Interpreting Data from Graphs - ACT Science
Card 1 of 30
Find the median value in the dataset: 3, 5, 7, 8, 12.
Find the median value in the dataset: 3, 5, 7, 8, 12.
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- The middle value when data is arranged in order.
- The middle value when data is arranged in order.
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Determine the slope between points $(3, 4)$ and $(7, 8)$.
Determine the slope between points $(3, 4)$ and $(7, 8)$.
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- $m = \frac{8-4}{7-3} = \frac{4}{4} = 1$
- $m = \frac{8-4}{7-3} = \frac{4}{4} = 1$
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Identify the type of correlation: as $x$ increases, $y$ decreases.
Identify the type of correlation: as $x$ increases, $y$ decreases.
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Negative correlation. Variables move in opposite directions.
Negative correlation. Variables move in opposite directions.
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If two error bars overlap substantially, what is the safest conclusion about a difference?
If two error bars overlap substantially, what is the safest conclusion about a difference?
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The difference may not be significant. Overlapping error bars suggest statistically similar values.
The difference may not be significant. Overlapping error bars suggest statistically similar values.
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Identify the axis typically representing the dependent variable.
Identify the axis typically representing the dependent variable.
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Y-axis. Vertical axis shows the variable being measured or observed.
Y-axis. Vertical axis shows the variable being measured or observed.
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Find the mean of the numbers: 2, 4, 6, 8, 10.
Find the mean of the numbers: 2, 4, 6, 8, 10.
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- Sum of values divided by count: $30 ÷ 5 = 6$.
- Sum of values divided by count: $30 ÷ 5 = 6$.
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What is the term for the midpoint of a box in a box plot?
What is the term for the midpoint of a box in a box plot?
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Median. The line inside the box marks the middle value.
Median. The line inside the box marks the middle value.
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What does a downward trend in a line graph indicate?
What does a downward trend in a line graph indicate?
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Decrease in the dependent variable. The line slopes downward showing values are falling.
Decrease in the dependent variable. The line slopes downward showing values are falling.
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Identify the graph type that uses dots to show frequency distributions.
Identify the graph type that uses dots to show frequency distributions.
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Dot plot. Each dot represents one data point at that value.
Dot plot. Each dot represents one data point at that value.
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What is the function of a key in a graph?
What is the function of a key in a graph?
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To define symbols or colors used. Same function as a legend - explains visual elements.
To define symbols or colors used. Same function as a legend - explains visual elements.
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What does the width of a box in a box plot represent?
What does the width of a box in a box plot represent?
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Interquartile range. Shows the spread of the middle 50% of the data.
Interquartile range. Shows the spread of the middle 50% of the data.
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What type of graph uses vertical bars to show frequency distributions?
What type of graph uses vertical bars to show frequency distributions?
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Histogram. Bars touch each other to show continuous data ranges.
Histogram. Bars touch each other to show continuous data ranges.
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What type of relationship is suggested by a flat line on a graph?
What type of relationship is suggested by a flat line on a graph?
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No relationship between variables. No change in y-value regardless of x-value changes.
No relationship between variables. No change in y-value regardless of x-value changes.
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Find the mode in a bar graph showing frequency of test scores.
Find the mode in a bar graph showing frequency of test scores.
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Score with highest bar. The category with the highest frequency has the tallest bar.
Score with highest bar. The category with the highest frequency has the tallest bar.
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Find the slope between $(2,5)$ and $(6,13)$.
Find the slope between $(2,5)$ and $(6,13)$.
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$m=2$. $\frac{13-5}{6-2}=\frac{8}{4}=2$
$m=2$. $\frac{13-5}{6-2}=\frac{8}{4}=2$
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What does a vertical line ($x$ constant) indicate about the independent variable across points?
What does a vertical line ($x$ constant) indicate about the independent variable across points?
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$x$ is constant for all plotted points. Vertical lines show no variation in the independent variable.
$x$ is constant for all plotted points. Vertical lines show no variation in the independent variable.
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Which option gives the correct units for slope if $y$ is in meters and $x$ is in seconds?
Which option gives the correct units for slope if $y$ is in meters and $x$ is in seconds?
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Meters per second ($\text{m},\text{s}^{-1}$). Slope units equal output units divided by input units.
Meters per second ($\text{m},\text{s}^{-1}$). Slope units equal output units divided by input units.
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Identify the $x$-intercept of the line $y=3x-12$.
Identify the $x$-intercept of the line $y=3x-12$.
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$x=4$. Set $y=0$: $0=3x-12$, so $x=4$.
$x=4$. Set $y=0$: $0=3x-12$, so $x=4$.
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Identify the $y$-intercept of the line passing through $(0,-3)$ and $(2,1)$.
Identify the $y$-intercept of the line passing through $(0,-3)$ and $(2,1)$.
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$-3$. The $y$-intercept is where the line crosses $y$-axis.
$-3$. The $y$-intercept is where the line crosses $y$-axis.
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Find the average rate of change from $(1,10)$ to $(4,4)$.
Find the average rate of change from $(1,10)$ to $(4,4)$.
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$\frac{\Delta y}{\Delta x}=-2$. $\frac{4-10}{4-1}=\frac{-6}{3}=-2$
$\frac{\Delta y}{\Delta x}=-2$. $\frac{4-10}{4-1}=\frac{-6}{3}=-2$
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What does the interquartile range (IQR) on a box plot equal?
What does the interquartile range (IQR) on a box plot equal?
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$\text{IQR}=Q_3-Q_1$. IQR measures spread between first and third quartiles.
$\text{IQR}=Q_3-Q_1$. IQR measures spread between first and third quartiles.
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What does the median on a box-and-whisker plot represent?
What does the median on a box-and-whisker plot represent?
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The $50$th percentile (middle value). Median divides ordered data into equal halves.
The $50$th percentile (middle value). Median divides ordered data into equal halves.
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What does a histogram (not a bar chart) display?
What does a histogram (not a bar chart) display?
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Frequency across continuous bins. Histograms show distribution of continuous data in intervals.
Frequency across continuous bins. Histograms show distribution of continuous data in intervals.
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What does a bar graph most directly compare?
What does a bar graph most directly compare?
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Values across discrete categories. Bar graphs compare quantities between distinct groups.
Values across discrete categories. Bar graphs compare quantities between distinct groups.
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What does it mean if two lines on the same graph intersect at a point?
What does it mean if two lines on the same graph intersect at a point?
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They have equal $y$ at that $x$. Intersection points represent equal values at shared coordinates.
They have equal $y$ at that $x$. Intersection points represent equal values at shared coordinates.
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What does a plateau region on a graph indicate about the dependent variable?
What does a plateau region on a graph indicate about the dependent variable?
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It levels off (approximately constant). Plateaus show equilibrium or steady-state conditions.
It levels off (approximately constant). Plateaus show equilibrium or steady-state conditions.
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Identify the term for a graph segment where the slope becomes steeper over time.
Identify the term for a graph segment where the slope becomes steeper over time.
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Increasing rate of change (accelerating). Steepening slopes indicate accelerating change rates.
Increasing rate of change (accelerating). Steepening slopes indicate accelerating change rates.
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On a velocity-versus-time graph, what does the area under the curve represent?
On a velocity-versus-time graph, what does the area under the curve represent?
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Displacement (change in position). Area under velocity curve equals total distance traveled.
Displacement (change in position). Area under velocity curve equals total distance traveled.
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On a velocity-versus-time graph, what does the slope represent?
On a velocity-versus-time graph, what does the slope represent?
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Acceleration (rate of velocity change). Acceleration equals the rate of velocity change over time.
Acceleration (rate of velocity change). Acceleration equals the rate of velocity change over time.
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On a distance-versus-time graph, what does the slope represent?
On a distance-versus-time graph, what does the slope represent?
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Speed (rate of distance change). Velocity equals the rate of distance change over time.
Speed (rate of distance change). Velocity equals the rate of distance change over time.
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