Questions and Answers
What is the definition of Statistics?
What does 'Data' refer to?
Pieces of information collected about cases
The Five W's of data are: Who, What, When, Where, _____
Why
What is meant by 'Categorical Variables'?
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What describes 'Quantitative Variables'?
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Which of the following is a way to summarize the distribution of a categorical variable?
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What is a 'Contingency Table'?
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What do Rows represent in a Contingency Table?
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What does a Pie Chart compare?
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If lines in a graph do not line up and conditional distributions are different, what does this indicate?
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What is a Histogram?
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What is the 'Mode' in statistics?
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What does 'Unimodal' refer to?
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The 'Range' of a dataset is the difference between the maximum and minimum values.
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What does the '5 Number Summary' include?
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Study Notes
Statistics
- Involves understanding data and making informed decisions amidst uncertainty.
- Examines variability to guide decision-making processes.
Data
- Comprises pieces of information collected about specific cases, which gain meaning through context.
Five W's of Data
- Who, What, When, Where, Why, and How are crucial aspects to consider in data collection.
Who
- Refers to the subjects or entities (people, places, things) on which data has been gathered.
What
- Represents the information or characteristics collected during the data gathering process.
When
- Details the time frame in which the data collection occurred.
Where
- Indicates the source or origin of the collected data.
Why
- Defines the objectives or purposes behind gathering the data.
How
- Describes the methodologies employed for collecting data.
Variables
- Categorical Variables: Recorded as labels, categorized into distinct groups.
- Quantitative Variables: Measured numerically, representing numeric values with defined units.
Cases and Variables
- Cases: Represented as rows in data tables.
- Variables: Represented as columns in data tables.
Categorical Variable Distribution Summaries
- Frequency table, pie chart, and bar chart are used to summarize categorical variable distributions.
Frequency Table
- Displays the distribution of responses from a survey or study.
Pie Chart
- Visualizes the proportional sizes of various categories, summing to 100%.
Bar Chart
- Illustrates categorical data; measures height to denote differences without requiring a specific order.
Contingency Table
- Examines distribution patterns for two categorical variables, identifying potential relationships.
Counts and Proportions
- Count: Number of observations in a category; when divided by the total, results in a proportion.
Frequency/Relative Frequency Table
- Summarizes the distribution and proportions for a categorical variable with counts.
Mosaic Plot
- Graphically represents conditional distributions from a contingency table, comparable to bar charts.
Association
- Identifies a relationship between variables; closer lines indicate less association, while diverging lines indicate more.
No Association
- Indicates similarity in conditional distributions; lines may not align perfectly yet reflect the absence of association.
Conditional Distribution
- Summarizes one variable's distribution based on specific categories of other variables.
Marginal Distribution
- Represents distributions of individual variables while ignoring other categories.
Quantitative Variable Distribution Summaries
- Shape, center, and variability are key in summarizing quantitative distributions.
Modes
- Mode: The peak(s) observed in a histogram, indicating the most common values.
Distribution Types
- Unimodal: One peak in the distribution.
- Bimodal: Two distinct peaks present.
- Multimodal: More than two peaks observed.
- Uniform: No discernible peaks detected.
- Symmetric: Left and right halves mirror each other in height.
Measures of Dispersion
- Interquartile Range (IQR): Calculated as Q3 minus Q1, measuring variability.
- Range: Difference between the maximum and minimum values in a dataset.
Five Number Summary
- Consists of Minimum, Q1 (first quartile), Median, Q3 (third quartile), and Maximum values.
Sample Mean
- Represents the average of a quantitative variable, essential for central tendency analysis.
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