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Questions and Answers
What is the primary goal of descriptive statistics?
What is the primary goal of descriptive statistics?
What is the measure of central tendency that represents the middle value of a dataset?
What is the measure of central tendency that represents the middle value of a dataset?
What is the term for the average of the squared differences from the mean?
What is the term for the average of the squared differences from the mean?
What is the purpose of hypothesis testing in inferential statistics?
What is the purpose of hypothesis testing in inferential statistics?
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What is the probability of an event that is certain to occur?
What is the probability of an event that is certain to occur?
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What is the type of plot that shows the relationship between two continuous variables?
What is the type of plot that shows the relationship between two continuous variables?
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What is the term for the set of all possible outcomes of an experiment?
What is the term for the set of all possible outcomes of an experiment?
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What is the type of plot that shows the distribution of a single variable and compares across different groups?
What is the type of plot that shows the distribution of a single variable and compares across different groups?
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Study Notes
Descriptive Statistics
- Measures that summarize and describe the basic features of a dataset
- Types:
- Measures of central tendency:
- Mean (average value)
- Median (middle value)
- Mode (most frequent value)
- Measures of variability:
- Range (difference between largest and smallest values)
- Interquartile range (IQR, difference between Q3 and Q1)
- Variance (average of squared differences from the mean)
- Standard deviation (square root of variance)
- Measures of central tendency:
Inferential Statistics
- Uses sample data to make inferences about a population
- Types:
- Estimation:
- Point estimation (single value estimate of a population parameter)
- Interval estimation (range of values within which a population parameter is likely to lie)
- Hypothesis testing:
- Null hypothesis (H0, a statement of no difference or effect)
- Alternative hypothesis (H1, a statement of difference or effect)
- Test statistic (a value calculated from sample data to test H0)
- P-value (probability of observing the test statistic by chance)
- Estimation:
Probability
- The study of chance events and their likelihood of occurrence
- Key concepts:
- Event: a set of outcomes of an experiment
- Sample space: the set of all possible outcomes of an experiment
- Probability of an event: a number between 0 and 1 that represents the likelihood of the event occurring
- Conditional probability: the probability of an event occurring given that another event has occurred
- Independence: two events are independent if the occurrence of one does not affect the probability of the other
Data Visualization
- The use of graphical representations to communicate information about data
- Types of plots:
- Histograms: show the distribution of a single variable
- Bar charts: compare categorical data across different groups
- Scatter plots: show the relationship between two continuous variables
- Box plots: show the distribution of a single variable and compare across different groups
Descriptive Statistics
- Summarize and describe the basic features of a dataset
- Central tendency measures:
- Mean: average value of a dataset
- Median: middle value of a dataset when arranged in order
- Mode: most frequent value in a dataset
- Variability measures:
- Range: difference between largest and smallest values in a dataset
- Interquartile range (IQR): difference between Q3 (75th percentile) and Q1 (25th percentile)
- Variance: average of squared differences from the mean
- Standard deviation: square root of variance, measures spread of data
Inferential Statistics
- Uses sample data to make inferences about a population
- Estimation:
- Point estimation: single value estimate of a population parameter
- Interval estimation: range of values within which a population parameter is likely to lie
- Hypothesis testing:
- Null hypothesis (H0): statement of no difference or effect
- Alternative hypothesis (H1): statement of difference or effect
- Test statistic: value calculated from sample data to test H0
- P-value: probability of observing the test statistic by chance
Probability
- Study of chance events and their likelihood of occurrence
- Event: set of outcomes of an experiment
- Sample space: set of all possible outcomes of an experiment
- Probability of an event: number between 0 and 1 representing likelihood of event occurring
- Conditional probability: probability of an event occurring given that another event has occurred
- Independence: two events are independent if occurrence of one does not affect probability of the other
Data Visualization
- Use of graphical representations to communicate information about data
- Types of plots:
- Histograms: show distribution of a single variable
- Bar charts: compare categorical data across different groups
- Scatter plots: show relationship between two continuous variables
- Box plots: show distribution of a single variable and compare across different groups
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Description
Test your knowledge of descriptive statistics, including measures of central tendency and variability, and their applications.
