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: Calculate the variance: data set 2, 2, 3, 3.

Answer: Variance = 0.25. Mean is 2.5, deviations squared and averaged.

Flashcard 2: What are quartiles?

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

Flashcard 3: 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 4: What does the skewness of a distribution indicate?

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

Flashcard 5: What is the standard deviation if variance is 16?

Answer: Standard Deviation = 4. Standard deviation is the square root of variance: $\sqrt{16} = 4$.

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

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

Flashcard 7: Find the mode: 3, 3, 6, 6, 6, 2, 1.

Answer: Mode = 6. 6 appears most frequently (3 times).

Flashcard 8: What is an outlier in a data set?

Answer: An outlier is a data point significantly different from others. Falls far from typical data pattern.

Flashcard 9: 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 10: Find the standard deviation: data set 4, 4, 5, 5.

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

Flashcard 11: How is range calculated in a data set?

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

Flashcard 12: Identify the shape of a symmetric distribution.

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

Flashcard 13: What does a box plot display?

Answer: A box plot displays the distribution, median, and quartiles of a data set. Five-number summary in visual format.

Flashcard 14: Find the mode: 3, 3, 6, 6, 6, 2, 1.

Answer: Mode = 6. 6 appears most frequently (3 times).

Flashcard 15: 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 16: 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 17: Find the interquartile range: Q1 = 5, Q3 = 15.

Answer: IQR = 10. $Q^3 - Q^1 = 15 - 5 = 10$

Flashcard 18: Find the range: data set 8, 8, 9, 10, 10.

Answer: Range = 2. $10 - 8 = 2$

Flashcard 19: What is the mode of a data set?

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

Flashcard 20: 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 21: State the formula for variance.

Answer: $Variance = \frac{\sum (x_i - \text{mean})^2}{n}$. Square deviations from mean, then average.

Flashcard 22: What is the interquartile range (IQR)?

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

Flashcard 23: What is the shape of a uniform distribution?

Answer: A uniform distribution has equal frequency across values. All intervals have same probability.

Flashcard 24: State the formula for variance.

Answer: $Variance = \frac{\sum (x_i - \text{mean})^2}{n}$. Square deviations from mean, then average.

Flashcard 25: Describe a positively skewed distribution.

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

Flashcard 26: What is the range of the data set: 8, 14, 3, 20, 7?

Answer: Range = 17. Difference between maximum and minimum values: $20 - 3 = 17$.

Flashcard 27: Which measure of center is most affected by outliers?

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

Flashcard 28: What does the skewness of a distribution indicate?

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

Flashcard 29: Describe a negatively skewed distribution.

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

Flashcard 30: How is the geometric mean calculated?

Answer: $Geometric mean = \sqrt[n]{x_1 \cdot x_2 \cdot ... \cdot x_n}$. Multiply all values, take nth root.

Flashcard 31: What does the standard deviation measure?

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

Flashcard 32: What does a box plot display?

Answer: A box plot displays the distribution, median, and quartiles of a data set. Five-number summary in visual format.

Flashcard 33: What is the range of the data set: 8, 14, 3, 20, 7?

Answer: Range = 17. Difference between maximum and minimum values: $20 - 3 = 17$.

Flashcard 34: Identify the shape of a symmetric distribution.

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

Flashcard 35: 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 36: Identify the median in the data set: 3, 5, 7, 9, 11.

Answer: Median = 7. Middle value when data is ordered from least to greatest.

Flashcard 37: Find the mean: 4, 8, 6, 5.

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

Flashcard 38: Calculate the range: 12, 7, 19, 5, 10.

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

Flashcard 39: 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 40: Find the interquartile range: Q1 = 5, Q3 = 15.

Answer: IQR = 10. $Q^3 - Q^1 = 15 - 5 = 10$

Flashcard 41: 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 42: How does a dot plot display data?

Answer: A dot plot uses dots to represent frequency of data values. Each dot equals one data point.

Flashcard 43: Which shape of distribution is symmetric with one peak?

Answer: Normal distribution. Bell-shaped curve with mean, median, and mode all equal.

Flashcard 44: 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 45: Find the interquartile range (IQR) for Q1 = 25 and Q3 = 75.

Answer: IQR = 50. Difference between third and first quartiles: $75 - 25 = 50$.

Flashcard 46: Find the z-score: x = 10, mean = 8, std dev = 1.

Answer: z = 2. $(10-8) ÷ 1 = 2$ standard deviations.

Flashcard 47: What does a scatter plot show?

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

Flashcard 48: What are quartiles?

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

Flashcard 49: What is the interquartile range (IQR)?

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

Flashcard 50: State the formula for the variance of a data set.

Answer: Variance = $\frac{\text{Sum of squared deviations from mean}}{\text{Number of data points}}$. Measures spread by averaging squared distances from mean.

Flashcard 51: What is an outlier in a data set?

Answer: An outlier is a data point significantly different from others. Falls far from typical data pattern.

Flashcard 52: Identify the median in the data set: 3, 5, 7, 9, 11.

Answer: Median = 7. Middle value when data is ordered from least to greatest.

Flashcard 53: 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 54: Calculate the range: 12, 7, 19, 5, 10.

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

Flashcard 55: 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 56: 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 57: How is the geometric mean calculated?

Answer: $Geometric mean = \sqrt[n]{x_1 \cdot x_2 \cdot \dots \cdot x_n}$. Multiply all values, take nth root.

Flashcard 58: What is a bimodal distribution?

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

Flashcard 59: Describe a negatively skewed distribution.

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

Flashcard 60: Find the median: data set 5, 9, 3.

Answer: Median = 5. Ordered: 3,5,9; middle value is 5.

Flashcard 61: How does a dot plot display data?

Answer: A dot plot uses dots to represent frequency of data values. Each dot equals one data point.

Flashcard 62: 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 63: Calculate the mean absolute deviation: 2, 4, 4, 6.

Answer: Mean absolute deviation = 1. Average distance from mean is 1.

Flashcard 64: What is the mode of a data set?

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

Flashcard 65: Find the z-score: x = 10, mean = 8, std dev = 1.

Answer: z = 2. $(10-8) ÷ 1 = 2$ standard deviations.

Flashcard 66: Describe a positively skewed distribution.

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

Flashcard 67: Calculate the mean absolute deviation: 2, 4, 4, 6.

Answer: Mean absolute deviation = 1. Average distance from mean is 1.

Flashcard 68: How is the median of a data set defined?

Answer: The median is the middle value when data is ordered. Sort values first, then find center.

Flashcard 69: What does a scatter plot show?

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

Flashcard 70: How is range calculated in a data set?

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

Flashcard 71: 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 72: What is the formula for the mean of a data set?

Answer: Mean = $\frac{\text{Sum of all data points}}{\text{Number of data points}}$. Sum all values and divide by count.

Flashcard 73: 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 74: Find the standard deviation: data set 4, 4, 5, 5.

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

Flashcard 75: Which measure of center is most affected by outliers?

Answer: Mean. Outliers pull the mean toward extreme values more than median or mode.

Flashcard 76: What is the range of a data set?

Answer: The range is the difference between the highest and lowest values. Span from minimum to maximum value.

Flashcard 77: Find the interquartile range (IQR) for Q1 = 25 and Q3 = 75.

Answer: IQR = 50. Difference between third and first quartiles: $75 - 25 = 50$.

Flashcard 78: Calculate the variance: data set 2, 2, 3, 3.

Answer: Variance = 0.25. Mean is 2.5, deviations squared and averaged.

Flashcard 79: What is a histogram used for?

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

Flashcard 80: What does a frequency polygon represent?

Answer: It represents the frequencies of data points in a line graph. Connected dots show frequency distribution.

Flashcard 81: Which measure of center is most affected by outliers?

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

Flashcard 82: What is the formula for the z-score of a data point?

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

Flashcard 83: What is the standard deviation if variance is 16?

Answer: Standard Deviation = 4. Standard deviation is the square root of variance: $\sqrt{16} = 4$.

Flashcard 84: What is the shape of a uniform distribution?

Answer: A uniform distribution has equal frequency across values. All intervals have same probability.

Flashcard 85: What does the standard deviation measure?

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

Flashcard 86: Find the range: data set 8, 8, 9, 10, 10.

Answer: Range = 2. $10 - 8 = 2$

Flashcard 87: 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 88: What is the mode of the data set: 4, 4, 5, 6, 6, 6, 7?

Answer: Mode = 6. Value that appears most frequently in the data set.

Flashcard 89: How is the median of a data set defined?

Answer: The median is the middle value when data is ordered. Sort values first, then find center.

Flashcard 90: Find the median: 3, 1, 4, 2, 5.

Answer: Median = 3. Ordered: 1,2,3,4,5; middle is 3.

Flashcard 91: 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 92: What is the mode of the data set: 4, 4, 5, 6, 6, 6, 7?

Answer: Mode = 6. Value that appears most frequently in the data set.

Flashcard 93: What is the range of a data set?

Answer: The range is the difference between the highest and lowest values. Span from minimum to maximum value.

Flashcard 94: 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 95: 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 96: Find the median: data set 5, 9, 3.

Answer: Median = 5. Ordered: 3,5,9; middle value is 5.

Flashcard 97: What is a bimodal distribution?

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

Flashcard 98: 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 99: Which shape of distribution is symmetric with one peak?

Answer: Normal distribution. Bell-shaped curve with mean, median, and mode all equal.

Flashcard 100: What does a frequency polygon represent?

Answer: It represents the frequencies of data points in a line graph. Connected dots show frequency distribution.