Organizing Data and Correlations

Organizing raw data can help us see patterns and trends. One way to organize data is to use a line plot

A line plot uses a number line to show how often a value occurs in a data set

To make a line plot, find the least value and the greatest value in the data set and draw a number line. Place an ‘X’ above each number on the number line for each time it appears in the data set

Venn diagrams are used to show relationships between sets

To make a Venn diagram, draw as many circles as there are data sets and label them. The region that overlaps represents the characteristics shared by both sets of data

A stem-and-leaf plot is a graph used to organize and display data to compare frequencies

Each leaf on a plot represents the right-hand digit in a data value. Each stem represents the remaining left-hand digits

A back-to-back stem-and-leaf plot can be used to compare two sets of data. The stems are in the center, and the left leaves are read in reverse

In a back-to-back stem-and-leaf plot, |3|1 means 31 and 1|2| means 21

A scatter plot is a graph that shows the relationship between two sets of data

In this type of graph, two sets of data are graphed as ordered pairs on a coordinate plane

The line that passes through or is very close to most of the data points is called the best-fit line

The slope of a straight line is given by: m = (y₂ –y₁)/(x₂ – x₂), where (x₁, y₁) and (x₂, y₂) are two points on the line

The equation of a straight line is: y = mx + b (slope-intercept form). The equation of the best-fit line can be used to predict values

Correlation is the relationship between two data sets. There can be positive, negative, or no correlation

When both the data sets increase together, it indicates a positive correlation

If an increase in one data set results in a decrease in the other, it indicates a negative correlation

If changes in one data set do not affect the other data set, there is no correlation