ACT Science Flashcards: Comparing Data Sets

What this deck covers

This deck focuses on Comparing Data Sets, giving you a quick way to review the definitions, rules, and examples that matter most for ACT Science.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Define the range in a data set.

Answer: Difference between the maximum and minimum values. Measures the spread of the data set.

Flashcard 2: Define standard deviation in the context of data sets.

Answer: Standard deviation measures data spread around the mean. It quantifies how much individual data points deviate from the average.

Flashcard 3: What is the definition of an outlier when comparing two distributions or series?

Answer: A value far from the overall pattern of the data. An unusual data point that doesn't fit the pattern.

Flashcard 4: What does a box plot visually represent?

Answer: Distribution, median, quartiles, and outliers. Shows the five-number summary of a data set graphically.

Flashcard 5: Find the slope between $(2,5)$ and $(6,13)$ using $\frac{y_2-y_1}{x_2-x_1}$.

Answer: $2$. $\frac{13-5}{6-2} = \frac{8}{4} = 2$.

Flashcard 6: Calculate the mean of the data set: 2, 4, 6, 8, 10.

Answer:

1. Sum (30) divided by count (5).

Flashcard 7: Identify the correct conclusion if two data sets share a correlation with $x$ but differ in magnitude.

Answer: They show similar trends but different levels (different $y$-values). Similar patterns but different scales or intensities.

Flashcard 8: What does it mean if one data set is a constant multiple of another across all $x$?

Answer: They differ by a multiplicative factor (scaling). One is proportionally larger at all points.

Flashcard 9: What is the effect of outliers on the mean of a data set?

Answer: Outliers can skew the mean. Outliers pull the mean toward their extreme values.

Flashcard 10: Identify range: 1, 3, 5, 7, 10.

Answer:

1. Maximum (10) minus minimum (1).

Flashcard 11: Define frequency distribution in data analysis.

Answer: A summary of how often values occur. It counts how many times each value appears.

Flashcard 12: What is the median of 3, 7, 8, 12, 14?

Answer:

1. Middle value of 5 ordered numbers.

Flashcard 13: Identify the median of 6, 8, 10, 12.

Answer:

1. Average of middle two values (8+10)/2.

Flashcard 14: Calculate the percent change from $40$ to $50$ using \frac{F-I}{I}\times 100\text{%}.

Answer: 25\text{%}. $\frac{50-40}{40} \times 100\% = 25\%$.

Flashcard 15: In a data set, what is an outlier?

Answer: A value significantly higher or lower than most others. Extreme value that deviates from the pattern.

Flashcard 16: What is the mode of the data set: 4, 4, 5, 6, 7?

Answer: The mode is 4. The value that appears most frequently in the data set.

Flashcard 17: How is variance related to standard deviation?

Answer: Variance is the square of the standard deviation. Variance equals standard deviation squared, or $σ^2$.

Flashcard 18: What is the most direct way to compare rates of change of two data sets on a line graph?

Answer: Compare slopes over the same $x$-interval. Calculate how steep each line is.

Flashcard 19: What is the range of the data set: 10, 15, 20, 25, 30?

Answer: The range is 20. Subtract the minimum (10) from the maximum (30).

Flashcard 20: Define 'mode' in statistics.

Answer: Most frequently occurring value in a data set. Value with highest frequency.

Flashcard 21: What is the definition of a dependent variable when comparing two data sets?

Answer: The measured response, often on the $y$-axis. The output variable that responds to changes.

Flashcard 22: What does it mean if two data sets have the same shape but one is shifted upward?

Answer: They differ mainly by an additive offset in $y$. Same pattern with a constant vertical displacement.

Flashcard 23: Identify the median in the data set: 2, 4, 6, 8, 10.

Answer: The median is 6. The middle value when data is arranged in order.

Flashcard 24: Find the mode of this data set: 1, 2, 2, 3, 4.

Answer: The mode is 2. The value 2 appears twice, more than any other value.

Flashcard 25: What is the formula for calculating the mean?

Answer: $\frac{\text{sum of values}}{\text{number of values}}$. Standard formula for arithmetic mean.

Flashcard 26: What is a bimodal distribution?

Answer: A distribution with two modes. Two values occur with the highest frequency.

Flashcard 27: Calculate the percent difference between $20$ and $24$ using \frac{|A-B|}{\frac{A+B}{2}}\times 100\text{%}.

Answer: 18.2\text{%}. $\frac{|20-24|}{22} \times 100\% = 18.2\%$.

Flashcard 28: What is the mode of the data set: 5, 5, 9, 14, 14, 14?

Answer:

1. 14 appears most frequently (3 times).

Flashcard 29: Identify the data set with greater variability: A: 3, 3, 3, 3, 3; B: 1, 5, 9, 13, 17.

Answer: Set B has greater variability. Set A has no variation while Set B spans a wide range.

Flashcard 30: What is the meaning of a higher slope for data set A than data set B on the same axes?

Answer: A changes faster per unit $x$ than B. Set A increases more rapidly than set B.

Flashcard 31: What does a correlation coefficient of 0 indicate?

Answer: No linear relationship. The variables have no linear association with each other.

Flashcard 32: What is an outlier in a data set?

Answer: A value significantly different from others. An extreme value that falls far from the typical range.

Flashcard 33: Which measure is resistant to outliers: mean, median, or mode?

Answer: Median is resistant to outliers. Median doesn't change much when extreme values are present.

Flashcard 34: Find the mode: 7, 8, 9, 9, 10.

Answer:

1. 9 appears twice, most frequent.

Flashcard 35: Define 'median' in statistics.

Answer: Middle value when data is ordered. Central position in ordered data.

Flashcard 36: Identify the range of the data set: 4, 8, 10, 15, 22.

Answer:

1. Maximum (22) minus minimum (4).

Flashcard 37: Identify the correct conclusion if two data sets share a correlation with $x$ but differ in magnitude.

Answer: They show similar trends but different levels (different $y$-values). Similar patterns but different scales or intensities.

Flashcard 38: What is the mode of the data set: 5, 5, 9, 14, 14, 14?

Answer:

1. 14 appears most frequently (3 times).

Flashcard 39: What is the range of the data set: 10, 15, 20, 25, 30?

Answer: The range is 20. Subtract the minimum (10) from the maximum (30).

Flashcard 40: Define frequency distribution in data analysis.

Answer: A summary of how often values occur. It counts how many times each value appears.

Flashcard 41: What is the most direct way to compare rates of change of two data sets on a line graph?

Answer: Compare slopes over the same $x$-interval. Calculate how steep each line is.

Flashcard 42: What is the formula for absolute difference between two values $A$ and $B$?

Answer: $|A-B|$. Distance between values, always positive.

Flashcard 43: Identify the correct comparison if two bars represent different sample sizes $n$.

Answer: Compare proportions or rates, not raw counts. Use ratios to account for different group sizes.

Flashcard 44: What is the correct interpretation if error bars do not overlap for two means?

Answer: The means likely differ more than the displayed uncertainty. Non-overlapping bars suggest a clearer difference.

Flashcard 45: Calculate the mode: 3, 3, 6, 9.

Answer:

1. 3 appears twice, most frequent.

Flashcard 46: In a normal distribution, what percentage of data falls within one standard deviation of the mean?

Answer: Approximately 68%. This follows the empirical rule for normal distributions.

Flashcard 47: What is the range of: 9, 15, 22, 25?

Answer:

1. Maximum (25) minus minimum (9).

Flashcard 48: Which is more robust to outliers: mean or median?

Answer: Median. Median is less influenced by extreme values.

Flashcard 49: Which option best describes a fair comparison when units differ (e.g., mg vs g)?

Answer: Convert to the same units before comparing values. Use consistent units to make meaningful comparisons.

Flashcard 50: How do you find the median?

Answer: Arrange data in order, pick the middle value. Standard method for finding median.

Flashcard 51: What is the definition of variability in a data set?

Answer: How spread out the values are around a typical value. Measures how much the data points differ from each other.

Flashcard 52: Identify the median in the data set: 2, 4, 6, 8, 10.

Answer: The median is 6. The middle value when data is arranged in order.

Flashcard 53: Find the slope between $(2,5)$ and $(6,13)$ using $\frac{y_2-y_1}{x_2-x_1}$.

Answer: $2$. $\frac{13-5}{6-2} = \frac{8}{4} = 2$.

Flashcard 54: In a data set, what is an outlier?

Answer: A value significantly higher or lower than most others. Extreme value that deviates from the pattern.

Flashcard 55: Identify which comparison is most appropriate for exponential growth across data sets.

Answer: Compare multiplicative changes or slopes on a log scale. Log scales better show exponential growth patterns.

Flashcard 56: What type of graph shows the cumulative frequency of data?

Answer: Ogive or cumulative frequency graph. Also called a cumulative frequency curve.

Flashcard 57: How is variance related to standard deviation?

Answer: Variance is the square of the standard deviation. Variance equals standard deviation squared, or $σ^2$.

Flashcard 58: What is the formula for the difference (A minus B) at the same $x$ when comparing data sets?

Answer: $A-B$. Subtracts one value from the other.

Flashcard 59: What does it mean if two data set curves intersect at an $x$-value?

Answer: They have equal $y$-values at that $x$. The data sets have the same value at that point.

Flashcard 60: What is the mode of 1, 2, 2, 3, 4?

Answer:

1. 2 appears twice, most frequent.

Flashcard 61: What type of graph shows the cumulative frequency of data?

Answer: Ogive or cumulative frequency graph. Also called a cumulative frequency curve.

Flashcard 62: What does it mean if two data sets have the same mean but different spread?

Answer: They have similar centers but different variability. Central tendency is similar but consistency differs.

Flashcard 63: What is the mean of the data set: 3, 5, 7, 9, 11?

Answer: The mean is 7. Sum all values and divide by the count of values.

Flashcard 64: What is the definition of a data set in an ACT Science table or graph?

Answer: A collection of measured or observed values for one or more variables. Information gathered from measurements or observations.

Flashcard 65: What is a key characteristic of a normal distribution?

Answer: Symmetry around the mean. The distribution is bell-shaped with equal sides around the center.

Flashcard 66: How does a histogram differ from a bar chart?

Answer: Histograms display frequency of numerical data. Bar charts show categories; histograms show continuous data ranges.

Flashcard 67: Identify the correct comparison if two bars represent different sample sizes $n$.

Answer: Compare proportions or rates, not raw counts. Use ratios to account for different group sizes.

Flashcard 68: What does it mean if two lines on a graph are parallel over an interval?

Answer: They have the same slope (same rate of change). Both lines change at the same rate.

Flashcard 69: Define standard deviation in the context of data sets.

Answer: Standard deviation measures data spread around the mean. It quantifies how much individual data points deviate from the average.

Flashcard 70: Which measure is resistant to outliers: mean, median, or mode?

Answer: Median is resistant to outliers. Median doesn't change much when extreme values are present.

Flashcard 71: What is the formula for calculating the interquartile range?

Answer: $Q3 - Q1$. Standard IQR calculation notation.

Flashcard 72: What is the effect of outliers on the mean of a data set?

Answer: Outliers can skew the mean. Outliers pull the mean toward their extreme values.

Flashcard 73: What is the formula for percent change from an initial value $I$ to a final value $F$?

Answer: $\frac{F-I}{I}\times 100\%$. Shows relative change from the starting value.

Flashcard 74: What is the formula for the ratio of data set A to data set B at the same $x$?

Answer: $\frac{A}{B}$. Divides one value by the other for comparison.

Flashcard 75: What is the formula for the range?

Answer: Maximum value - Minimum value. Basic range calculation formula.

Flashcard 76: Find the mean of 5, 10, 15, 20.

Answer: 12.5. Sum (50) divided by count (4).

Flashcard 77: Define correlation in the context of data analysis.

Answer: A measure of the strength and direction of a relationship. Ranges from -1 to +1, indicating linear association strength.

Flashcard 78: What is the definition of a trend when comparing data sets across an $x$-variable?

Answer: A consistent pattern of increase, decrease, or no change. A pattern showing how values change consistently.

Flashcard 79: What does it mean if data is negatively skewed?

Answer: Tail on the left side; mean < median. The distribution has a longer tail on the left side.

Flashcard 80: At the same $x$, data set A has $y=12$ and B has $y=9$; what is $A-B$?

Answer: $3$. $12 - 9 = 3$.

Flashcard 81: What measure is least affected by outliers?

Answer: Median. Resistant to extreme values.

Flashcard 82: How is the interquartile range calculated?

Answer: Subtract the first quartile from the third quartile. Formula: $Q_3 - Q_1$.

Flashcard 83: Calculate the IQR for the data set: 1, 3, 5, 7, 9.

Answer: The IQR is 4. $Q^1 = 3$, $Q^3 = 7$, so $IQR = 7 - 3 = 4$.

Flashcard 84: What statistical measure is best for skewed data: mean, median, or mode?

Answer: Median is best for skewed data. Median is less affected by extreme values than the mean.

Flashcard 85: Define 'median' in statistics.

Answer: Middle value when data is ordered. Central position in ordered data.

Flashcard 86: In a positively skewed distribution, which is greater: mean or median?

Answer: Mean is greater. Outliers in the right tail pull the mean higher.

Flashcard 87: How do you identify an outlier in a box plot?

Answer: Points outside the whiskers. Whiskers extend to the most extreme non-outlier values.

Flashcard 88: What does a flat histogram indicate about data distribution?

Answer: Uniform distribution. All values occur with approximately equal frequency.

Flashcard 89: How do you find the median?

Answer: Arrange data in order, pick the middle value. Standard method for finding median.

Flashcard 90: What does it mean if one data set is a constant multiple of another across all $x$?

Answer: They differ by a multiplicative factor (scaling). One is proportionally larger at all points.

Flashcard 91: Calculate the mean of the data set: 2, 4, 6, 8, 10.

Answer:

1. Sum (30) divided by count (5).

Flashcard 92: What is the purpose of a stem-and-leaf plot?

Answer: To display quantitative data distribution. It organizes data by stems (tens) and leaves (units).

Flashcard 93: Define the range in a data set.

Answer: Difference between the maximum and minimum values. Measures the spread of the data set.

Flashcard 94: What is the interquartile range (IQR) of the data set: 1, 3, 5, 7, 9?

Answer:

1. Third quartile (7) minus first quartile (3).

Flashcard 95: What is the mode of 2, 4, 4, 6, 8?

Answer:

1. 4 appears twice, most frequent.

Flashcard 96: Identify the mean of: $1, 3, 5, 7$.

Answer:

1. Sum ($16$) divided by count ($4$).

Flashcard 97: What is the mode of 2, 4, 4, 6, 8?

Answer:

1. 4 appears twice, most frequent.

Flashcard 98: What does it mean if two data sets have the same shape but one is shifted upward?

Answer: They differ mainly by an additive offset in $y$. Same pattern with a constant vertical displacement.

Flashcard 99: What is the median of the ordered set $[2,4,7,9,12]$?

Answer: $7$. The middle value when data is arranged in order.

Flashcard 100: What is a negative correlation?

Answer: As one variable increases, the other decreases. Both variables move in opposite directions to each other.