PSYC 243 Exam 1 Study Guide: Statistics
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Which of the following best defines a population in statistics?

  • A type of variable that can take any value within a range
  • The entire group of individuals or items that are of interest (correct)
  • A subset of individuals from a larger group
  • A measurement calculated from a sample

    • A statistic can be defined as a characteristic or measure obtained by using the data values from a sample.

    True

    What type of variable is used to categorize data without a specific order?

    Nominal variable

    In an experimental study, the variable that is manipulated by the researcher is known as the ______.

    <p>independent variable</p> Signup and view all the answers

    Which type of study is best suited for determining a causal relationship?

    <p>Experimental study</p> Signup and view all the answers

    Match the type of variable to its appropriate definition:

    <p>Discrete = A variable that has distinct and separate values Continuous = A variable that can take any value within a range Nominal = A variable that categorizes data without an order Ratio = A variable that has a true zero point and equal intervals</p> Signup and view all the answers

    Frequency tables are used to display the number of times each value occurs in a dataset.

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

    Why can't non-experimental studies determine causation?

    <p>They do not manipulate independent variables.</p> Signup and view all the answers

    What is the Z-score when 𝜎 is 6, given that X is 62 and µ is 70?

    <p>-1.33</p> Signup and view all the answers

    The formula for variance includes dividing the sum of squares by N.

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

    What is the formula for calculating a Z-score?

    <p>Z = (X - µ) / σ</p> Signup and view all the answers

    The Z-score for 𝜎=9 when X is 62 and µ is 70 is _______.

    <p>-0.89</p> Signup and view all the answers

    Match the following statistical terms with their formulas:

    <p>Z-score = $Z = \frac{X - \mu}{\sigma}$ Variance = $\sigma^{2} = \frac{\sum\left( X - \mu \right)^{2}}{N}$ Standard Deviation = $\sigma = \sqrt{\frac{\sum\left( X - \mu \right)^{2}}{N}}$ Sum of Squares = $\sum(X - \mu)^{2}$</p> Signup and view all the answers

    Which characteristic is NOT a property of the normal curve?

    <p>It is always positively skewed.</p> Signup and view all the answers

    The standard deviation can be calculated without a dataset if the variance is known.

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

    What is a z-score?

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

    In a symmetrical distribution, the mean, median, and mode are all ______.

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

    Match the type of distribution with its characteristic:

    <p>Positive Skew = The tail on the right side is longer or fatter Negative Skew = The tail on the left side is longer or fatter Bimodal = Two different modes Symmetrical = Equally balanced around the mean</p> Signup and view all the answers

    Which of the following is the most common measure of variability?

    <p>Standard Deviation</p> Signup and view all the answers

    A stem and leaf plot is useful for both organizing and visualizing data.

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

    Under what circumstances does the mean not provide a representative value?

    <p>When the data is skewed or has outliers.</p> Signup and view all the answers

    The formula for variance is often denoted as ______ for a sample and ______ for a population.

    <p>s^2, σ^2</p> Signup and view all the answers

    What does a z-score of 0 indicate?

    <p>The value is equal to the mean.</p> Signup and view all the answers

    What is the z-score for X = 70 given M = 65 and σ = 10?

    <p>1.0</p> Signup and view all the answers

    If the mean is 65 and the standard deviation is 10, then a score of 55 corresponds to a negative z-score.

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

    What is the mean of the dataset: 2, 2, 2, 3, 4.5, 1, 7, 3.5, 4, 3.5?

    <p>3.25</p> Signup and view all the answers

    For the given dataset, the mode is __________.

    <p>2</p> Signup and view all the answers

    Match the statistical measurements with their definitions:

    <p>Mean = Average of the dataset Median = Middle value when ordered Mode = Most frequently occurring value Standard Deviation = Measure of dispersion</p> Signup and view all the answers

    A z-score represents how many standard deviations an element is from the mean.

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

    The independent variable in a study is the one that __________.

    <p>is manipulated</p> Signup and view all the answers

    If M = 80 and σ = 5, what is the z-score for a score of 87.5?

    <p>1.5</p> Signup and view all the answers

    Which distribution shows the greatest negative skew?

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

    What was the student's z-score on the test?

    <p>-2</p> Signup and view all the answers

    The mean score (μ) of the class on the exam was 70.

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

    What is the sample standard deviation from the data set 2, 12, 8, 18, 0, 20?

    <p>8.20</p> Signup and view all the answers

    If the mean (M) of the data set is ___, then X - M is calculated by subtracting M from each X value.

    <p>10</p> Signup and view all the answers

    Which standard deviation would result in the lowest percentile rank for the student scoring X=62?

    <p>6</p> Signup and view all the answers

    Match the statistical term to its definition:

    <p>Mean = The average of a set of numbers Range = The difference between the highest and lowest scores Variance = A measure of how far a set of numbers are spread out from their average Standard Deviation = The square root of the variance</p> Signup and view all the answers

    What is the range for the data set {2, 12, 8, 18, 0, 20}?

    <p>20</p> Signup and view all the answers

    What score corresponds to a z-score of -2 when the mean is 80 and the standard deviation is 5?

    <p>60</p> Signup and view all the answers

    The sum of squared deviations in the second problem is 100.

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

    The __ of the dataset 2, 2, 2, 3, 4.5, 1, 7, 3.5, 4, 3.5 is calculated to be 3.25.

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

    Study Notes

    Exam 1 Study Guide: Statistical Analysis & Design (PSYC 243)

    • Exam Content: Covers the material from chapters 1-5 of the readings and lectures.
    • Question Types: 32 multiple-choice questions (2.5 points each), and 20-point problem set.
    • Review Session: A review session will be offered before the exam.
    • TA Review Sessions: Undergraduate TAs will also hold review sessions during office hours (listed in the syllabus).
    • Required Materials: Pen/pencil, student ID, and an ACT/SAT-approved calculator.

    Chapter 1: Introduction to Statistics

    • Population: The entire group of interest.
    • Sample: A subset of the population.
    • Parameter: A numerical description of a population.
    • Statistic: A numerical description of a sample.
    • Discrete Variables: Variables that can only take on specific values (e.g., whole numbers).
    • Continuous Variables: Variables that can take on any value within a given range (e.g., height, weight).
    • Nominal Variables: Variables that categorize data into distinct groups (e.g., gender, eye color).
    • Ordinal Variables: Variables that categorize and rank data (e.g., education level, satisfaction rating).
    • Interval Variables: Variables that categorize, rank and have equal intervals between values (e.g., temperature in Celsius).
    • Ratio Variables: Variables that categorize, rank, have equal intervals and possess a true zero point (e.g., height, weight).
    • Correlational Studies: Examine the relationship between two or more variables.
    • Experimental Studies: Manipulate one or more variables to examine their effect on another.
    • Non-Experimental Studies: Observe variables without manipulation to identify relationships.
    • Independent Variables: The variable manipulated in a study.
    • Dependent Variables: The variable measured in a study.
    • Causation: Experimental studies are necessary to determine causality.

    Chapter 2: Frequency Distributions

    • Frequency Tables: Tables that summarize the frequency of data values.
    • Bar Graphs: Graphs that display categorical data.
    • Histograms: Graphs that display continuous data, with bars touching.
    • Polygons: Graphs that connect points representing frequencies, sometimes used with histograms.
    • Normal Curve: A bell-shaped curve, often observed in natural phenomena.
    • Stem-and-Leaf Plots: Data visualization method for ordered data.
    • Central Tendency Measures of central tendency are the value at the centre of the data. Mean, Median and Mode are examples.

    Chapter 3: Central Tendency

    • Mean: The average of the data.
    • Median: The middle value in a sorted dataset.
    • Mode: The most frequent value.
    • Symmetrical Distributions: Mean, median, and mode are equal.
    • Skewed Distributions: Mean, median, and mode not equal, skewed to the direction of outlier data.
    • Positive Skew: The tail of the distribution extends to the right.
    • Negative Skew: The tail of the distribution extends to the left.

    Chapter 4: Variability

    • Sum of Squares: A calculation in statistics to measure the spread of data.
    • Variance: A measure of how spread out the data is.
    • Standard Deviation: A measure of the dispersion of a dataset relative to its mean.
    • Range: Distance between the highest and lowest values in a dataset.

    Chapter 5: Z-Scores

    • Z-score: A standardized score that shows the distance of a data point from the mean in terms of standard deviations.
    • Z-score Interpretation: Expresses how many standard deviations a score is above or below the mean. A z-score of zero means the score is equal to the mean. A positive z-score means the score is above the mean and a negative z-score means the score is below the mean.

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    STATS Exam 1 Study Guide Fall 2024 PDF

    Description

    Prepare for your PSYC 243 Exam 1 with this comprehensive study guide covering chapters 1-5. Expect multiple-choice questions and a problem set that will test your understanding of key statistical concepts and terminology. Utilize the review sessions for additional support and guidance.

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