Interpreting Graphs and Tables - SSAT Upper Level: Quantitative
Card 1 of 25
What is the average rate of change from $x=a$ to $x=b$ on a graph?
What is the average rate of change from $x=a$ to $x=b$ on a graph?
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$\frac{f(b)-f(a)}{b-a}$. The average rate of change is computed as the difference in function values divided by the difference in x-values over the interval.
$\frac{f(b)-f(a)}{b-a}$. The average rate of change is computed as the difference in function values divided by the difference in x-values over the interval.
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What is the meaning of the $y$-intercept of a line graph in context?
What is the meaning of the $y$-intercept of a line graph in context?
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The value of $y$ when $x=0$. The y-intercept indicates the initial value of the dependent variable when the independent variable is at its starting point of zero.
The value of $y$ when $x=0$. The y-intercept indicates the initial value of the dependent variable when the independent variable is at its starting point of zero.
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What does the slope between two points $(x_1,y_1)$ and $(x_2,y_2)$ represent on a line graph?
What does the slope between two points $(x_1,y_1)$ and $(x_2,y_2)$ represent on a line graph?
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Rate of change: $\frac{y_2-y_1}{x_2-x_1}$. The slope formula calculates the rate of change in the dependent variable per unit change in the independent variable between two points on the graph.
Rate of change: $\frac{y_2-y_1}{x_2-x_1}$. The slope formula calculates the rate of change in the dependent variable per unit change in the independent variable between two points on the graph.
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A scatter plot trend is downward from left to right. What correlation sign does this suggest?
A scatter plot trend is downward from left to right. What correlation sign does this suggest?
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Negative correlation. A downward trend in a scatter plot shows that as one variable increases, the other decreases, indicating negative correlation.
Negative correlation. A downward trend in a scatter plot shows that as one variable increases, the other decreases, indicating negative correlation.
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Identify the independent variable on a standard graph with labeled axes.
Identify the independent variable on a standard graph with labeled axes.
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The variable on the $x$-axis. In standard graphing conventions, the independent variable is plotted on the horizontal x-axis as it is manipulated or controlled.
The variable on the $x$-axis. In standard graphing conventions, the independent variable is plotted on the horizontal x-axis as it is manipulated or controlled.
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Identify the dependent variable on a standard graph with labeled axes.
Identify the dependent variable on a standard graph with labeled axes.
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The variable on the $y$-axis. The dependent variable, which responds to changes in the independent variable, is conventionally placed on the vertical y-axis.
The variable on the $y$-axis. The dependent variable, which responds to changes in the independent variable, is conventionally placed on the vertical y-axis.
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What is the range of a data set shown on a graph or in a table?
What is the range of a data set shown on a graph or in a table?
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Maximum value minus minimum value. The range measures the spread of data by subtracting the smallest value from the largest in the set.
Maximum value minus minimum value. The range measures the spread of data by subtracting the smallest value from the largest in the set.
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What does a negative slope on a line graph indicate about the relationship between $x$ and $y$?
What does a negative slope on a line graph indicate about the relationship between $x$ and $y$?
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As $x$ increases, $y$ decreases. A negative slope shows an inverse relationship where the dependent variable decreases as the independent variable increases.
As $x$ increases, $y$ decreases. A negative slope shows an inverse relationship where the dependent variable decreases as the independent variable increases.
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What does a positive slope on a line graph indicate about the relationship between $x$ and $y$?
What does a positive slope on a line graph indicate about the relationship between $x$ and $y$?
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As $x$ increases, $y$ increases. A positive slope indicates a direct relationship where the dependent variable increases proportionally with the independent variable.
As $x$ increases, $y$ increases. A positive slope indicates a direct relationship where the dependent variable increases proportionally with the independent variable.
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What does it mean if a line graph is horizontal over an interval of $x$?
What does it mean if a line graph is horizontal over an interval of $x$?
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The value of $y$ is constant on that interval. A horizontal line segment signifies no change in the dependent variable despite variations in the independent variable over that period.
The value of $y$ is constant on that interval. A horizontal line segment signifies no change in the dependent variable despite variations in the independent variable over that period.
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What is the median of the values $2,5,7,9,12$ (as might appear in a table column)?
What is the median of the values $2,5,7,9,12$ (as might appear in a table column)?
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$7$. For an odd number of sorted values, the median is the middle value in the ordered list.
$7$. For an odd number of sorted values, the median is the middle value in the ordered list.
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Find the mean of the table values $3,6,9$.
Find the mean of the table values $3,6,9$.
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$6$. The mean is calculated by summing all values and dividing by the number of values in the set.
$6$. The mean is calculated by summing all values and dividing by the number of values in the set.
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Find the range of the table values $4,10,1,7$.
Find the range of the table values $4,10,1,7$.
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$9$. The range is determined by subtracting the minimum value from the maximum value in the data set.
$9$. The range is determined by subtracting the minimum value from the maximum value in the data set.
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If a line passes through $(2,3)$ and $(6,11)$, what is its slope?
If a line passes through $(2,3)$ and $(6,11)$, what is its slope?
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$2$. Slope is found using the formula $\frac{y_2 - y_1}{x_2 - x_1}$ applied to the given points.
$2$. Slope is found using the formula $\frac{y_2 - y_1}{x_2 - x_1}$ applied to the given points.
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If a line has slope $-3$ and passes through $(0,5)$, what is $y$ when $x=2$?
If a line has slope $-3$ and passes through $(0,5)$, what is $y$ when $x=2$?
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$-1$. Using the line equation $y = mx + b$ with given slope and y-intercept, substitute x=2 to find y.
$-1$. Using the line equation $y = mx + b$ with given slope and y-intercept, substitute x=2 to find y.
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A table shows $x=1,2,3$ with $y=2,4,6$. What is the constant rate of change?
A table shows $x=1,2,3$ with $y=2,4,6$. What is the constant rate of change?
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$2$ per $1$ unit of $x$. The constant rate of change is the consistent increase in y for each unit increase in x, as shown in the table.
$2$ per $1$ unit of $x$. The constant rate of change is the consistent increase in y for each unit increase in x, as shown in the table.
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A table lists $x=0,1,2$ with $y=5,8,11$. What is the $y$-intercept?
A table lists $x=0,1,2$ with $y=5,8,11$. What is the $y$-intercept?
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$5$. The y-intercept is the y-value corresponding to x=0 in the linear relationship depicted in the table.
$5$. The y-intercept is the y-value corresponding to x=0 in the linear relationship depicted in the table.
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A bar chart shows counts $A=12$, $B=9$, $C=15$. Which category is greatest?
A bar chart shows counts $A=12$, $B=9$, $C=15$. Which category is greatest?
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$C$. The greatest category in a bar chart is identified by comparing the heights of the bars representing each count.
$C$. The greatest category in a bar chart is identified by comparing the heights of the bars representing each count.
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A pie chart shows $40%$ for $A$. What fraction of the whole is category $A$?
A pie chart shows $40%$ for $A$. What fraction of the whole is category $A$?
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$\frac{2}{5}$. Convert the percentage to a fraction by dividing by 100 and simplifying to lowest terms.
$\frac{2}{5}$. Convert the percentage to a fraction by dividing by 100 and simplifying to lowest terms.
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A pie chart shows $25%$ for a category. What central angle (in degrees) represents it?
A pie chart shows $25%$ for a category. What central angle (in degrees) represents it?
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$90^\circ$. The central angle is calculated as the percentage times 360 degrees, the total degrees in a circle.
$90^\circ$. The central angle is calculated as the percentage times 360 degrees, the total degrees in a circle.
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A line graph shows $y$ increases from $10$ to $16$ while $x$ increases from $2$ to $5$. Find slope.
A line graph shows $y$ increases from $10$ to $16$ while $x$ increases from $2$ to $5$. Find slope.
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$2$. Slope is computed as the change in y divided by the change in x over the given interval.
$2$. Slope is computed as the change in y divided by the change in x over the given interval.
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A graph point is labeled $(4,9)$. What is the value of $y$ when $x=4$?
A graph point is labeled $(4,9)$. What is the value of $y$ when $x=4$?
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$9$. In a coordinate pair (x, y), the second number directly gives the y-value for the specified x.
$9$. In a coordinate pair (x, y), the second number directly gives the y-value for the specified x.
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A scatter plot trend is upward from left to right. What correlation sign does this suggest?
A scatter plot trend is upward from left to right. What correlation sign does this suggest?
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Positive correlation. An upward trend in a scatter plot indicates that as one variable increases, the other tends to increase, suggesting positive correlation.
Positive correlation. An upward trend in a scatter plot indicates that as one variable increases, the other tends to increase, suggesting positive correlation.
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If a graph uses a scale of $2$ units per tick mark, what value is $3$ ticks above $0$ on that axis?
If a graph uses a scale of $2$ units per tick mark, what value is $3$ ticks above $0$ on that axis?
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$6$. Multiply the number of tick marks by the scale value per tick to find the distance from zero.
$6$. Multiply the number of tick marks by the scale value per tick to find the distance from zero.
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A table gives total cost $C$ for $n$ items: $(n,C)=(2,10),(5,25)$. What is the unit cost $\frac{C}{n}$?
A table gives total cost $C$ for $n$ items: $(n,C)=(2,10),(5,25)$. What is the unit cost $\frac{C}{n}$?
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$5$. The unit cost is the constant ratio of total cost to number of items, verified as consistent across table entries.
$5$. The unit cost is the constant ratio of total cost to number of items, verified as consistent across table entries.
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