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: Find the mean: 4, 6, 8, 10.

Answer:

1. Sum (28) divided by count (4).

Flashcard 2: 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 3: What is the interquartile range (IQR)?

Answer: IQR = Q3 - Q1. The range of the middle 50% of the data.

Flashcard 4: What is the mode of the data set: 5, 5, 9, 14, 14, 14?

Answer:

1. 14 appears most frequently (3 times).

Flashcard 5: Identify the median of 6, 8, 10, 12.

Answer:

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

Flashcard 6: What is the range of 12, 15, 18, 21, 24?

Answer:

1. Maximum (24) minus minimum (12).

Flashcard 7: What is the formula for slope between points $(x_1,y_1)$ and $(x_2,y_2)$?

Answer: $\frac{y_2-y_1}{x_2-x_1}$. Rise over run between two points.

Flashcard 8: 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 9: What is the mode of the data set: 5, 5, 9, 14, 14, 14?

Answer:

1. 14 appears most frequently (3 times).

Flashcard 10: What is the median of: 8, 10, 12, 14?

Answer:

1. Average of middle two values (10+12)/2.

Flashcard 11: Calculate the mean of the data set: 2, 4, 6, 8, 10.

Answer:

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

Flashcard 12: 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 13: What is the median of: 8, 10, 12, 14?

Answer:

1. Average of middle two values (10+12)/2.

Flashcard 14: 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 15: 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 16: What is a bimodal distribution?

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

Flashcard 17: Calculate the mean of 4, 8, 10, 12, 14.

Answer: The mean is 9.6. Sum the values (48) and divide by count (5).

Flashcard 18: 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 19: What graphical representation is best for categorical data?

Answer: Bar chart. Shows frequency of different categories or groups.

Flashcard 20: 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 21: 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 22: 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 23: Identify the skewness of data: 1, 2, 2, 3, 10.

Answer: Positively skewed. The tail extends toward larger values; mean > median.

Flashcard 24: What is the purpose of a line graph?

Answer: To show trends over time. It displays how data changes across time intervals.

Flashcard 25: 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 26: What is a negative correlation?

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

Flashcard 27: Interpret a correlation coefficient of -0.8.

Answer: Strong negative correlation. The variables have a strong inverse relationship.

Flashcard 28: What is a positive correlation?

Answer: As one variable increases, the other also increases. Both variables move in the same direction together.

Flashcard 29: What does a flat histogram indicate about data distribution?

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

Flashcard 30: Define frequency distribution in data analysis.

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