Center, Shape, & Spread of Data - SAT Math

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

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

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

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 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.

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

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. $(4+8+6+5) ÷ 4 = 5.75$

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

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