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Introductory Statistics: Describing and Summarizing Data

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  • What is the goal of graphs in statistics?
    Graphs help identify patterns, trends, missing values, shape, and outliers in data.
  • What is an outlier?
    An outlier is an observation that is unusually high or low compared to the rest of the data.
  • Name five common types of graphs used to display data.
    Pie chart, Bar chart, Histogram, Dotplot, and Boxplot.
  • What does a frequency table show?
    A frequency table summarizes one categorical variable by showing how many observations fall into each category.
  • How do you calculate the proportion of a category in a dataset?
    Divide the count in that category by the total sample size.
  • When is a pie chart appropriate for displaying data?
    When the focus is on percentages and the number of categories is small.
  • What is a contingency table?
    A table that summarizes two categorical variables simultaneously to show how they are related.
  • What is the difference between marginal and conditional proportions in contingency tables?
    Marginal proportions consider the entire dataset; conditional proportions focus on a specific group.
  • What are the key features of a symmetric distribution?
    Left and right sides are mirror images; mean and median are approximately equal and centered.
  • Describe a right-skewed distribution.
    Has a long tail to the right; most data values are low; mean is greater than the median.
  • Describe a left-skewed distribution.
    Has a long tail to the left; most data values are high; mean is less than the median.
  • What is a uniform distribution?
    A distribution where all outcomes occur approximately equally often with no dominant peak.
  • What does modality refer to in a distribution?
    The number of distinct peaks or modes in the data: unimodal, bimodal, or multimodal.
  • What is the difference between a histogram and a bar chart?
    Histogram displays quantitative data with touching bars; bar chart displays categorical data with spaced bars.
  • What are the three common measures of center?
    Mean (average), Median (middle value), and Mode (most frequent value).
  • When is the median preferred over the mean?
    When data are skewed or have outliers, because the median is resistant to outliers.
  • How is the range calculated?
    Range = Maximum value - Minimum value.
  • What are quartiles?
    Values that divide the ordered dataset into four equal parts: Q1 (25th percentile), Q2 (median), Q3 (75th percentile).
  • How do you calculate the interquartile range (IQR)?
    IQR = Q3 - Q1; it measures the spread of the middle 50% of the data.
  • What does the standard deviation measure?
    How far observations typically are from the mean; a measure of spread or variability.
  • Why is standard deviation preferred over variance?
    Because standard deviation has the same units as the data, making it more intuitive.
  • What is a boxplot and what does it show?
    A graphical summary showing the median, spread (IQR), and potential outliers of a dataset.
  • How are outliers identified in a boxplot?
    Data points outside the fences calculated as Lower Fence = Q1 - 1.5*IQR and Upper Fence = Q3 + 1.5*IQR.
  • What is a z-score?
    A measure of how many standard deviations an observation is from the mean.
  • What does a positive or negative z-score indicate?
    Positive z-score means the value is above the mean; negative means below the mean.
  • What is the Empirical Rule for bell-shaped distributions?
    Approximately 68% of data fall within 1 SD, 95% within 2 SDs, and 99.7% within 3 SDs of the mean.
  • How does adding a constant to all data values affect measures of center and spread?
    Measures of center shift by the constant; measures of spread (range, IQR, SD) remain unchanged.
  • How does multiplying all data values by a constant affect measures of center and spread?
    Both measures of center and spread are multiplied by that constant.
  • What can side-by-side boxplots be used for?
    To compare the distribution (center, spread, shape, outliers) of a quantitative variable across categories.