Introductory Statistics Exam 1
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Questions and Answers

What does it mean for two events to be mutually exclusive?

Mutually exclusive events cannot occur at the same time.

What are the two branches of statistics?

Descriptive and Inferential Statistics

How do you write the notation for 2 events that are independent?

P(A and B) = P(A) * P(B)

What is a Z score? List the characteristics. Include the formula.

<p>A Z-score measures how many standard deviations an element is from the mean.</p> Signup and view all the answers

How do we define population? How is a sample different from a population?

<p>A population is the entire group we are interested in studying, while a sample is a subset of the population.</p> Signup and view all the answers

Give an example of a population and its sample.

<p>Population: All students at a university. Sample: A group of 100 students selected from that university.</p> Signup and view all the answers

Describe the difference between quantitative and qualitative variables/data. Give examples.

<p>Quantitative data is numerical (e.g., height, weight), while qualitative data is categorical (e.g., color, gender).</p> Signup and view all the answers

Describe the difference between descriptive and inferential data. Give examples.

<p>Descriptive statistics summarizes data (e.g., mean, median), while inferential statistics uses data to make predictions or inferences about a population.</p> Signup and view all the answers

Why would you subset your data?

<p>To focus on a specific part of the data, to remove outliers, or to analyze different groups within the data.</p> Signup and view all the answers

How do you make a Horizontal Bar Chart?

<p>Horizontal bar charts display categorical data with rectangular bars where the length of each bar is proportional to the value it represents; categories are displayed on the vertical axis and values on the horizontal axis.</p> Signup and view all the answers

What graphical tool is best used to display the relative frequency of a numerical variable?

<p>A histogram</p> Signup and view all the answers

Can you understand a frequency table, find relative frequency?

<p>Relative frequency = (Frequency of a class) / (Total frequency).</p> Signup and view all the answers

How do you find relative frequency?

<p>Divide the frequency of a particular value by the total number of values.</p> Signup and view all the answers

What is the difference between relative frequency and percent frequency?

<p>Relative frequency is a proportion, while percent frequency is the relative frequency multiplied by 100.</p> Signup and view all the answers

If I spent 35% of my weekly budget on food and my monthly budget was $200 how much money did I spend on Food?

<p>$70</p> Signup and view all the answers

Define Frequency!

<p>The number of times a value occurs in a dataset.</p> Signup and view all the answers

What proportion of the observations are at least 18 but less than 24?

<p>7/20 = 0.35</p> Signup and view all the answers

What statistic is MOST influenced by outliers?

<p>The mean</p> Signup and view all the answers

At a local bar...What is the probability that a randomly selected customer orders beer?

<p>0.614</p> Signup and view all the answers

Given that the camera was purchased at Amazon.com, the probability that it that is was a Canon brand is _______

<p>0.189</p> Signup and view all the answers

What is a statistic?

<p>A numerical value summarizing sample data.</p> Signup and view all the answers

Do you remember mean, median, and mode? Which one is most influenced by outliers?

<p>Mean: Average. Median: Middle value. Mode: Most frequent value. The mean is most influenced by outliers.</p> Signup and view all the answers

Can you use a table to take a statistic like a percent or relative frequency and find the number given the population size?

<p>Yes</p> Signup and view all the answers

What is the empirical rule?

<p>Approximately 68% of the data falls within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.</p> Signup and view all the answers

What is the most common statistics to show dispersion?

<p>Standard deviation and variance.</p> Signup and view all the answers

What is Variance, what does it show, and how is it related to standard deviation?

<p>Variance measures the average squared deviation from the mean. It shows the spread of data. It is the square of the standard deviation.</p> Signup and view all the answers

What is covariance?

<p>A measure of how two variables change together.</p> Signup and view all the answers

How can an event be collectively exhaustive?

<p>If the events include all possible outcomes.</p> Signup and view all the answers

What is a union in probability and what is the notation?

<p>The union of events includes all outcomes in either event. Notation: A ∪ B.</p> Signup and view all the answers

What is the intersection of 2 events in probability notation?

<p>The intersection of events includes the outcomes in BOTH events. Notation: A ∩ B.</p> Signup and view all the answers

The intersection of events A = {The Porch, Louie's, The Library, O'Connell's} and B = { The Library, O'Connell's, Logies, Volare} is _______

<p>{The Library, O'Connell's}</p> Signup and view all the answers

The union of events A = {The Porch, Louie's, The Library, O'Connell's} and B = { The Library, O'Connell's, Logies, Volare} is _______

<p>{The Porch, Louie's, The Library, O'Connell's, Logies, Volare}</p> Signup and view all the answers

When looking at the probability of an event, all the probabilities must add up to _______

<p>1</p> Signup and view all the answers

When an event has one outcome we call that an _______ event.

<p>elementary</p> Signup and view all the answers

What is a sample space? What would the sample space be for letter grades in this class?

<p>A sample space is the set of all possible outcomes of a random experiment. For letter grades: {A, B, C, D, F}.</p> Signup and view all the answers

What does the complement of A given sample space S mean?

<p>All outcomes in S that are NOT in A.</p> Signup and view all the answers

What is the correlation coefficient, the formula, and if given numbers can you calculate it?

<p>Measures the strength and direction of a linear relationship between two variables.</p> Signup and view all the answers

If you are given variance how do you get the Standard deviation?

<p>Take the square root of the variance.</p> Signup and view all the answers

If the average on exam 1 is an 85 with a standard deviation of 1.5, what is the probability you score less than 75?

<p>Almost 0</p> Signup and view all the answers

If the average on exam 1 is an 85 with a standard deviation of 1.5, what is the probability you score greater than a 90?

<p>0.00003</p> Signup and view all the answers

Flashcards

Mutually Exclusive Events

Events that cannot occur at the same time. If one event happens, the other cannot.

Branches of Statistics

Descriptive statistics summarize data, while inferential statistics makes predictions or inferences about a population based on a sample.

Independent Events Notation

P(A|B) = P(A). The occurrence of one event does not affect the probability of the other.

What is a Z-score?

A measure of how many standard deviations a data point is from the mean. Formula: z = (x - μ) / σ

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Population vs. Sample

Population is the entire group you want to study. A sample is a subset of the population.

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Quantitative vs. Qualitative Data

Quantitative data is numerical (e.g., height), while qualitative data is categorical (e.g., eye color).

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Descriptive vs. Inferential Statistics

Descriptive statistics summarize data, while inferential statistics draw conclusions about a population.

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Why Subset Data?

To analyze specific subgroups or remove irrelevant data.

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Horizontal Bar Chart

Represent categories along the horizontal axis, with bar lengths indicating frequency or relative frequency.

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Best graph for numerical variable's relative frequency?

Histogram

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Define Frequency

Frequency is the number of times a value occurs.

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How to find Relative Frequency?

Divide the frequency of a category by the total number of observations.

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Relative Frequency vs. Percent Frequency

Relative frequency is a proportion, while percent frequency is a percentage (relative frequency * 100).

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Define Frequency

The number of times a value occurs in a dataset.

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Outlier Influence

A value that differs greatly from other values in a set of data.

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What is a Statistic?

The number of times a value occurs in a dataset.

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Mean, Median, and Mode

Mean is the average, median is the middle value, and mode is the most frequent. The mean is most influenced by outliers.

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Empirical Rule

Approximately 68% of data falls within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3.

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Common Statistics for Dispersion

Standard deviation and variance.

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Variance

Variance measures how far a set of numbers are spread out from their average value. Standard deviation is the square root of the variance.

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What is Covariance?

Measures the degree to which two variables change together.

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Collectively Exhaustive Events

A set of events where at least one of the events must occur.

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Union in Probability

The event that either A or B or both occur. Notation: A ∪ B

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Intersection of 2 Events

The event that both A and B occur. Notation: A ∩ B

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Intersection of Events

{The Library, O'Connell's}

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Union of Events

{The Porch, Louie's, The Library, O'Connell's, Logies, Volare}

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Sum of all probabilities

One

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Event with one outcome

Elementary event.

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What is a Sample Space?

The set of all possible outcomes of an experiment. {A, B, C, D, F}

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The Complement of A

All outcomes in the sample space that are not in A.

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Study Notes

  • Exam 1 will consist of 40 questions to be answered in 50 minutes.
  • The exam is in person, on paper, and a scantron will be provided.

Mutually Exclusive Events

  • Be able to give an example.

Branches of Statistics

  • There are two branches of statistics.

Independent Events Notation

  • Be able to write the notation for 2 events that are independent.

Z Score

  • Be able to define a Z Score.
  • Know its characteristics.
  • Know the formula.
  • Be able to calculate if given numbers.

Population vs. Sample

  • Understand how population is defined.
  • Understand how a sample differs from a population.
  • Be able to give an example of a population and its sample.

Variable Data

  • Differentiate between Quantitative and Qualitative variables/data and give examples.
  • Differentiate between Descriptive and Inferential data and know examples.

Data Subset

  • Understand why you would subset your data.

Horizontal Bar Chart

  • Know how to make a Horizontal Bar Chart.

Numerical Variable

  • Understand what graphical tool is best used to display the relative frequency of a numerical variable.

Frequency Table

  • Be able to understand a frequency table.
  • Be able to find relative frequency.

Relative Frequency

  • Understand how to find relative frequency.
  • Understand the difference between relative frequency and percent frequency.

Budget Calculation

  • If 35% of a weekly budget of $200/month is spent on food, then be able to calculate the exact amount spent on food.

Frequency

  • Be able to define frequency

Observations Proportion

  • Be able to calculate the proportion of observations in a frequency table

Influenced Statistic

  • Determine is statistic is most influenced by outliers

Probability Calculation

  • Determine what is the probability that a randomly selected customer orders beer, with information on customer orders.

Camera Probability

  • Given that a camera was purchased at Amazon.com, the probability that it was a Canon brand is blank.

Data Types

  • Differentiate between Time series data compared to cross-sectional data.

Statistic definition

  • Be able to define statistics.

Measures of Central Tendency

  • Remember mean, median, and mode.
  • Identify which is most influenced by outliers.

Frequency

  • Use a table to take a statistic like a percent or relative frequency and find the number given the population size

Empirical Rule

  • What is the empirical rule

Dispersion

  • What are the most common statistics to show dispersion.

Variance

  • Define Variance.
  • What does it show.
  • How is it related to standard deviation.

Covariance

  • Be able to define covariance

Exhaustive Event

  • How can an event be collectively exhaustive?

Union in Probability

  • Define ‘union’ in probability, know the notation.

Intersection of Events

  • Define ‘intersection’ of events in probability notation.
  • The intersection of events A = {The Porch, Louie's, The Library, O'Connell's} and B = {The Library, O'Connell's, Logies, Volare}

Union of Events

  • Describe the union of events A = {The Porch, Louie's, The Library, O'Connell's} and B = { The Library, O'Connell's, Logies, Volare}

Probability

  • When looking at the probability of an event, all the probabilities must add up to blank.
  • When an event has one outcome, is termed a blank event.
  • Define what a sample space is, and provide an example of the sample space for letter grades in a class.
  • Define what the complement of A given sample space S means.

Correlation Coefficient

  • Define the correlation coefficient, including the formula.
  • Calculate if given numbers.

Standard Deviation

  • If given variance, how do you get the standard deviation?

Exam Score Probability

  • If the average on exam 1 is 85 with a standard deviation of 1.5, what is the probability you score less than 75 or score greater than a 90?

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Description

Concepts for exam 1 include mutually exclusive events, branches of statistics, independent events notation, and Z scores. Differentiating between population and sample, quantitative/qualitative variables, and descriptive/inferential data is important. Creating horizontal bar charts and understanding data subsets are tested.

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