SAT Math Flashcards: Center Shape And Spread Of Data

What this deck covers

This deck focuses on Center Shape And Spread Of Data, giving you a quick way to review the definitions, rules, and examples that matter most for SAT Math.

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

Answer: It displays quantitative data to show distribution details. Separates tens and ones digits clearly.

Flashcard 2: Describe a positively skewed distribution.

Answer: Positively skewed: tail extends to the right. Most data on left, few high values.

Flashcard 3: Calculate the range: 12, 7, 19, 5, 10.

Answer: Range = 14. $19 - 5 = 14$

Flashcard 4: State the formula for the z-score of a data point.

Answer: $z = \frac{x - \text{mean}}{\text{standard deviation}}$. Standardizes distance from mean in units.

Flashcard 5: What is the formula for the mean of a data set?

Answer: $Mean = \frac{\sum x_i}{n}$. Sum all values, divide by count.

Flashcard 6: Identify the measure of central tendency least affected by outliers.

Answer: The median is least affected by outliers. Extreme values don't shift median much.

Flashcard 7: What is the mean of the data set: 4, 8, 6, 10, 2?

Answer: The mean is 6. Sum all values (30) and divide by count (5).

Flashcard 8: What is the median of the data set: 3, 7, 9, 2, 4?

Answer: The median is 4. Middle value when ordered: 2, 3, 4, 7, 9.

Flashcard 9: Identify the shape of a distribution with a long right tail.

Answer: The shape is right-skewed. Long tail extends toward higher values on the right.

Flashcard 10: What is the median of the data set: 3, 7, 9, 2, 4?

Answer: The median is 4. Middle value when ordered: 2, 3, 4, 7, 9.

Flashcard 11: Identify the shape of a symmetric distribution.

Answer: A symmetric distribution is mirrored around its center. Both sides look identical when folded.

Flashcard 12: What does the standard deviation measure?

Answer: The standard deviation measures data spread around the mean. Shows how far values deviate from center.

Flashcard 13: How is range calculated in a data set?

Answer: Range = Maximum value - Minimum value. Subtract smallest from largest value.

Flashcard 14: Identify the best measure of center for skewed data.

Answer: The median is the best measure for skewed data. Outliers don't affect median much.

Flashcard 15: What is the mean of the data set: 4, 8, 6, 10, 2?

Answer: The mean is 6. Sum all values (30) and divide by count (5).

Flashcard 16: Which measure of center is most affected by outliers?

Answer: The mean is most affected. Outliers pull the mean toward extreme values.

Flashcard 17: Identify the shape of a distribution with a long right tail.

Answer: The shape is right-skewed. Long tail extends toward higher values on the right.

Flashcard 18: Find the mean: 4, 8, 6, 5.

Answer: Mean = 5.75. $(4+8+6+5) ÷ 4 = 5.75$

Flashcard 19: Find the standard deviation: data set 4, 4, 5, 5.

Answer: Standard deviation = 0.5. Mean is 4.5, deviations squared and averaged.

Flashcard 20: What is a bimodal distribution?

Answer: A distribution with two distinct peaks or modes. Two separate frequency peaks exist.

Flashcard 21: What is the interquartile range (IQR)?

Answer: IQR = Q3 - Q1. Third quartile minus first quartile.

Flashcard 22: What does the term 'spread of data' refer to?

Answer: It refers to the variability or dispersion of data points. How scattered data points are.

Flashcard 23: What is the mode of a data set?

Answer: The mode is the most frequently occurring value. Count frequency of each value.

Flashcard 24: What are quartiles?

Answer: Quartiles divide data into four equal parts. 25%, 50%, 75% split points.

Flashcard 25: What is a cumulative frequency graph?

Answer: It shows cumulative totals of data points up to each class. Running total increases at each point.

Flashcard 26: Identify the effect of skewness on mean and median.

Answer: In skewed data, mean is pulled toward the tail. Median stays centered, mean shifts.

Flashcard 27: What does a scatter plot show?

Answer: A scatter plot shows the relationship between two variables. Points reveal correlation patterns.

Flashcard 28: What is a histogram used for?

Answer: A histogram displays the frequency distribution of data. Bars show count in each interval.

Flashcard 29: What does the skewness of a distribution indicate?

Answer: Skewness indicates the asymmetry of a distribution. Measures if distribution leans left or right.

Flashcard 30: Describe a negatively skewed distribution.

Answer: Negatively skewed: tail extends to the left. Most data on right, few low values.