Define or give examples of the following

Here’s a comprehensive definition and examples for each of the terms you've listed:

Statistical Question

A statistical question is one that anticipates variability in the data and can be answered by collecting data.

• Example: "What is the average height of students in a high school?" This question implies that heights will vary among students.

Biased vs Unbiased

• Biased: A biased sample is one that is not representative of the population from which it is drawn. It leads to systematic errors in data collection.

  • Example: Surveying only college students about their study habits to understand all adult study habits.

• Unbiased: An unbiased sample accurately reflects the population and avoids systematic errors.

  • Example: Randomly selecting adults from a population to survey their study habits.

Probabilistic vs Deterministic Interpretation

• Probabilistic Interpretation: Involves uncertainty and variability; outcomes are random and can be described using probabilities.

  • Example: Predicting the chance of rain tomorrow (50% chance).

• Deterministic Interpretation: Involves certainty; given an input, there is a predictable outcome with no variability.

  • Example: If you drop a ball from a height, you can predict precisely how long it will take to hit the ground assuming no air resistance.

Extrapolation Using a Scatter Plot

Extrapolation involves estimating values beyond the range of the data based on the observed trend.

• Example: If you have data on the sales of a product over the last five years plotted on a scatter plot and you see a positive trend, you can extend that trend line to predict sales for the next few years.

Making Inferences from a Scatter Plot

Making inferences from a scatter plot involves drawing conclusions about the relationship or correlation between two variables depicted on the plot.

• Example: Observing that as study time increases, grades tend to increase, suggesting a positive correlation.

Making Predictions from a Scatter Plot

Predictions are made by using the trend line (or line of best fit) to estimate values for new observations based on established data.

• Example: If a scatter plot shows the relationship between hours studied (X-axis) and exam scores (Y-axis), you could use the trend line to predict the score for a student who studies for 10 hours.

Qualitative Variable

Qualitative variables are non-numeric categories or attributes used to represent characteristics or traits.

• Example: Colors (red, blue, green), types of cuisine (Italian, Mexican, Chinese).

Quantitative Variable

Quantitative variables are numeric and can be measured or counted.

• Example: Height (170 cm), weight (75 kg), age (30 years).

Trend Line of Best Fit

A trend line of best fit (or regression line) is a straight line that best represents the data on a scatter plot, indicating the general direction of the data points.

• Example: A line drawn through a scatter plot of home prices vs. square footage that minimizes the distance between the line and all the data points.

Negative vs Positive Association

• Negative Association: As one variable increases, the other variable tends to decrease.

  • Example: The relationship between hours spent playing video games and grades in school, where increased gaming correlates with lower grades.

• Positive Association: As one variable increases, the other variable also tends to increase.

  • Example: The relationship between the number of hours studied and test scores.

No Association

No association indicates that there is no discernible relationship between two variables; changes in one variable do not predict changes in the other.

• Example: The amount of time someone spends exercising and their favorite type of music.

Linear vs Nonlinear Relationship

• Linear Relationship: The relationship between two variables can be described with a straight line, indicating a constant rate of change.

  • Example: The relationship between temperature in Celsius and Fahrenheit.

• Nonlinear Relationship: The relationship between variables is not constant and cannot be described with a straight line; it may curve.

  • Example: The relationship between speed and fuel consumption; as speed increases, fuel efficiency may change in a non-linear manner.

Bivariate Data

Bivariate data involves two variables that can be analyzed to determine relationships between them.

• Example: The height and weight of a group of individuals.

Cluster

A cluster refers to a group of data points in a scatter plot that are closely packed together, indicating a concentration of values in that area.

• Example: In a scatter plot of test scores versus hours studied, one cluster might represent students who studied between 5 to 10 hours.

Outlier

An outlier is a data point that is significantly different from other observations, often appearing distant from the main group of data in a plot.

• Example: In a scatter plot of students' heights and weights, a very tall or extremely short person may appear as an outlier if they do not fit the general pattern of the other data points.