1. **Stating the problem:** We want to understand the 3 chiastic properties in statistics related to Variation, Frequency, and Proportion. 2. **Chiastic property of Variation:** Variation measures how data points differ from each other. - Formula: $$\text{Variation} = \text{Max value} - \text{Min value}$$ - This shows the range of data. 3. **Chiastic property of Frequency:** Frequency counts how often a value appears. - If $f_i$ is the frequency of value $x_i$, then total frequency $N = \sum f_i$. - Frequency helps us understand data distribution. 4. **Chiastic property of Proportion:** Proportion is the relative frequency. - Formula: $$\text{Proportion} = \frac{f_i}{N}$$ - It shows the fraction of total data for each value. 5. **Explanation:** - Variation tells us the spread. - Frequency tells us the count. - Proportion tells us the part of the whole. 6. **Example:** Suppose data values are 2, 2, 3, 5. - Variation = $5 - 2 = 3$ - Frequencies: $f_2=2$, $f_3=1$, $f_5=1$ - Total $N=4$ - Proportions: $\frac{2}{4}=0.5$, $\frac{1}{4}=0.25$, $\frac{1}{4}=0.25$ This completes the explanation of the 3 chiastic properties in statistics.