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### Measuring the Dispersion of Data

- Quartiles, outliers and boxplots
**Quartiles**: Q1 (25th percentile), Q3 (75th percentile)**Inter-quartile range**: IQR = Q3 – Q1**Five number summary**: min, Q1, median, Q3, max**Boxplot**: ends of the box are the quartiles; median is marked; add whiskers, and plot outliers individually**Outlier**: usually, a value higher/lower than 1.5 x IQR- Variance and standard deviation (
*sample:**s, population: σ)* **Variance**: (algebraic, scalable computation)

\[
{s^{2}}=\frac{1}{n-1}\sum_{i=1}^{n}(x_{i}-\bar{x})^2=\frac{1}{n-1}[\sum_{i=1}^{n}x_{i}^2-\frac{1}{n}(\sum_{i=1}^{n}x_{i})^2]
\]

\[ {\sigma ^{2}}=\frac{1}{N}\sum_{i=1}^{n}(x_{i}-\mu)^2=\frac{1}{N}\sum_{i=1}^{n}x_{i}^2-\mu ^2 \]

**Standard deviation***s (or σ)*is the square root of variance*s2 (or σ2)*

**Speaker notes:**

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