JMU Math 220 Statistics Flashcards

Questions and Answers

What are ordered pairs?

Consists of values of two variables for each individual in the data set

What is bivariate data?

Data that consists of ordered pairs

What is a scatterplot used for?

Used to study bivariate data

What describes a positive association?

Two variables, large values of one associated with large values of the other Signup and view all the answers

What is the least-squares regression line?

Line that fits best is the line for which the sum of squared distances is as small as possible Signup and view all the answers

What describes a negative association?

Large values of one associated with small values of the other Signup and view all the answers

What indicates a linear relationship in data?

Data tends to cluster around a straight line when plotted on a scatterplot Signup and view all the answers

What is the correlation coefficient?

Summary statistic most often used to measure the closeness of the relationship between two variables Signup and view all the answers

If r is positive, then two variables have a negative linear association.

False Signup and view all the answers

If r is close to 1, then the linear association is strong and positive.

True Signup and view all the answers

The residual is the difference between the observed value and the predicted value.

True Signup and view all the answers

What is the arithmetic mean?

Add the values and divide by the number of values in the set Signup and view all the answers

Which measure is influenced more by extreme values?

Mean Signup and view all the answers

What condition indicates data is skewed to the right?

Mean > median Signup and view all the answers

What indicates data is skewed to the left?

Mean < median Signup and view all the answers

When is data approximately symmetrical?

Mean = median Signup and view all the answers

What is the range of a data set?

The difference between the largest value and the smallest value Signup and view all the answers

What does variance measure?

Measure of how far the values in the data set are from the mean, on average Signup and view all the answers

What is a deviation?

Difference between a population value and the population mean Signup and view all the answers

What is sample variance?

Average of the squared deviations (from sample) using n-1 as the denominator Signup and view all the answers

What does degrees of freedom represent?

n-1 Signup and view all the answers

What is the standard deviation?

Square root of the variance Signup and view all the answers

What is Chebyshev's Inequality?

Proportion of the data that will be within K standard deviations of the mean is at least 1-(1/K^2) Signup and view all the answers

What information does a z-score provide?

How many standard deviations that value is from its population mean Signup and view all the answers

Define a pie chart.

Show the distribution of a categorical variable as a "pie" whose slices are sized by the frequencies or relative frequencies of the categories Signup and view all the answers

What defines a bar graph?

Represent each category as a bar, where bar heights show the frequencies or relative frequencies of the categories Signup and view all the answers

What is a histogram?

A graph based on frequency distributions using rectangles to represent data Signup and view all the answers

How are classes defined in frequency distributions?

Classes must not overlap, must be of equal width, and must cover all observations without gaps Signup and view all the answers

What does a simple random sample entail?

Size n consists of n individuals from the population chosen such that every set of n individuals has an equal chance to be selected Signup and view all the answers

What is cluster sampling?

Items are drawn from the population in groups Signup and view all the answers

What is stratified sampling?

Population is divided into groups and a simple random sample is drawn from each group Signup and view all the answers

What is convenience sampling?

Often produces unrepresentative data Signup and view all the answers

What is an observational study?

Observes individuals and measures variables of interest without influencing response Signup and view all the answers

What is a randomized experiment?

A study in which the investigator assigns the treatments to the experimental units at random Signup and view all the answers

What defines qualitative or categorical variables?

Classify individuals into categories, with two types: ordinal and nominal Signup and view all the answers

What are ordinal variables?

Categories that have a natural ordering Signup and view all the answers

What defines nominal variables?

Categories that have no natural ordering Signup and view all the answers

What are quantitative variables?

Tell how much or how many of something there is, with types: discrete and continuous Signup and view all the answers

What are discrete variables?

Take values that are countable Signup and view all the answers

What are continuous variables?

Take on any values in some interval Signup and view all the answers

Study Notes

Statistical Concepts

Ordered pairs represent values of two variables for each individual within a data set, forming the foundation of bivariate data.
Bivariate data consists of these ordered pairs, useful for analyzing relationships between two variables.
Scatterplots are visual tools used to study the relationship between bivariate data, highlighting associations.

Associations Between Variables

Positive associations indicate that large values of one variable correspond with large values of another.
Negative associations mean that large values of one variable are related to small values of the other.
Linear relationships occur when data points cluster around a straight line when plotted.

Regression Analysis

The least-squares regression line minimizes the sum of squared distances between the observed values and predicted values.
The point of averages is central in regression analysis, ensuring the least-squares line passes through this calculated point.

Residuals and Predictions

A residual is calculated by subtracting the predicted value from the observed value, providing insight into prediction accuracy.
Predictions from the regression line can be made using an explanatory variable to estimate the outcome variable.

Measures of Central Tendency

The arithmetic mean is the average of a data set obtained by dividing the sum of the values by the number of observations.
The median serves as the midpoint of a distribution, determined by sorting data and finding the middle value or averaging the two central values in even sets.
The mode is the most frequently occurring value in a data set.

Variability and Distribution

Variance reflects how far the values in a data set deviate from the mean, with sample variance using n-1 as a denominator.
Standard deviation is the square root of variance and indicates the dispersion of data points around the mean.
The Interquartile Range (IQR) measures statistical dispersion, representing the range between the first (Q1) and third quartiles (Q3).

Outliers and Their Detection

Outliers are values that fall outside the lower and upper bounds, defined as Q1 - 1.5×IQR and Q3 + 1.5×IQR, respectively.
Identifying outliers helps in understanding data distribution and potential anomalies.

Probability Concepts

Probability values range from 0 to 1, representing the likelihood of an event occurring.
Equally likely events permit simple calculations where the probability of an event is the number of favorable outcomes divided by the total outcomes.
The general addition rule accounts for overlapping events in probability calculations.

Sampling Methods

Simple random samples ensure every individual from the population has an equal chance of selection, minimizing bias.
Cluster sampling involves grouping individuals and selecting entire clusters randomnly, while stratified sampling divides the population into specific groups and samples from each.
Convenience and voluntary response samples may lead to unrepresentative data due to selection bias.

Research Design

Observational studies focus on measuring variables without intervention, while experiments involve assigning treatments to assess outcomes.
Randomized experiments ensure treatments are assigned randomly, reducing bias in results.
In double-blind experiments, neither participants nor researchers know the treatment assignments, eliminating personal bias effects.

Variable Types

Qualitative variables categorize individuals, divided into ordinal (with logical order) and nominal (without a specific order).
Quantitative variables provide measurable quantities, categorized into discrete (countable) and continuous (capable of taking any value within a range).

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Description

Explore key concepts of Statistics in JMU Math 220 through these flashcards. Each card highlights important terms and definitions relevant to bivariate data, scatterplots, and associations. Perfect for quick review and mastery of statistical principles.