Intro to Statistics Exam 1 Flashcards

Questions and Answers

Is the statement '75% of the class plans to take another math class' an example of descriptive or inferential statistics?

Inferential statistics: the results of the class sample are extended to make a generalization about the population of all students at the school. (correct)

Descriptive statistics: the results of the class sample are described without making any generalizations about the population of all students at the school.

Inferential statistics: the results of the class sample are described without making any generalizations about the population of all students.

What type of variable is 'eye color'?

Categorical

What is the process of coding in statistics?

The process of representing categorical variables with numbers.

What percentage of a class of 12 men and 25 women is male?

32.4% Signup and view all the answers

How many men are there in a class of 271 students if 46.5% of them are men?

126 males Signup and view all the answers

What is the total number of students in a class with 15 women that is made up of 54% women?

28 students Signup and view all the answers

What information is missing that might contradict the claim that women prefer earlier statistics classes?

The age and class standing of the students is unknown. Signup and view all the answers

Why are percentages or rates often better than counts for making comparisons?

They take into account possible differences among the sizes of the groups. Signup and view all the answers

Is the study observing teenagers and adults choosing diet soft drinks observational or controlled?

Observational study Signup and view all the answers

What type of study is it when boys are divided into two groups to compare violent actions after watching different types of cartoons?

Controlled experiment Signup and view all the answers

What is the response variable in a question about causality?

The outcome variable Signup and view all the answers

Which method of data collection is suitable for making conclusions about causal relationships?

Controlled experiments Signup and view all the answers

What is an identifying mark of an observational study?

Subjects are put into treatment or control groups by their own actions or external decisions. Signup and view all the answers

What is the difference between two groups in an observational study that explains different outcomes called?

A confounding variable Signup and view all the answers

What type of sample is obtained by dividing a population into homogeneous groups and selecting individuals from each group?

Stratified sample Signup and view all the answers

A simple random sample is always preferred because it obtains the same information as other sampling plans but requires a smaller sample size.

False Signup and view all the answers

A frequency distribution lists the of each category of data, while a relative frequency distribution lists the of occurrences of each category of data.

Number & Proportion Signup and view all the answers

After constructing any relative frequency distribution, what should be the sum of the relative frequencies?

1 or 100% Signup and view all the answers

What is it called when a distribution has most values relative small but also has a few very large values?

Right-skewed Signup and view all the answers

What indicates the existence of multiple mounds in a distribution?

Two very different groups have been combined into a single collection. Signup and view all the answers

What are values so large or so small that they do not fit into the pattern of the distribution called?

Outliers Signup and view all the answers

What are two commonly used graphs to display the distribution of a sample of categorical data?

Bar graph and pie chart Signup and view all the answers

What are Pareto charts?

They are bar charts that are sorted from most frequent to least frequent. Signup and view all the answers

Which of the following is not a difference between bar charts and histograms?

A bar chart is used for numerical variables while a histogram is used for categorical variables. Signup and view all the answers

True or False? A bar chart is used for numerical variables while a histogram is used for categorical variables.

True Signup and view all the answers

When describing the distribution of a categorical variable, the category that appears most often is called the _____?

Mode Signup and view all the answers

A categorical variable is only called bimodal under what circumstances?

Two categories are nearly tied for most frequent outcomes. Signup and view all the answers

What is the most common trick to mislead readers of bar graphs?

Change the scale of the vertical axis so that it does not start at 0. Signup and view all the answers

For what type of distribution does the mean represent the typical value?

For distributions that are roughly symmetric. Signup and view all the answers

What is statistics?

The science of collecting, organizing, summarizing, and analyzing data to answer questions. Signup and view all the answers

What is the definition of a population in statistics?

Collection of all data values that ever will occur for a group. Signup and view all the answers

What is a sample?

A subset of the population that represents the population at large. Signup and view all the answers

What does categorical describe in statistics?

A quality or class; can be numbers, but no arithmetic is possible. Signup and view all the answers

What does numerical describe in statistics?

A quantity or measurement. Signup and view all the answers

What is coded data?

Using numbers to record categorical data. Signup and view all the answers

Give an example of using coded data.

0= No, 1= Yes Signup and view all the answers

What is stacked data?

Each row contains data for a single individual. Signup and view all the answers

What is unstacked data?

Each column is a variable from a different group. Signup and view all the answers

What are two-way tables?

Displays results from two potentially related variables. Signup and view all the answers

What is a treatment variable?

Whether or not a specific treatment is used. Signup and view all the answers

What is the outcome (response) variable?

Whether or not a certain outcome is seen. Signup and view all the answers

What is the objective of treatment vs. outcome variable analysis?

To determine if the treatment variable causes a change in the outcome variable. Signup and view all the answers

What is a treatment group?

A group that receives the treatment. Signup and view all the answers

What is a control group?

A group that does not receive the treatment. Signup and view all the answers

What is the placebo effect?

Reacting to a treatment after being told you are receiving the treatment when you aren't. Signup and view all the answers

What is a controlled experiment?

Researchers assign subjects to a treatment group that can show causality. Signup and view all the answers

______ are a variable that has not been accounted for but which is causing a difference in the groups being studied.

Confounding Variables Signup and view all the answers

What are the three main components of a Numerical Distribution?

Shape, Center, Variability Signup and view all the answers

Describe Histograms (3 things).

They group data into intervals, count how many data values fall into each bin, and the height of each rectangle corresponds to the count. Signup and view all the answers

According to the Empirical Rule, what percentage of observations will be within two standard deviations of the mean?

Approximately 95% Signup and view all the answers

What types of distributions does the Empirical Rule apply to?

Symmetric and unimodal Signup and view all the answers

If an observation has a z-score of 0, which statement is true?

The observation is equal to the mean. Signup and view all the answers

Name two measures of the center of a distribution and state the conditions under which each is preferred for describing the typical value of a single data set.

Median, Mean Signup and view all the answers

Under what conditions is the median preferred?

When the data is strongly skewed. Signup and view all the answers

Under what conditions is the mean preferred?

When the data is relatively symmetric. Signup and view all the answers

When a distribution is skewed, the _ is used to measure the center and the _ is used to measure variation.

Median, Interquartile range Signup and view all the answers

Study Notes

Statistics Concepts

Statistics involves collecting, organizing, summarizing, and analyzing data to make conclusions.
Descriptive statistics summarize characteristics of a sample, while inferential statistics generalize findings from a sample to a larger population.

Types of Variables

Categorical variables describe qualities or classes, such as "eye color".
Numerical variables describe quantities or measurements and can be subjected to arithmetic operations.

Sampling Techniques

A simple random sample is preferred for obtaining unbiased information but other methods may yield more cost-effective results.
Stratified sampling divides the population into homogenous groups and selects randomly from each group to ensure representation.

Data Collection Methods

Controlled experiments assign subjects to treatment groups, allowing for causal inferences.
Observational studies record data without manipulating conditions, revealing correlations but not causations.

Data Representations

Frequency distributions list data categories with counts, while relative frequency distributions show proportions relative to the total.
Bar graphs illustrate categorical data, and pie charts represent proportions. Histograms display numerical distributions.

Distribution Characteristics

Right-skewed distributions contain most values as small with a few large values, resulting in a longer tail on the right side.
Outliers are extreme values that do not fit the overall distribution pattern, potentially distorting analysis.

Measures of Center

The mode defines the most frequently occurring category in a dataset, while the mean and median serve as central tendency measures.
The median is preferred for skewed data or datasets with outliers, whereas the mean is better for symmetric distributions.

Key Statistical Rules

The Empirical Rule applies to symmetric, unimodal distributions, stating that approximately 95% of observations fall within two standard deviations from the mean.

Experimental Design

Control groups do not receive the treatment, serving as a baseline for comparison.
The placebo effect can occur when subjects respond to the belief that they are receiving treatment, even if they are not.

Confounding Variables

These additional variables can skew results if not accounted for, leading to erroneous conclusions about relationships in observational studies.

Visualization Aids

Histograms consist of consecutive bins that touch, with heights corresponding to counts of observations in each interval.
Pareto charts sort data from most to least frequent, emphasizing the most impactful factors.

Understanding Statistical Terms

A response variable measures outcomes in relation to treatment variables.
Coded data utilizes numbers to represent categorical responses for easier analysis.

Summary of Key Points

Use percentages for accurate group comparisons by accounting for size differences.
In a bimodal distribution, two categories have nearly the same frequency.
Statistical graphs should be designed to avoid misleading representations through scale manipulations or other tactics.

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Description

Test your knowledge on statistics with these flashcards covering key concepts from the introductory course. This quiz focuses on understanding the difference between descriptive and inferential statistics through practical examples.