average sales

2. To summarize data

3. To predict what probably might happen

4. To calculate turnover ratios

To predict what probably might happen

What is a tool used in Six Sigma that graphs process changes over time?

1. Probability

2. Control chart

3. Just-in-time inventory

4. Sample size

Control chart

What does Six Sigma refer to?

1. Using descriptive statistics to make inferential decisions

2. Creating a statistical model based on probabilty

3. Having enough in your sample size to have accurate statistics

4. Having no more than 3.4 defects out of a million

Having no more than 3.4 defects out of a million

How are descriptive statistics used?

1. Use historical data

2. To summarize numbers

3. All of these

4. To provide an average

All of these

What is an example of probability?

1. The number of cars sold last month

2. The likelihood that a product will be defective

3. The total profit of a company

4. The average production time

The likelihood that a product will be defective

qualitative variables

categories that result in descriptive values or labels

nominal variables

qualitative variables that only refer to information by name and do not have to be listed in any order

ordinal variables

results that are listed in a certain order or follow some type of ranking system

binary variables

categories that will only result in one of two options

quantitative variables

categories that result in numerical values or real numbers

continuous variable

a measurement that can assume an endless number of values

discrete variable

used when there is a rating system or scale of measurement to follow

Looking at the chart of quantitative variables below, which variable is continuous?

1. Rating

2. Salary

3. 4-Somewhat likely

4. No continuous variable is listed.

Salary

Looking at the data listed under the Position variable, why would the Position variable be considered a nominal variable?

1. The label lists the positions in order.

2. The label ranks the positions.

3. The label describes the position by name.

4. The label rates the positions.

The label describes the position by name.

Looking at the data given for the Rating variable, what type of variable is being used?

A discrete variable

Using the chart of qualitative variables below, which variable is binary?

1. Tenure Track

2. Position

3. Education

4. No binary variable is listed.

Tenure Track

Looking at the chart of qualitative variables below, what type of variable is 'Education'?

1. Discrete

2. Ordinal

3. Nominal

4. Binary

Ordinal

Population

a group that has been designated for gathering data from

Data

information collected from the population

Descriptive Statistics

give information that describes the data in some manner

Inferential Statistics

makes inferences about populations, using data drawn from the population

• probability distributions, hypothesis testing, correlation testing and regression analysis

Sample

a set of data taken from the population to represent the population

What are two examples of inferential statistics?

1. mean and probability distributions.

2. Regression analysis and hypothesis testing.

3. Range and percentiles.

4. Variance and correlation.

Regression analysis and hypothesis testing.

What is statistical estimation?

1. Methods for rounding answers in statistical calculations.

2. Methods for reducing errors in descriptive statistics.

3. Methods for reducing errors in inferential statistics.

4. Methods to determine the best graph to represent statistical data.

Methods for reducing errors in inferential statistics.

How do descriptive and inferential statistics differ?

1. Descriptive statistics only attempt to describe data, while inferential statistics attempt to make predictions based on data.

2. Descriptive statistics are more computationally sophisticated than inferential statistics.

3. Inferential statistics are more computationally sophisticated than descriptive statistics.

4. Inferential statistics only attempt to describe data, while descriptive statistics attempt to make predictions based on data.

Descriptive statistics only attempt to describe data, while inferential statistics attempt to make predictions based on data.

Which two are examples of descriptive statistics?

1. Mean and standard deviation.

2. Hypothesis testing and histograms.

3. Variance and regression analysis.

4. Median and correlation.

Mean and standard deviation.

In statistics, a sample:

1. Can be used for inferences but not for predictions.

2. Is another word for population.

3. Is a set of data taken from the population to represent the population.

4. Is only used in descriptive statistics.

Is a set of data taken from the population to represent the population.

Statistical Model

a combination of inferences based on collected data and population understanding used to predict information in an idealized form

Correlation

the relationship between two variables or sets of data

Response Variable

the observed variable, or variable in question

Dependent Variable

a condition or piece of data in an experiment that is controlled or influenced by an outside factor, most often the independent variable

Explanatory Variable

a variable, or set of variables, that can influence the response variable

Independent Variable

a condition or piece of data in an experiment that can be controlled or changed

Nominal Data

categorical data that assigns numerical values as an attribute to an object, animal, person or any other non-number

Ordinal Data

is data that can be ordered and ranked, but not measured

Discrete Data

data that cannot be divided, it is distinct and can only occur in certain values

Continuous Data

data that can be divided infinitely, it does not have any value distinction

Variables are collected in the form of data. What are the two major forms of data?

1. categorical and quantitative

2. numerical and ordinal

3. measurable and non-measurable

4. explanatory and response

categorical and quantitative

Sheila is a baker experimenting with a cake recipe. Specifically, she is monitoring how changes in the volume of cream affect the moistness of the cake. What kind of variable is the volume of cream, and why?

1. it is the response variable, because it has an influence on the dependent variable

2. it is a response variable, because it is a condition in the experiment that is being changed.

3. it is an independent variable because it is a condition in the experiment that can be changed.

4. it is an independent variable, because it can be divided infinitely

it is an independent variable because it is a condition in the experiment that can be changed.

Jim is studying how differences in the screen color of electronic devices make an impact on eye strain experienced by the user. In these experiments, which is the response variable and which is the explanatory variable.

1. the response variable is eye strain; the explanatory variable is screen color

2. the response variable is screen color; the explanatory variable is eye strain

3. the response variable is eye strain; the explanatory variable is not mentioned

4. the response variable is eye strain; the explanatory variable is the electronic device

the response variable is eye strain; the explanatory variable is screen color

Why do different types of statistical models exist?

1. to determine which variables should be controlled or changed

2. because there is no way to find relationships between all of the variables that exist

3. because there are many different types of variables and the models provide ways to analyze them

4. to explain why a set of variables incur a response in the variable in question

because there are many different types of variables and the models provide ways to analyze them

The _____ is a condition or piece of data in an experiment that is controlled or influenced by an outside factor, most often the independent variable.

1. independent variable

2. dependent variable

3. explanatory variable

4. statistical model

Dependent variable

Bivariate Data

deals with two variables that can change and are compared to find relationships

Independent Variable

condition or piece of data in an experiment that can be controlled or changed

Dependent Variable

a condition or piece of data in an experiment that is controlled or influenced by an outside factor, most often the independent variable

Univariate Data

one variable in a data set that is analyzed to describe a scenario or experiment

Positive Correlation

dependent variables and independent variables in a data set increase or decrease together

Negative Correlation

dependent variables and independent variables in a data set either increase or decrease opposite from one another

When you find a relationship in bivariate data, you are looking at a positive or a negative _____.

1. bivariate

2. correlation

3. dependent

4. independent

5. univariate

correlation

One variable in a data set that is analyzed to describe a scenario or experiment is called _____

1. correlation

2. independent

3. dependent

4. univariate

5. bivariate

univariate

What type of data uses two sets of variables that can change and are compared to find relationships?

1. Dependent

2. Bivariate

3. Univariate

4. Correlation

5. Independent

Bivariate

A condition or piece of data in an experiment that is controlled or influenced by an outside factor is considered what type of variable?

1. Univariate

2. Correlation

3. Dependent

4. Bivariate

5. Independent

Dependent

A scientist is conducting an experiment on mice, seeing how their weight is affected by the volume of cheese they're given. What is the independent variable in this experiment, and why?

1. The volume of cheese is the independent variable, because it's being affected by the weight of the mice.

2. The volume of cheese is the independent variable, because it's being changed to measure the effect on weight.

3. The weight of the mice is the independent variable, because it's being changed to measure the volume of cheese.

4. The weight of the mice is the independent variable, because it's being affected by the volume of cheese.

The volume of cheese is the independent variable, because it's being changed to measure the effect on weight.

Data

information that is collected for analysis

Nominal data

categorial data that assigns numerical values as an attribute to an object, animal, person or any other non-number

Ordinal data

data that can be ordered and ranked, but not measured (levels of achievement, prizes, rankings, and placements)

Interval Measurement

data that is grouped in evenly distributed values and measured based on the group to which the variable is attributed

Ratio

a mathematical comparison between two numbers

What is information that is collected for analysis?

1. Ordinal Data

2. Ratio

3. Interval measurement

4. Data

5. Nominal Data

Data

What is a mathematical comparison between two numbers?

1. Nominal Data

2. Interval measurement

3. Ordinal Data

4. Ratio

5. Data

Ratio

The numbers on lacrosse jerseys are an example of _____ data.

1. Nominal

2. Ordinal

3. Ratio

4. Discrete

5. Interval

Nominal

A coach records the levels of ability in martial arts of various kids. What type of data is this?

1. Interval

2. Discrete

3. Nominal

4. Ordinal

5. Ratio

Ordinal

What is data that is grouped in evenly distributed values and measured based on the group to which the variable is attributed?

1. Ratio

2. Ordinal Data

3. Nominal Data

4. Data

5. Interval measurement

Interval measurement

Variable

an alphabetical character that represents an unknown number

Random Variable

a variable that is subject to randomness, which means it can take on different values

discrete random variable

when the variable represents isolated points on the number line

X is discrete

the numbers that X represents are isolated points on the number line

probability distribution

all the possible values of the random variable and the associated probabilities

X is continuous

X represents an infinite number of values on the number line

density curve

a plot of the relative frequencies of a continuous random variable

An agency decides to conduct a survey on household incomes in their county. Let x = the household income. What type of variable is x?

1. x is a discrete random variable.

2. x is a continuous random variable.

3. x is a binomial random variable.

4. x is both discrete and continuous.

5. x is not a random variable.

x is a continuous random variable.

You decide to conduct a survey of families with two children. You are interested in counting the number of boys (out of 2 children) in each family. Is this a random variable, and if it is, what are all its possible values?

1. No, it is not a random variable, since it is not random.

2. Yes, it is a random variable, and its values can be 1 and 2.

3. Yes, it is a random variable, and its values can be 2 or 4.

4. Yes, it is a random variable, and its values are 0, 1, or 2.

Yes, it is a random variable, and its values are 0, 1, or 2.

You decide to collect a bunch of cans of soda and measure the volume of soda in each can. Let x = the number of mL of soda in each can. What type of variable is x?

1. x is a continuous random variable.

2. x is a discrete random variable.

3. x is a constant.

4. x is not a random variable.

x is a continuous random variable.

Which of the following is NOT a property of a random variable?

1. A random variable can be discrete or continuous.

2. The sum of the probabilities of a random variable is equal to 1.

3. A random variable cannot be negative.

4. A random variable represents numerical outcomes for different situations or events.

A random variable cannot be negative.

You conduct an experiment where you want to measure the number of rolls it takes to get two 6's in a row when you roll a fair six-sided die. State whether the random variable is discrete or continuous and give a summary of its values.

1. Discrete with values ranging from 0 to 1

2. Discrete with values 2, 3, 4, 5, 6, etc.

3. Continuous with values ranging from 1 to 6

4. Discrete with values ranging from 1 to 6

Discrete with values 2, 3, 4, 5, 6, etc.

Bias

the intentional or unintentional favoring of one group or outcome over other potential groups or outcomes in the population

• selection bias

• response bias

selection bias

• non-representative sample

• nonresponse bias

• voluntary bias

Non-representative Sample

when the method with which a sample is collected specifically excludes certain groups from the research, whether intentionally or unintentionally

Nonresponse Bias

the members of a sample that do not choose to respond or participate in the research and the characteristics of those members

Voluntary Bias

the members of a sample that choose to respond or participate in the research, whether intentionally or unintentionally

response bias

• leading questions

• social desirability

Leading Questions

questions that encourage the answer expected from the researcher

Social Desirability

the tendency of participants to answer inaccurately, based on the way they feel they should answer rather than the truth

Why is it important to avoid a non-representative sample when conducting a survey?

1. A non-representative sample means the survey results will be diverse

2. It is harder to identify the characteristics of a non-representative sample

3. The survey will reflect the characteristics only of the group that was sampled

4. The survey will reflect the characteristics only of the group that was excluded

The survey will reflect the characteristics only of the group that was sampled

A survey is handed out by loud volunteers on a street corner. Some people are suspicious of the volunteers and choose to not participate in the survey. This is an example of:

1. Non-representative sample

2. Nonresponse bias

3. Leading questions

4. Voluntary bias

5. Social desirability

Nonresponse bias

A political group invites people in the local communities to participate in a survey about prayer in schools. This is an example of:

1. Nonresponse bias

2. Leading questions

3. Social desirability

4. Non-selection bias

5. Voluntary bias

Voluntary bias

In a survey, people on average responded that they floss seven times a week despite the fact that the actual averages are drastically lower. Which form of bias likely accounts for this discrepancy?

1. Social desirability

2. Nonresponse bias

3. Cultural desirability

4. Voluntary bias

5. Selection bias

Social desirability