#businessarticle12 #mathematics #statistics

Rules for statistics in pure mathematics

By Lona Matshingana 

2026/01/01

# Statistics in Pure Mathematics (High School Level)

Here's an overview of key statistical concepts and rules typically covered in high school pure mathematics:

## Measures of Central Tendency

**Mean (Average)**
- Sum of all values divided by the number of values
- Formula: x̄ = (Σx)/n
- Affected by outliers

**Median**
- Middle value when data is ordered
- For even datasets, average the two middle values
- Resistant to outliers

**Mode**
- Most frequently occurring value
- A dataset can have no mode, one mode, or multiple modes

## Measures of Spread

**Range**
- Difference between maximum and minimum values
- Range = Max - Min

**Interquartile Range (IQR)**
- IQR = Q3 - Q1 (difference between upper and lower quartiles)
- Represents the middle 50% of data
- Resistant to outliers

**Variance**
- Average of squared deviations from the mean
- Population variance: σ² = Σ(x - μ)²/N
- Sample variance: s² = Σ(x - x̄)²/(n-1)

**Standard Deviation**
- Square root of variance
- σ = √(variance)
- Measures typical distance from the mean

## Quartiles and Percentiles

- Q1 (25th percentile): 25% of data below this value
- Q2 (50th percentile): The median
- Q3 (75th percentile): 75% of data below this value

## Key Properties

**Linear transformations**: If you add/subtract a constant to all values, measures of center shift by that amount but spread measures stay the same. If you multiply/divide all values by a constant, all measures (center and spread) are affected proportionally.

**Outlier detection**: Values beyond Q1 - 1.5(IQR) or Q3 + 1.5(IQR) are often considered outliers.

Thank you for reading!!! 

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