Unit 5 Scatter Plots and Data Analysis
Vocabulary
Key Terms
Meaning - Description - Picture
Example - All work shown
U5 L1
Data Modeling
U5 L2
Bivariate Data
U5 L2
Scatter Plot
U5 L2
Outlier
U5 L2
Clustering
U5 L5
Linear/NonLinear
Association
U5 L5
Association/
Correlation
Positive
Negative
None
U5 L5
Qualitative Variable
U5 L5
Quantitative Variable
U5 L5
Line of Best Fit
U5 L6
Interpreting key points of trend lines
The y-intercept represents the amount when x = 0.
The x-intercept represents the amount when y = 0.
U5 L6
Interence
U5 L7
Interpreting the Slope of a trend line or line of best fit
U5 L7
Extrapolate from a line of best fit
U5 L10
How do you Interpret a graph?
U5 L10
Probabilistic vs
Deterministic
Probabilistic
Deterministic
Through this unit, I have learned about various concepts in scatter plots and data analysis. I now understand the process of data modeling, which involves creating mathematical representations of real-world data to make predictions and gain insights. Bivariate data, consisting of two variables for each observation, can be effectively visualized using scatter plots. I have also learned to identify outliers, which are observations that significantly deviate from the overall pattern of the data, and recognize clustering, where data points gather in specific areas.
Furthermore, I now understand the different types of associations or correlations that can be observed in scatter plots. Positive associations show an increase in one variable corresponding to an increase in the other, while negative associations display a decrease in one variable as the other increases. In cases where no association is apparent, it indicates that there is no clear relationship between the variables being analyzed.
Moreover, I have gained knowledge about qualitative and quantitative variables. Qualitative variables represent attributes that cannot be numerically measured, while quantitative variables deal with numerical measurements or quantities. I have also learned how to determine the line of best fit in a scatter plot, which represents the overall pattern of the data points.
Additionally, I now understand how to interpret key points of trend lines, such as the y-intercept and x-intercept, which provide valuable information about the data. With the concepts of inference and extrapolation, I can draw conclusions and make predictions based on the observed data and trends. Lastly, I have learned to interpret graphs by distinguishing between probabilistic and deterministic data, understanding the level of certainty in predictions or outcomes.
U5 L1
Data Modeling - the process of creating a mathematical representation or model of real-world data in order to understand and make predictions about the data.
Example: In data modeling, you might use a scatter plot to represent the relationship between two variables, such as the temperature and ice cream sales.
U5 L2
Bivariate Data - data that consists of two variables or attributes for each individual or observation.
Example: Bivariate data could be the heights and weights of a group of people.
U5 L2
Scatter Plot - a graph that displays bivariate data as a collection of points on a coordinate plane, with one variable represented on the x-axis and the other variable represented on the y-axis.
Example: A scatter plot could show the relationship between the number of hours studied and the test scores of students.
U5 L2
Outlier - an observation that significantly deviates from the overall pattern or trend of the data.
Example: In a scatter plot of students' ages and heights, an outlier could be a student who is much taller or shorter than the rest.
U5 L2
Clustering - a pattern in a scatter plot where the data points gather or cluster together in certain areas.
Example: In a scatter plot of students' ages and grades, if there are several data points that form a cluster at the top right corner, it could indicate a group of high-achieving students.
U5 L5
Linear/Nonlinear Association - the type of relationship or pattern between two variables in a scatter plot. A linear association shows a straight-line pattern, while a nonlinear association shows a curved or non-linear pattern.
Example: A linear association would be a scatter plot where the data points form a line. A nonlinear association could be a scatter plot where the data points form a curved shape.
U5 L5
Association/Correlation - the strength and direction of the relationship between two variables in a scatter plot. The association can be positive, negative, or none.
Example: A scatter plot showing a positive association would have data points that increase as you move from left to right. A scatter plot showing a negative association would have data points that decrease as you move from left to right. A scatter plot showing no association would have data points that have no clear pattern.
U5 L5
Qualitative Variable - a variable that represents characteristics or attributes that cannot be measured numerically.
Example: The color of a car or the type of fruit are qualitative variables.
U5 L5
Quantitative Variable - a variable that represents numerical measurements or quantities.
Example: The height, weight, or age of a person are quantitative variables.
U5 L5
Line of Best Fit - a straight line that represents the overall trend or pattern of the data points in a scatter plot.
Example: The line of best fit in a scatter plot would be the line that best represents the overall relationship between the two variables.
U5 L6
Interpreting key points of trend lines:
- The y-intercept represents the value of the dependent variable (y) when the independent variable (x) is equal to 0.
- The x-intercept represents the value of the independent variable (x) when the dependent variable (y) is equal to 0.
Example: In a scatter plot of time and distance traveled, the y-intercept of the trend line would represent the starting point (when time is 0), and the x-intercept would represent the time it takes to travel 0 distance.
U5 L6
Inference - a conclusion or prediction made based on the data and observations in a scatter plot.
Example: From a scatter plot showing the relationship between study time and test scores, you might infer that students who study more tend to have higher test scores.
U5 L7
Interpreting the Slope of a trend line or line of best fit - the slope represents the rate of change or the amount of change in the dependent variable (y) for a given change in the independent variable (x).
Example: In a scatter plot of distance and time, the slope of the trend line would represent the speed or rate at which the object is traveling.
U5 L7
Extrapolate from a line of best fit - making predictions or estimating values beyond the range of the available data based on the trend observed in the scatter plot.
Example: Using the line of best fit in a scatter plot of population growth over time, you can extrapolate to estimate the population at a future time.
U5 L10
How do you Interpret a graph? - understanding and analyzing the data and patterns represented in a graph.
Example: When interpreting a line graph showing temperature over time, you would look for trends, seasonal patterns, or significant changes in temperature.
U5 L10
Probabilistic vs Deterministic:
- Probabilistic refers to situations or data where there is uncertainty or randomness involved, and the outcome cannot be predicted with certainty.
- Deterministic refers to situations or data where the outcome can be predicted or determined with complete certainty based on the given information.
Example: The outcome of a coin toss is probabilistic, as it can result in either heads or tails and is not predictable. The result of adding two numbers together is deterministic, as it can be calculated accurately using the given numbers.
For U5 L5
Association/
Correlation
can u do the
Positive -
Negative -
None -
U5 L5
Association/Correlation:
- Positive - a positive association or correlation means that as one variable increases, the other variable also tends to increase. The data points in a scatter plot would show a general upward trend.
Example: A positive association or correlation could be seen in a scatter plot of study time and test scores, where students who study more tend to have higher test scores.
- Negative - a negative association or correlation means that as one variable increases, the other variable tends to decrease. The data points in a scatter plot would show a general downward trend.
Example: A negative association or correlation could be seen in a scatter plot of temperature and snowfall, where as temperature increases, the amount of snowfall decreases.
- None - a scatter plot showing no association or correlation means that there is no clear relationship between the two variables. The data points do not follow a consistent trend.
Example: A scatter plot of shoe size and favorite color would likely show no association or correlation, as the two variables are unrelated.
what do I put for what I learned
Based on the given key terms and their meanings, here's an example of what you could put for what you learned:
I learned about data modeling, which is the process of creating a mathematical representation or model of real-world data to understand and make predictions about the data. I also learned that bivariate data consists of two variables for each observation, and that a scatter plot is a graph that displays bivariate data as points on a coordinate plane. Additionally, I learned that an outlier is an observation that significantly deviates from the overall pattern or trend of the data, and clustering refers to a pattern in a scatter plot where data points gather or cluster together in certain areas.
I also learned about the different associations or correlations that can be observed in a scatter plot. A positive association indicates that as one variable increases, the other variable also tends to increase. A negative association indicates that as one variable increases, the other variable tends to decrease. And a scatter plot showing no association indicates that there is no clear relationship between the two variables.
Furthermore, I learned about qualitative and quantitative variables, with qualitative variables representing characteristics or attributes that cannot be measured numerically, and quantitative variables representing numerical measurements or quantities. I also learned that a line of best fit represents the overall trend or pattern of the data points in a scatter plot, and that interpreting key points of trend lines such as the y-intercept and x-intercept can provide valuable information. Lastly, I learned about the concepts of inference, extrapolation, and how to interpret graphs in terms of probabilistic and deterministic data.