chad 2

Range

value.

Definition: The range measures the spread of a dataset by subtracting the smallest value from the largest

Formula: Range = Maximum - Minimum

Example: Data: 3, 7, 8, 12, 15

Range = 15 - 3 = 12

Key Idea: - Simple measure of spread - Uses only two values (min and max) - Sensitive to outliers

2. Quartiles

Definition: Quartiles divide a dataset into four equal parts.

• Q1 (First Quartile): 25% of data below

• Q2 (Median): 50% of data below

• Q3 (Third Quartile): 75% of data below

Steps to Find Quartiles: 1. Order the data from smallest to largest 2. Find the median (Q2) 3. Find the median of the lower half → Q1 4. Find the median of the upper half → Q3

Example: Data: 2, 4, 6, 8, 10, 12, 14 - Q2 = 8 - Q1 = 4 - Q3=12

Interquartile Range (IQR): IQR = Q3 - Q1

Key Idea: - Describes the middle 50% of data - Less affected by outliers

3. Standard Deviation

Definition: Standard deviation measures how far data values typically are from the mean.

Population Formula: 0 = /[[(x / N]

Sample Formula: 5 = / [2(x-x)2/ (n- 1)]Steps (Conceptual): 1. Find the mean 2. Subtract the mean from each value 3. Square the differences 4.

Find the average of squared differences 5. Take the square root

Key Idea: - Small standard deviation → data is close to the mean - Large standard deviation → data is spread out

4. Percentiles

Definition: A percentile tells you the percentage of data values that are at or below a certain value.

• Example: The 70th percentile means 70% of the data is at or below that value.

Common Percentiles: - 25th percentile = Q1 - 50th percentile = Median (Q2) - 75th percentile = Q3

Steps to Find a Percentile (Conceptual): 1. Order the data from smallest to largest 2. Find the position using a percentile formula (varies slightly by method) 3. Identify or interpolate the value at that position

Special Note: - If there are multiple identical values in the dataset, all of them count in the calculation.

Percentiles are based on the position in the ordered dataset, so repeated values simply share the same percentile range.

Key Idea: - Shows relative standing within a dataset - Useful for comparing individuals (test scores, rankings)

Summary Comparison

Measure

What it Uses

What it Tells You

Sensitive to Outliers?

Range

Min & Max

Total spread

Yes

Quartiles (IQR)

Middle 50%

Central spread

No

Standard Deviation All data

Typical distance from mean Yes

Percentiles

Position in data

Relative standing

No

When to Use

• Range: Quick overview of spread

• Quartiles/IQR: When data has outliers or is skewed

• Standard Deviation: When working with mean and normal distributions

• Percentiles: To compare position within a dataset (e.g., test scores)