Center, Shape, & Spread of Data - SAT Math

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

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

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

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

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

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

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

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

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

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

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

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

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

Mean = 5.75. $(4+8+6+5) ÷ 4 = 5.75$

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

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

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

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

Range = 2. $10 - 8 = 2$

Range = 14. $19 - 5 = 14$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Range = 14. $19 - 5 = 14$

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

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

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

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

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

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

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

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

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

Range = 2. $10 - 8 = 2$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Mean = 5.75. $(4+8+6+5) ÷ 4 = 5.75$

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

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

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

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

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

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

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

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

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

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