Psych 105 Chapter 2: Descriptive Statistics
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Questions and Answers

What symbol is used to represent standard deviation in populations?

  • δ
  • s
  • sd
  • σ (correct)
  • If the sum of squares is 30 and the sample size is 10, what is the value of the sample standard deviation?

  • 3.00
  • 2.00
  • 1.83 (correct)
  • 1.73
  • What does a higher standard deviation indicate about a dataset?

  • Data points are more spread out from the mean (correct)
  • There are no outliers in the dataset
  • Data points are closer to the mean
  • The mean is higher than the median
  • What is the sample variance if the sum of squares is 30 and the sample size is 10?

    <p>3.33</p> Signup and view all the answers

    What does a lower standard deviation imply about the data points in comparison to the mean?

    <p>Data points are closer to the mean</p> Signup and view all the answers

    What is the primary purpose of descriptive statistics?

    <p>To summarize and describe the main features of a dataset.</p> Signup and view all the answers

    Which of the following is NOT a type of descriptive statistic?

    <p>Hypothesis Testing</p> Signup and view all the answers

    What is the arithmetic mean represented by when referring to a population?

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

    Which measure of central tendency is most sensitive to changes in the data distribution?

    <p>Arithmetic Mean</p> Signup and view all the answers

    In a dataset with an odd number of values, how is the median determined?

    <p>It is the middle value when the values are ordered.</p> Signup and view all the answers

    What do descriptive statistics include when analyzing the variability of a dataset?

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

    What does the mode represent in a dataset?

    <p>The most frequently occurring value.</p> Signup and view all the answers

    If the mean of a dataset is significantly affected by outliers, which measure of central tendency is likely a better representation?

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

    How is the median calculated in a data set with an even total count?

    <p>By averaging the two middle values after arranging the data in order.</p> Signup and view all the answers

    What characteristic of the median makes it unaffected by extreme values?

    <p>It is a positional measure.</p> Signup and view all the answers

    In Distribution A (2, 4, 6, 10, 11, 12, 13), what is the median value?

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

    Which set of data illustrates the calculation of the median as averaging 9 and 10?

    <p>2, 4, 6, 9, 10, 11, 12, 13</p> Signup and view all the answers

    Why is the mode considered the least used measure of central tendency?

    <p>It often provides unstable results, especially in small datasets.</p> Signup and view all the answers

    What is the primary advantage of using the mean as a measure of central tendency?

    <p>It is the most stable measure.</p> Signup and view all the answers

    What is a significant disadvantage of using the median as a measure of central tendency?

    <p>It is not computed from the actual scores.</p> Signup and view all the answers

    Which measure of variability reflects the simplest form of spread in a dataset?

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

    In the context of variance, what does 'N-1' refer to?

    <p>Degrees of freedom.</p> Signup and view all the answers

    How is variance calculated in a dataset?

    <p>By averaging the squared differences from the mean.</p> Signup and view all the answers

    What characteristic does the mode have in a dataset?

    <p>It is the least stable of the measures of central tendency.</p> Signup and view all the answers

    Which of the following statements accurately describes the range?

    <p>It is sensitive to extreme values in the dataset.</p> Signup and view all the answers

    Which measure of dispersion gives insight into the average distance of each score from the mean?

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

    Study Notes

    Descriptive Statistics

    • Descriptive statistics summarize and describe dataset features.
    • Types include Measures of Central Tendency, Measures of Dispersion, and Measures of Shape.

    Measures of Central Tendency

    • Measures indicate the typical score within a dataset:
      • Mean (μ or x̄): Calculated as the sum of all scores divided by the number of scores. Sensitive to all changes in data.
      • Median: The middle value of an ordered dataset. For odd counts, it's the center value; for even counts, it's the average of the two middle values. Not influenced by extreme values.
      • Mode: The most frequently occurring score. Least stable and least used, especially in smaller datasets.

    Mean Properties

    • The algebraic sum of deviations from the mean is zero.
    • It considers every score in the dataset, making it representative.

    Median Characteristics

    • More stable across groups than the mode. Not affected by outliers, making it a good measure for skewed distributions.

    Mode Characteristics

    • Simple to find but may not be a unique value. Less effective for small datasets due to potential instability.

    Summary of Measures

    • Mean: Represents all data; affected by outliers; suitable for ratio and interval scales.
    • Median: More stable; ordinal and interval scale applicable; not suitable for further statistical analysis.
    • Mode: Easy to calculate; applicable for nominal and ordinal scales; may not exist or be unique.

    Measures of Dispersion or Variability

    • Range: The difference between the maximum and minimum values; sensitive to outliers.
    • Variance (σ² or s²): The average of squared differences from the mean; indicates data spread. Normal divisor for population is N, while for sample it is n-1.
    • Standard Deviation (σ or s): Represents the average distance of data points from the mean. Higher values indicate more spread, while lower values indicate data clustering around the mean.

    Standard Deviation Details

    • Population SD uses σ; sample SD uses s or sd.
    • Squaring the differences gives more weight to outliers.

    Calculation Examples

    • If the sum of squares equals 30 with n = 10:
      • Population variance = 3
      • Population SD ≈ 1.73.
      • Sample SD ≈ 1.83
      • Sample variance = 3.33.

    Fun Facts About Statistics

    • 11% of people are left-handed.
    • August has the highest birth percentage.
    • Koalas sleep about 18 hours daily.
    • An average person sleeps for 25 years during their lifetime.
    • Commonly forgotten travel item is a toothbrush.
    • The index finger is the most sensitive.
    • Average golf ball has 336 dimples.
    • Monopoly is the most played board game.
    • A piece of paper cannot be folded more than 7 times.
    • Hiccups typically last around 5 minutes.

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    Description

    Dive into the fundamentals of descriptive statistics with this quiz focusing on measuring central tendency, dispersion, and shape. Explore concepts such as mean, median, mode, range, variance, and more as you test your understanding of data summarization techniques. Perfect for Psychology 105 students looking to reinforce their knowledge.

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