Business Statistics Test #1

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Questions and Answers

Which of the following is an example of categorical data? (Select all that apply)

Social security number (correct)

Height, in meters, of a diving board

Score on a multiple-choice exam

Number of square feet of carpet

What is an observation in data collection?

The set of measurements collected for a particular element.

What is categorical data?

May be either numeric or nonnumeric, including nominal and ordinal variables.

Is income an example of categorical data or quantitative data?

Quantitative data Signup and view all the answers

What are descriptive statistics?

Summaries of data, which may be tabular, graphical, or numerical (median, mode, mean). Signup and view all the answers

The sum of frequencies for all classes will always equal:

The number of items in a data set Signup and view all the answers

How is the relative frequency of a class computed?

By dividing the frequency of the class by the sample size. Signup and view all the answers

In a cumulative frequency distribution, the last class will always have a cumulative frequency equal to what?

The total number of elements in the data set. Signup and view all the answers

What kind of data is a bar chart used with?

Categorical data. Signup and view all the answers

What are nominal variables?

Unordered categories and labels (e.g., race, state, major in college). Signup and view all the answers

What are ordinal variables?

Variables where order and rank are meaningful (e.g., bond ratings, approve/disapprove/neutral, hotel star ratings). Signup and view all the answers

What are ratio variables?

Variables where two ratios are important (e.g., time, distance, height, weight, price). Signup and view all the answers

What are interval variables?

Variables where the interval between observations has meaning (e.g., IQ test score). Signup and view all the answers

What is quantitative data?

Data that can be measured on an interval or ratio scale. Signup and view all the answers

What is cross-sectional data?

Data collected at the same or approximately the same point in time. Signup and view all the answers

What is time-series data?

Data collected over several time periods. Signup and view all the answers

What is a population in statistics?

All the elements in a data set. Signup and view all the answers

What is a sample?

A subset of the population. Signup and view all the answers

What is a census?

Collecting data for an entire population. Signup and view all the answers

What are statistics?

The art and science of collecting, analyzing, presenting, and interpreting data. Signup and view all the answers

What is experimental data?

Data generated in a controlled experiment. Signup and view all the answers

What is observational data?

Data that are not generated in an experiment controlled by the researcher. Signup and view all the answers

What is statistical inference?

Learning about the characteristics of a population by looking at a subset or sample of the population. Signup and view all the answers

What is frequency distribution?

A tabular summary of data showing the number (frequency) of observations in each of several non-overlapping categories or classes. Signup and view all the answers

What is the formula for relative frequency of a class?

Frequency of a class divided by n. Signup and view all the answers

What is percent frequency?

Relative frequency (frequency of a class divided by n) times 100. Signup and view all the answers

What is the equation for finding the midpoint of a class?

Lower class limit + (upper class limit - lower class limit) / 2. Signup and view all the answers

What is a histogram?

Used for quantitative data. Signup and view all the answers

What does 𝑥̅ represent?

Sample average. Signup and view all the answers

What does μ represent?

Population average. Signup and view all the answers

What is the percentile formula?

𝐿𝑝 = (𝑃/100) (𝑛 + 1) Signup and view all the answers

What is the formula for population variance?

∑[(𝑥𝑖 − 𝜇)^2]/N Signup and view all the answers

What is the formula for sample variance?

∑[(𝑥𝑖 − 𝑥̅)^2]/(n-1) Signup and view all the answers

What is the population standard deviation?

Square root of population variance. Signup and view all the answers

What is the sample standard deviation?

Square root of sample variance. Signup and view all the answers

What is the formula for a z-score?

(𝑥𝑖 − 𝑥̅)/s Signup and view all the answers

What does Chebyshev's Inequality enable us to do?

(1 −[1/(𝑧^2)] allows us to make statements about the minimum percentage of data values that must be within a specified number of standard deviations from the mean. Signup and view all the answers

Can crosstabulation use both categorical and quantitative variables?

Yes. Signup and view all the answers

What do positive values of covariance indicate?

A positive relation between the x and the y variables. Signup and view all the answers

What is discrete statistics?

Statistics that only take on certain values (e.g., yes/no, how did you get to work). Signup and view all the answers

What is continuous statistics?

Statistics that could have an infinite number of answers (e.g., what is your favorite number). Signup and view all the answers

What is a population parameter?

A numerically valued attribute of a model for a population (μ), probably cannot measure it. Signup and view all the answers

What is a sample statistic?

Different answers as you sample one group and another, not necessarily exact. Signup and view all the answers

What is a measure of dispersion?

How spread out the data set is (e.g., variance, range, interquartile range, standard deviation). Signup and view all the answers

What is the scale of measurement?

Whether data is ordinal, nominal, ratio, or interval scale. Signup and view all the answers

Study Notes

Categorical Data

Categorical data can be numeric or nonnumeric and includes nominal and ordinal variables.
An example of categorical data is a social security number, while income is classified as quantitative data.

Observations and Data Types

Observation refers to the set of measurements collected for a specific element.
Cumulative frequency distributions show the total number of elements in the last class.
Cross-sectional data is collected at a single point in time, while time-series data is gathered over multiple time periods.

Statistics Fundamentals

Descriptive statistics summarize data through tabular, graphical, or numerical formats, including median, mode, and mean.
Frequency distribution summarizes data showing the number of observations in non-overlapping categories.
A census involves collecting data for an entire population, while a sample is a subset of that population.

Statistical Concepts

Statistical inference allows conclusions about a population based on a sample.
Observational data is gathered without controlled experimental conditions, unlike experimental data obtained in a controlled environment.

Variable Types

Nominal variables have unordered categories (e.g., race, state).
Ordinal variables possess meaningful order and ranking (e.g., bond ratings, survey responses).
Interval variables have meaningful intervals between values (e.g., IQ scores), while ratio variables have meaningful ratios (e.g., height, weight).

Measures of Central Tendency and Dispersion

Sample average is represented as 𝑥̅, whereas the population average is denoted by μ.
Population variance is calculated using the formula ∑[(𝑥𝑖 − 𝜇)^2]/N; sample variance uses ∑[(𝑥𝑖 − 𝑥̅)^2]/(n-1).
Sample and population standard deviation are the square roots of their respective variances.

Distribution Characteristics

Right-skewed and left-skewed distributions indicate the direction of data skewness.
Covariance is positive when there's a positive relationship between two variables.

Percentiles and Dispersion Measures

Percentile location is calculated using Lp = (P/100)(n + 1).
The measure of dispersion indicates how spread out data is, encompassing variance, range, interquartile range, and standard deviation.

Graphical Representations

Bar charts visually represent categorical data, while histograms illustrate quantitative data.

Additional Statistical Tools

Chebyshev's Inequality helps quantify the data values within a specified number of standard deviations from the mean.
The z-score formula (𝑧 = (𝑥𝑖 − 𝑥̅)/s) measures how far a value deviates from the mean based on standard deviation.

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Description

This quiz assesses your understanding of key concepts in Business Statistics, including categorical data and observational measurements. Test your knowledge with flashcards that highlight important definitions and examples. Perfect for students preparing for exams in business-related courses.