Evidence in Tables & Graphs - SAT Reading & Writing

The difference may not be clearly distinguishable given uncertainty. Overlapping error bars suggest the observed difference could be due to random variation, not a real effect.

Multiply or interpret values using the stated scale factor. Scaling adjusts reported figures to actual magnitudes, preventing underestimation of values.

Identify the most frequent value. Mode is the value that appears most often.

Per person; a total divided by population. Per capita normalizes totals by population size, enabling fair comparisons across groups of different sizes.

State that the variables are correlated, not that one causes the other. Without causal evidence, claims must limit to observed associations to avoid unsubstantiated inferences.

$25%$. The ratio $18/72 = 0.25$, multiplied by $100%$, provides the proportional contribution.

The greatest difference between two relevant values for each category. Comparing differences per category identifies the maximum change, supporting claims of largest growth.

The series with the smallest variation (smallest range or spread). Consistency implies low variability, so smallest spread supports claims of stability over time.

$25%$. The absolute decrease is $20$, but relative to the original, it's $(60-80)/80 \times 100% = -25%$, focusing on proportional change.

Relationship between two variables. Points plotted to reveal patterns or correlations.

The overall direction or pattern of change across the x-axis. Trends capture the general movement or pattern in data over the independent variable, often time, to support claims about directionality.

Read the title and axis labels. Establishes context and understanding before analyzing data.

Maximum minus minimum. Range measures the spread of data by subtracting the smallest from the largest value.

$\frac{y_2-y_1}{x_2-x_1}$. Slope calculates the rate of change in $y$ per unit $x$, indicating line steepness.

Mean = 10. Sum of values $(5+8+12+15=40)$ divided by count $(40÷4=10)$.

Relative increase is percent change; absolute increase is the raw difference. Relative focuses on proportional change, while absolute uses raw differences, affecting interpretation of magnitude.

$\frac{x_1+x_2+\cdots+x_n}{n}$. The mean represents the central tendency by equally distributing the total sum across all values.

Estimate a value between labeled data points on the graph. Interpolation estimates within the data range, assuming continuity between known points.

A pie chart. Shows proportional relationships within a total.

A line graph. Shows continuous change and patterns across time periods.

A point far from the overall pattern of the other points. Outliers deviate significantly from the trend, potentially indicating anomalies or errors in data.

The middle value when the data are ordered. Median identifies the central value in an ordered list, resistant to outliers unlike the mean.

$6$. Dividing total by population ($300/50$) gives the average per individual, standard for per-capita metrics.

A is higher than B throughout the displayed time period. The pattern holds for all shown data points, supporting a conclusion limited to the observed period.

The specific cell value paired with its row and column labels. Citing the exact cell with labels provides direct, verifiable support for the claim without ambiguity.

$17.5$. Using $(10\times^1 + 20\times^3)/(1+3) = 70/4$ accounts for the higher weight of $20$.

Identify the exact claim, then locate the relevant row/column/axis values. This approach ensures precise alignment between the claim and the data source, avoiding misinterpretation of irrelevant sections.

Slope = 2. Coefficient of $x$ represents rate of change.

Correlation is association; causation requires proof of a cause-effect link. Graphs show patterns of association, but causation demands experimental evidence or controls for confounding factors.

Predict a value beyond the observed data range (often less reliable). Extrapolation extends the trend outside observed data, introducing higher uncertainty.

How much $y$ changes for a given change in $x$. It quantifies the steepness of the line, indicating the speed of change in the dependent variable relative to the independent one.

Pie chart. Circular format naturally displays parts of a whole.

Source and units. Verifies data origin and measurement standards.

$20$ to $30$ ($50%$ vs. $20%$). Percent change is $(30-20)/20 = 50%$ vs. $(60-50)/50 = 20%$, emphasizing relative growth.

$2$. Applying the slope formula $(13-5)/(6-2) = 8/4$ confirms the constant rate between points.

Some values count more because they have larger weights. Weights adjust the influence of each value, reflecting their relative importance in the average.

Line graph. Connects data points to show trends over intervals.

Ignoring axis units or a nonzero baseline that changes visual impact. Misreading axes can distort perceived differences, as units and scales affect data interpretation.

Use “slightly higher/lower” rather than “dramatically higher/lower.”. Modest language like “slightly” accurately reflects small differences without exaggerating significance.

$5,6,5,6$. The set has a smaller range ($1$ vs. $7$), indicating less fluctuation and greater consistency.

Identify the most frequent value. Look for the category with the highest frequency count.

$\frac{\text{new}-\text{old}}{\text{old}}\times 100%$. This formula measures relative change, allowing comparison of growth or decline across different scales.

Bar chart. Easily compares discrete categories side by side.

Identify the variables and their units. This establishes what is being measured and how.

$12$ to $18$ (increase $6$ vs. $6$; they are equal). Both show an absolute increase of $6$, making them equivalent despite different starting points.

Consistent scales and units. Enables meaningful comparison across different data sets.

The rate of change between variables. Shows how much one variable changes per unit of another.

Show frequency distribution. Bars display how often values occur in ranges.

Range = 30. Difference between highest and lowest values $(40-10=30)$.

The middle value when data is ordered. Half the values are above and half below this point.

Examine the axis labels and scale. Understanding units and intervals ensures accurate interpretation.

Y-intercept = 7. Constant term where line crosses the y-axis.

$7$. For an even number of ordered values, average the two middle ones ($5$ and $9$) to find the median.

Cumulative frequency graph. Shows running totals as data accumulates.

The $y$-axis. The vertical axis shows the outcome being measured.

Outlier = 100. Value significantly different from the rest of the data.

The number of observations used to compute the displayed values. Sample size affects reliability; larger $n$ typically means more precise estimates in data presentations.

$20%$. The calculation $(60-50)/50 \times 100%$ yields the relative increase, standard for percent change.

Median = 11. Middle value when data is arranged in order.

$12$. Subtracting the minimum ($3$) from the maximum ($15$) quantifies the dataset's total variability.

$\frac{20}{3}$. Summing to $20$ and dividing by $3$ gives the arithmetic mean, balancing the values.

Independent variable. The variable that is controlled or manipulated.

$7.2$ million. The entry $7.2$ scaled by millions equals $7,200,000$, reflecting the true quantity.

A strong correlation. Points near a line indicate variables change together predictably.

$12$ to $18$ (increase $6$ vs. $6$; they are equal). Both show an absolute increase of $6$, making them equivalent despite different starting points.

State that the variables are correlated, not that one causes the other. Without causal evidence, claims must limit to observed associations to avoid unsubstantiated inferences.

A point far from the overall pattern of the other points. Outliers deviate significantly from the trend, potentially indicating anomalies or errors in data.

Ignoring axis units or a nonzero baseline that changes visual impact. Misreading axes can distort perceived differences, as units and scales affect data interpretation.

Per person; a total divided by population. Per capita normalizes totals by population size, enabling fair comparisons across groups of different sizes.

$6$. Dividing total by population ($300/50$) gives the average per individual, standard for per-capita metrics.

$\frac{\text{part}}{\text{total}}\times 100%$. This expresses the part's share of the whole as a percentage, useful for comparative analysis.

$25%$. The ratio $18/72 = 0.25$, multiplied by $100%$, provides the proportional contribution.

Some values count more because they have larger weights. Weights adjust the influence of each value, reflecting their relative importance in the average.

$17.5$. Using $(10\times^1 + 20\times^3)/(1+3) = 70/4$ accounts for the higher weight of $20$.

The number of observations used to compute the displayed values. Sample size affects reliability; larger $n$ typically means more precise estimates in data presentations.

The greatest difference between two relevant values for each category. Comparing differences per category identifies the maximum change, supporting claims of largest growth.

Relative increase is percent change; absolute increase is the raw difference. Relative focuses on proportional change, while absolute uses raw differences, affecting interpretation of magnitude.

$20$ to $30$ ($50%$ vs. $20%$). Percent change is $(30-20)/20 = 50%$ vs. $(60-50)/50 = 20%$, emphasizing relative growth.

$\frac{y_2-y_1}{x_2-x_1}$. Slope calculates the rate of change in $y$ per unit $x$, indicating line steepness.

$2$. Applying the slope formula $(13-5)/(6-2) = 8/4$ confirms the constant rate between points.

Estimate a value between labeled data points on the graph. Interpolation estimates within the data range, assuming continuity between known points.

Predict a value beyond the observed data range (often less reliable). Extrapolation extends the trend outside observed data, introducing higher uncertainty.

The series with the smallest variation (smallest range or spread). Consistency implies low variability, so smallest spread supports claims of stability over time.

$5,6,5,6$. The set has a smaller range ($1$ vs. $7$), indicating less fluctuation and greater consistency.

Multiply or interpret values using the stated scale factor. Scaling adjusts reported figures to actual magnitudes, preventing underestimation of values.

$7.2$ million. The entry $7.2$ scaled by millions equals $7,200,000$, reflecting the true quantity.

The difference may not be clearly distinguishable given uncertainty. Overlapping error bars suggest the observed difference could be due to random variation, not a real effect.

Use “slightly higher/lower” rather than “dramatically higher/lower.”. Modest language like “slightly” accurately reflects small differences without exaggerating significance.

A is higher than B throughout the displayed time period. The pattern holds for all shown data points, supporting a conclusion limited to the observed period.

Identify the exact claim, then locate the relevant row/column/axis values. This approach ensures precise alignment between the claim and the data source, avoiding misinterpretation of irrelevant sections.

The overall direction or pattern of change across the x-axis. Trends capture the general movement or pattern in data over the independent variable, often time, to support claims about directionality.

The specific cell value paired with its row and column labels. Citing the exact cell with labels provides direct, verifiable support for the claim without ambiguity.

How much $y$ changes for a given change in $x$. It quantifies the steepness of the line, indicating the speed of change in the dependent variable relative to the independent one.

$\frac{\text{new}-\text{old}}{\text{old}}\times 100%$. This formula measures relative change, allowing comparison of growth or decline across different scales.

$20%$. The calculation $(60-50)/50 \times 100%$ yields the relative increase, standard for percent change.

$25%$. The absolute decrease is $20$, but relative to the original, it's $(60-80)/80 \times 100% = -25%$, focusing on proportional change.

$\frac{x_1+x_2+\cdots+x_n}{n}$. The mean represents the central tendency by equally distributing the total sum across all values.

$\frac{20}{3}$. Summing to $20$ and dividing by $3$ gives the arithmetic mean, balancing the values.

The middle value when the data are ordered. Median identifies the central value in an ordered list, resistant to outliers unlike the mean.

$7$. For an even number of ordered values, average the two middle ones ($5$ and $9$) to find the median.

Maximum minus minimum. Range measures the spread of data by subtracting the smallest from the largest value.

$12$. Subtracting the minimum ($3$) from the maximum ($15$) quantifies the dataset's total variability.

Correlation is association; causation requires proof of a cause-effect link. Graphs show patterns of association, but causation demands experimental evidence or controls for confounding factors.

A pie chart. Shows proportional relationships within a total.

The middle value when data is ordered. Half the values are above and half below this point.

The $y$-axis. The vertical axis shows the outcome being measured.

A strong correlation. Points near a line indicate variables change together predictably.

Examine the axis labels and scale. Understanding units and intervals ensures accurate interpretation.

A line graph. Shows continuous change and patterns across time periods.

The rate of change between variables. Shows how much one variable changes per unit of another.

Outlier = 100. Value significantly different from the rest of the data.

Show frequency distribution. Bars display how often values occur in ranges.

Y-intercept = 7. Constant term where line crosses the y-axis.

Read the title and axis labels. Establishes context and understanding before analyzing data.

Relationship between two variables. Points plotted to reveal patterns or correlations.

Source and units. Verifies data origin and measurement standards.

Consistent scales and units. Enables meaningful comparison across different data sets.

Pie chart. Circular format naturally displays parts of a whole.

Median = 11. Middle value when data is arranged in order.

Slope = 2. Coefficient of $x$ represents rate of change.

Range = 30. Difference between highest and lowest values $(40-10=30)$.

Cumulative frequency graph. Shows running totals as data accumulates.

Independent variable. The variable that is controlled or manipulated.

Mean = 10. Sum of values $(5+8+12+15=40)$ divided by count $(40÷4=10)$.

Line graph. Connects data points to show trends over intervals.

Identify the most frequent value. Mode is the value that appears most often.

Bar chart. Easily compares discrete categories side by side.