Scatter Quartiles Percentiles 9F0460

1. **Understanding Scatter Graphs:** A scatter graph is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. 2. **Purpose of Scatter Graphs:** They help to visualize the relationship or correlation between two variables. 3. **Quartiles Definition:** Quartiles divide a ranked data set into four equal parts. The three quartiles are: - $Q_1$ (first quartile) is the median of the lower half of the data. - $Q_2$ (second quartile) is the median of the data. - $Q_3$ (third quartile) is the median of the upper half of the data. 4. **Finding Quartiles:** - Arrange the data in ascending order. - Find the median ($Q_2$). - Find the median of the lower half for $Q_1$. - Find the median of the upper half for $Q_3$. 5. **Percentiles Definition:** Percentiles divide the data into 100 equal parts. The $k^{th}$ percentile is the value below which $k\%$ of the data falls. 6. **Finding Percentiles:** - Arrange data in ascending order. - Calculate the rank $R = \frac{k}{100} \times (n+1)$ where $n$ is the number of data points. - If $R$ is an integer, the percentile is the value at position $R$. - If $R$ is not an integer, interpolate between the surrounding data points. 7. **Relation to Scatter Graphs:** Scatter graphs themselves do not directly find quartiles or percentiles but the data points plotted can be analyzed separately to find these statistics. **Final Note:** Scatter graphs visualize data relationships, while quartiles and percentiles summarize data distribution.