$$ \text{Chapter 1: Data Representation} $$

• Types of data:

Representation of data:

• Stem-and-leaf diagram
• Histogram
• Cumulative frequency graph

$$ \text{Chapter 2: Measure of tendency} $$

Types of averages:

• Mode

  • Most popular sample
  • Modal class: class with highest frequency density

• Mean

  <aside> ⭐ For ungrouped data set: $\displaystyle \bar{x}= \frac{\sum X_n}{n}$

  </aside>

  <aside> ⭐ For grouped data set: $\displaystyle \bar{x}=\frac {\sum xf}{\sum f}$

  </aside>

  • Coded mean: $\bar x= \frac{1}{a}.\overline{(ax-b)}+b$

• Median

$$ \text{Chapter 3: Measure of variation} $$

Quartiles:

• First (smaller) quartile: Q1 = $25^{th}$ value counted from the smallest
• Median: Q2
• Third (upper) quartile: Q3 = $75^{th}$ value counted from the smallest
• Interquartile: IQR $=3^{th}$ quartile $-1^{st}$ quartile

Box-and-whisker plots:

Variance: $Var(x)$

• Average distance^2 between all values and mean

• "Mean of the squares minus square of the mean"

• Ungrouped data:

<aside> ⭐ $\displaystyle\frac{\sum(x-\bar x)^2}{n}=\frac{\sum x^2}{n}-\bar x^2$

</aside>

• Grouped data:

  find mid class value for classes with boundaries

<aside> ⭐ $\displaystyle \frac{\sum(x-\bar x)^2f}{\sum f}=\frac{\sum x^2f}{\sum f}-\bar x^2$

</aside>