Data Types and Levels of Measurement

Qualitative Data: Non-numerical data that describes characteristics or attributes (e.g., gender, color, occupation)
Quantitative Data: Numerical data that can be measured or counted (e.g., height, weight, temperature)

Nominal Scale: Labels or categories with no inherent order or scale (e.g., gender, ethnicity)
Ordinal Scale: Labels or categories with a natural order or ranking, but no equal intervals (e.g., education level, movie ratings)
Interval Scale: Numerical data with equal intervals, but no true zero point (e.g., temperature in Celsius or Fahrenheit)
Ratio Scale: Numerical data with equal intervals and a true zero point (e.g., height, weight, time)

Measures of Central Tendency:
- Mean: The average value of a dataset
- Median: The middle value of a dataset when arranged in order
- Mode: The most frequently occurring value in a dataset
Measures of Variability:
- Range: The difference between the largest and smallest values in a dataset
- Interquartile Range (IQR): The difference between the 75th percentile and 25th percentile
- Variance: A measure of how spread out a dataset is from the mean
- Standard Deviation: The square root of the variance

Hypothesis Testing: A procedure for testing a hypothesis about a population based on a sample of data
Confidence Intervals: A range of values within which a population parameter is likely to lie
Significance Testing: A procedure for determining whether a result is statistically significant (i.e., unlikely to occur by chance)

Experiment: An action or situation that can produce a set of outcomes
Sample Space: The set of all possible outcomes of an experiment
Event: A set of one or more outcomes of an experiment
Probability: A measure of the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain)

Types of Plots:
- Histogram: A graphical representation of a frequency distribution
- Box Plot: A graphical representation of the five-number summary (minimum, Q1, median, Q3, maximum)
- Scatter Plot: A graphical representation of the relationship between two variables

Qualitative Data: Describes non-numerical attributes such as gender, color, and occupation.
Quantitative Data: Involves numerical measurements such as height, weight, and temperature, enabling counting or measuring.

Nominal Scale: Categorizes data without any inherent order (e.g., gender, ethnicity).
Ordinal Scale: Arranges categories in a ranked order but lacks equal intervals (e.g., education levels, movie ratings).
Interval Scale: Uses numerical data with equal intervals between values, but lacks a true zero (e.g., temperature in Celsius).
Ratio Scale: Contains numerical data with equal intervals and a meaningful zero point (e.g., height, weight, duration).

Measures of Central Tendency:
- Mean: Average value calculated by summing all data points and dividing by their count.
- Median: Middle value found when data points are ordered from least to greatest.
- Mode: Value that appears most frequently in the dataset.
Measures of Variability:
- Range: Difference between the highest and lowest values in the dataset.
- Interquartile Range (IQR): Difference between the 75th percentile (Q3) and the 25th percentile (Q1).
- Variance: Quantifies how much the data points differ from the mean.
- Standard Deviation: Represents the average distance of data points from the mean, calculated as the square root of variance.

Hypothesis Testing: A statistical method used to determine whether there is enough evidence to support a particular hypothesis about a population based on sample data.
Confidence Intervals: Provides a range of values that is expected to contain a population parameter with a specified level of confidence.
Significance Testing: Assesses whether a result is statistically significant, suggesting it is unlikely to have occurred by chance.

Experiment: An action that can yield a defined set of outcomes.
Sample Space: The complete set of all possible outcomes resulting from an experiment.
Event: A specific subset of outcomes from a sample space, representing one or more results.
Probability: Measures the likelihood of an event occurring, expressed as a value between 0 (impossible event) and 1 (certain event).

Types of Plots:
- Histogram: Visualizes frequency distribution of numerical data.
- Box Plot: Summarizes data through five key statistics: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.
- Scatter Plot: Illustrates the relationship or correlation between two variables, useful for identifying trends or patterns.