Scatterplots
55 flashcards covering Scatterplots for the SAT Math section.
A scatterplot is a simple graph that displays the relationship between two sets of data by plotting points on a coordinate plane. Each point represents a pair of values, one from each dataset, allowing you to spot patterns like trends, clusters, or outliers at a glance. For example, you might use a scatterplot to see if there's a connection between study hours and test scores, making it a useful tool for understanding how variables interact in real-world scenarios.
On the SAT Math section, scatterplots often appear in questions that ask you to interpret graphs, identify correlations (positive, negative, or none), or make predictions based on trends. Common traps include overlooking the scale of the axes or mistaking random scatter for a pattern, so pay close attention to the direction and strength of relationships. Focus on skills like describing line of best fit and recognizing outliers, as these are key to answering multiple-choice and grid-in problems accurately.
Remember to always label your axes when sketching a scatterplot for practice.
Terms (55)
- 01
Scatterplot
A graph that displays values for two variables for a set of data using dots, each representing a pair of values, to show possible relationships between the variables.
- 02
Positive Correlation
A relationship in a scatterplot where as one variable increases, the other variable also tends to increase, indicated by points generally rising from left to right.
- 03
Negative Correlation
A relationship in a scatterplot where as one variable increases, the other variable tends to decrease, shown by points generally falling from left to right.
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No Correlation
A situation in a scatterplot where there is no clear pattern between the two variables, with points scattered randomly without an upward or downward trend.
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Strong Correlation
A clear and consistent pattern in a scatterplot where the points closely follow a line or curve, indicating a reliable relationship between the variables.
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Weak Correlation
A vague or scattered pattern in a scatterplot where the points do not closely align with a line or curve, suggesting a less reliable relationship between the variables.
- 07
Line of Best Fit
A straight line drawn on a scatterplot that comes as close as possible to all the data points, used to summarize the overall trend and make predictions.
- 08
Trend Line
Another name for the line of best fit, which helps visualize the general direction of the data points in a scatterplot.
- 09
Outlier
A data point in a scatterplot that differs significantly from the other points and may not follow the overall pattern, potentially affecting the line of best fit.
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Cluster
A group of data points in a scatterplot that are concentrated in a particular area, indicating a subset of data with similar characteristics.
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Positive Association
Similar to positive correlation, it describes a scatterplot where higher values of one variable are paired with higher values of the other.
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Negative Association
Similar to negative correlation, it indicates a scatterplot where higher values of one variable are paired with lower values of the other.
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Interpolation
Estimating a value within the range of data points on a scatterplot by using the line of best fit to predict outcomes between existing points.
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Extrapolation
Extending the line of best fit beyond the range of the data points on a scatterplot to make predictions outside the observed values.
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Slope of Line of Best Fit
The steepness of the line of best fit in a scatterplot, which indicates the rate of change between the two variables, positive for increases and negative for decreases.
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Y-Intercept in Scatterplot
The point where the line of best fit crosses the y-axis in a scatterplot, representing the predicted value of the dependent variable when the independent variable is zero.
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Making Predictions from Scatterplot
Using the line of best fit on a scatterplot to estimate values for one variable based on given values of the other variable.
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Correlation vs. Causation
In scatterplots, correlation means a relationship exists between variables, but it does not imply that one causes the other, as other factors might be involved.
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Drawing Line of Best Fit
A method of sketching a straight line through the center of the data points on a scatterplot to minimize the distance from the line to the points.
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Residual
The vertical distance between a data point and the line of best fit on a scatterplot, indicating how well the line predicts the actual data.
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Bivariate Data
Data sets in a scatterplot that consist of pairs of values for two variables, allowing analysis of their relationship.
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Direction of Association
The way points in a scatterplot trend, such as upward for positive or downward for negative, to describe the relationship between variables.
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Strength of Association
How closely the points in a scatterplot follow a straight line, with stronger associations showing less scatter around the line.
- 24
Form of Association
The shape of the pattern in a scatterplot, such as linear for a straight trend or nonlinear for a curved one, though SAT focuses on linear.
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Identifying Patterns in Scatterplot
Examining the arrangement of points to detect trends like correlation or clusters, which helps in understanding variable relationships.
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Data Points
The individual dots on a scatterplot, each representing a pair of values from the data set being analyzed.
- 27
Axes in Scatterplot
The horizontal x-axis and vertical y-axis on a scatterplot that represent the two variables being compared.
- 28
Scale on Axes
The numbering and intervals on the axes of a scatterplot that determine how data points are spaced and interpreted.
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Units in Scatterplot
The measurement labels on the axes of a scatterplot that indicate what each variable represents, such as dollars or years.
- 30
Positive Slope
A slope greater than zero on the line of best fit in a scatterplot, indicating that both variables increase together.
- 31
Negative Slope
A slope less than zero on the line of best fit in a scatterplot, showing that one variable increases as the other decreases.
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Zero Slope
A horizontal line of best fit in a scatterplot with a slope of zero, indicating no change in one variable regardless of the other.
- 33
Linear Relationship
A straight-line pattern in a scatterplot where the variables change at a constant rate relative to each other.
- 34
Non-Linear Relationship
A curved or irregular pattern in a scatterplot where the rate of change between variables is not constant, though less common on the SAT.
- 35
Equation of Line of Best Fit
The linear equation, typically in the form y = mx + b, that represents the line of best fit on a scatterplot for making calculations.
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Using Two Points to Find Line
Selecting two points from a scatterplot to calculate the slope and y-intercept, helping to determine the equation of the line of best fit.
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How Outliers Affect Line of Best Fit
Outliers can skew the line of best fit, pulling it toward or away from them and potentially altering predictions based on the scatterplot.
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Common Trap: Over-Extrapolation
Mistakenly using a scatterplot's line of best fit to make predictions far beyond the data range, which may lead to inaccurate results.
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Common Trap: Ignoring Outliers
Failing to consider outliers in a scatterplot, which can result in a misleading line of best fit and incorrect interpretations.
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Strategy for Answering Scatterplot Questions
First, identify the overall trend, then use the line of best fit for predictions, and finally check for outliers or clusters to refine your analysis.
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Scatterplot with Positive Correlation Example
In a scatterplot of study hours vs. test scores, points might show that more hours generally lead to higher scores, illustrating positive correlation.
If a student studies 2 hours and scores 80, and another studies 4 hours and scores 90, the points trend upward.
- 42
Scatterplot with Negative Correlation Example
In a scatterplot of temperature vs. ice cream sales, points might indicate that higher temperatures lead to lower sales, showing negative correlation.
At 70 degrees, sales are 100 units; at 90 degrees, sales drop to 50 units.
- 43
Scatterplot with No Correlation Example
In a scatterplot of shoe size vs. favorite color, points would scatter randomly without any pattern, as the variables are unrelated.
Various shoe sizes paired with different colors show no clear trend.
- 44
Interpolation Example
On a scatterplot of age vs. height, interpolating between points might predict a 10-year-old's height based on data for 9- and 11-year-olds.
If a 9-year-old is 4 feet tall and an 11-year-old is 4.5 feet, a 10-year-old might be around 4.25 feet.
- 45
Extrapolation Example
Using a scatterplot of years vs. population to predict future population beyond the given data points.
If population grows steadily, extrapolating might estimate 2025 based on data up to 2020.
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Residual Example
In a scatterplot, a residual is the difference between an actual data point and the value predicted by the line of best fit.
If the line predicts 50 for a point at 55, the residual is 5 units.
- 47
Drawing Line of Best Fit Example
For a scatterplot of points mostly trending upward, draw a straight line that passes through the middle of the points, balancing above and below.
In a set of points from (1,2) to (5,6), the line might go through (3,4).
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Making Predictions Example
From a scatterplot of advertising spend vs. sales, predict sales for a new spend amount using the line of best fit.
If the line shows $1000 spend leads to $5000 sales, predict $6000 sales for $1200 spend.
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Outlier Example
A point in a scatterplot that stands apart from the rest, like a high value in an otherwise low cluster.
In height vs. weight data, a point for 6 feet and 300 pounds among mostly average weights.
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Cluster Example
A group of points in a scatterplot concentrated in one area, suggesting a subgroup in the data.
In a plot of exam scores vs. study time, points clustered around 2-4 hours indicate common behavior.
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Slope Calculation Example
Using two points from a scatterplot to find slope as rise over run, which is change in y divided by change in x.
For points (2,3) and (4,7), slope is (7-3)/(4-2) = 2.
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Equation from Two Points Example
Determine the line equation by first finding the slope from two points, then using one point to find the y-intercept.
For points (1,2) and (3,6), slope is 2; using (1,2), equation is y = 2x.
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Non-Linear Pattern Example
A scatterplot where points form a curve, like a parabola, instead of a straight line.
In distance vs. time for acceleration, points might curve upward.
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Strength of Correlation Example
Points tightly packed around the line indicate strong correlation, while spread-out points show weak.
In a tight upward trend, correlation is strong; in a loose one, it's weak.
- 55
Bivariate Data Example
Pairs of measurements, like height and weight, plotted as points in a scatterplot to explore relationships.
Data pairs: (160 cm, 50 kg), (170 cm, 60 kg).