Evaluating Trends & Making Predictions - ACT Science
Card 1 of 30
A table shows $(x,y)$: $(1,4)$ and $(3,12)$. Predict $y$ at $x=2$ assuming linearity.
A table shows $(x,y)$: $(1,4)$ and $(3,12)$. Predict $y$ at $x=2$ assuming linearity.
Tap to reveal answer
$y=8$. Slope is $4$, so $y = 4 + 4(1) = 8$.
$y=8$. Slope is $4$, so $y = 4 + 4(1) = 8$.
← Didn't Know|Knew It →
Predict the next value: A trend shows doubling each time, current value $3$.
Predict the next value: A trend shows doubling each time, current value $3$.
Tap to reveal answer
$6$. Doubling pattern: $3 × 2 = 6$.
$6$. Doubling pattern: $3 × 2 = 6$.
← Didn't Know|Knew It →
What is an outlier in the context of data trends?
What is an outlier in the context of data trends?
Tap to reveal answer
A data point that deviates significantly. A value that differs greatly from the general pattern.
A data point that deviates significantly. A value that differs greatly from the general pattern.
← Didn't Know|Knew It →
What is the purpose of a trend line in data analysis?
What is the purpose of a trend line in data analysis?
Tap to reveal answer
To show the general direction of data. Summarizes overall data movement for easy interpretation.
To show the general direction of data. Summarizes overall data movement for easy interpretation.
← Didn't Know|Knew It →
Identify the trend in data with a constant rate of change.
Identify the trend in data with a constant rate of change.
Tap to reveal answer
Linear trend. Data changes by the same amount in each time period.
Linear trend. Data changes by the same amount in each time period.
← Didn't Know|Knew It →
What does a scatter plot with no discernible pattern suggest?
What does a scatter plot with no discernible pattern suggest?
Tap to reveal answer
No trend. Data points show no clear relationship or direction.
No trend. Data points show no clear relationship or direction.
← Didn't Know|Knew It →
Identify the prediction: a dataset has a strong correlation.
Identify the prediction: a dataset has a strong correlation.
Tap to reveal answer
Predictions are likely to be accurate. Strong correlations enable reliable future value estimates.
Predictions are likely to be accurate. Strong correlations enable reliable future value estimates.
← Didn't Know|Knew It →
Find the prediction: current trend shows a 5% increase yearly.
Find the prediction: current trend shows a 5% increase yearly.
Tap to reveal answer
Future values increase by 5% each year. Extends the current growth rate into future periods.
Future values increase by 5% each year. Extends the current growth rate into future periods.
← Didn't Know|Knew It →
State the formula for calculating the slope of a trend line.
State the formula for calculating the slope of a trend line.
Tap to reveal answer
Slope = $\frac{y_2 - y_1}{x_2 - x_1}$. Calculates the rate of change between two points on a line.
Slope = $\frac{y_2 - y_1}{x_2 - x_1}$. Calculates the rate of change between two points on a line.
← Didn't Know|Knew It →
Identify the type of trend: data increases steadily.
Identify the type of trend: data increases steadily.
Tap to reveal answer
Positive trend. Values consistently rise over time, showing upward movement.
Positive trend. Values consistently rise over time, showing upward movement.
← Didn't Know|Knew It →
Which trend is shown by data decreasing steadily?
Which trend is shown by data decreasing steadily?
Tap to reveal answer
Negative trend. Values consistently fall over time, showing downward movement.
Negative trend. Values consistently fall over time, showing downward movement.
← Didn't Know|Knew It →
Identify the type of trend: data follows a repeating pattern.
Identify the type of trend: data follows a repeating pattern.
Tap to reveal answer
Cyclical trend. Data repeatedly rises and falls in predictable intervals.
Cyclical trend. Data repeatedly rises and falls in predictable intervals.
← Didn't Know|Knew It →
What does a flat trend line indicate about data?
What does a flat trend line indicate about data?
Tap to reveal answer
No significant change over time. Data remains constant without rising or falling.
No significant change over time. Data remains constant without rising or falling.
← Didn't Know|Knew It →
Identify the trend: Sales increase from 100 units to 500 units over 5 months.
Identify the trend: Sales increase from 100 units to 500 units over 5 months.
Tap to reveal answer
Increasing trend. Sales rise consistently from $100$ to $500$ units.
Increasing trend. Sales rise consistently from $100$ to $500$ units.
← Didn't Know|Knew It →
What type of graph is best for showing trends over time?
What type of graph is best for showing trends over time?
Tap to reveal answer
Line graph. Shows changes over time with connected points.
Line graph. Shows changes over time with connected points.
← Didn't Know|Knew It →
What is the term for a pattern or direction in data over time?
What is the term for a pattern or direction in data over time?
Tap to reveal answer
Trend. A pattern shows consistent direction in data over time.
Trend. A pattern shows consistent direction in data over time.
← Didn't Know|Knew It →
Which method estimates a value within a series based on surrounding data points?
Which method estimates a value within a series based on surrounding data points?
Tap to reveal answer
Interpolation. Estimates values between known data points.
Interpolation. Estimates values between known data points.
← Didn't Know|Knew It →
Determine the prediction: Temperature rises from 20°C to 30°C in 3 days. Day 4?
Determine the prediction: Temperature rises from 20°C to 30°C in 3 days. Day 4?
Tap to reveal answer
Likely 31°C or higher. Trend shows $10°C$ increase over $3$ days.
Likely 31°C or higher. Trend shows $10°C$ increase over $3$ days.
← Didn't Know|Knew It →
What is the term for predicting future values based on current trends?
What is the term for predicting future values based on current trends?
Tap to reveal answer
Extrapolation. Extends a trend beyond known data points.
Extrapolation. Extends a trend beyond known data points.
← Didn't Know|Knew It →
What type of variable is typically plotted on the x-axis when evaluating trends?
What type of variable is typically plotted on the x-axis when evaluating trends?
Tap to reveal answer
Independent variable. The variable that causes changes in the trend.
Independent variable. The variable that causes changes in the trend.
← Didn't Know|Knew It →
Choose the correct prediction: Data shows a consistent 5% monthly growth.
Choose the correct prediction: Data shows a consistent 5% monthly growth.
Tap to reveal answer
Next month: 5% increase. Consistent pattern continues into next period.
Next month: 5% increase. Consistent pattern continues into next period.
← Didn't Know|Knew It →
What type of relationship is indicated by a positive slope in a trend line?
What type of relationship is indicated by a positive slope in a trend line?
Tap to reveal answer
Positive correlation. Both variables increase together in same direction.
Positive correlation. Both variables increase together in same direction.
← Didn't Know|Knew It →
Predict the outcome: A trend line shows consistent decline in scores.
Predict the outcome: A trend line shows consistent decline in scores.
Tap to reveal answer
Scores will continue to decrease. Downward trend indicates continued decline.
Scores will continue to decrease. Downward trend indicates continued decline.
← Didn't Know|Knew It →
What does a negative slope in a trend line typically indicate?
What does a negative slope in a trend line typically indicate?
Tap to reveal answer
Negative correlation. One variable decreases as the other increases.
Negative correlation. One variable decreases as the other increases.
← Didn't Know|Knew It →
Predict: If a trend shows decreasing values, what is next if current is $50$?
Predict: If a trend shows decreasing values, what is next if current is $50$?
Tap to reveal answer
Lower than $50$. Downward trend means values will continue falling.
Lower than $50$. Downward trend means values will continue falling.
← Didn't Know|Knew It →
What is the conclusion when a trend line flattens after a period of increase?
What is the conclusion when a trend line flattens after a period of increase?
Tap to reveal answer
Stabilization. Growth levels off and becomes constant.
Stabilization. Growth levels off and becomes constant.
← Didn't Know|Knew It →
Identify the trend: Data points cluster tightly around a positive slope line.
Identify the trend: Data points cluster tightly around a positive slope line.
Tap to reveal answer
Strong positive trend. Close clustering shows strong linear relationship.
Strong positive trend. Close clustering shows strong linear relationship.
← Didn't Know|Knew It →
What does it mean when data points are widely scattered in a scatter plot?
What does it mean when data points are widely scattered in a scatter plot?
Tap to reveal answer
Weak correlation. Scattered points show little linear relationship.
Weak correlation. Scattered points show little linear relationship.
← Didn't Know|Knew It →
Predict the next value: Trend shows values increasing by $2$ each time, current $10$.
Predict the next value: Trend shows values increasing by $2$ each time, current $10$.
Tap to reveal answer
$12$. Adding $2$ to current value: $10 + 2 = 12$.
$12$. Adding $2$ to current value: $10 + 2 = 12$.
← Didn't Know|Knew It →
Identify the trend: A trend line in a graph is steeply rising.
Identify the trend: A trend line in a graph is steeply rising.
Tap to reveal answer
Rapid increase. Steep slope indicates fast rate of change.
Rapid increase. Steep slope indicates fast rate of change.
← Didn't Know|Knew It →