http://www.ck12.org Chapter 7. Organizing and Displaying Data - Basic
From the graph, it is clearly seen that there is no relationship between the number of lottery tickets sold and the
temperature of the surrounding environment.
Example 3:The table below represents the height of ten children in inches and their shoe size.
Height(in) 51 53 61 59 63 47 53 66 55 49
Shoe Size 2 4 6 5 7 1 3 9 4 2The information from the table can be displayed on a scatter plot.
Solution:
Yes, there is a relationship between the shoe size and the height of the child. Children who are short wear small-sized
shoes and those who are taller wear larger shoes.
In this case, there is a direct relationship (correlation) between the shoe size and the height of the children. Corre-
lation refers to the relationship or connection between two sets of data. The correlation between two sets of data
can be weak, strong, negative, or positive, or in some cases there can be no correlation. The characteristics of the
correlation between two sets of data can be readily seen from the scatter plot.
The scatter plot of the shoe sizes and the heights of the children show a strong, positive correlation. The scatter plot
of the lottery tickets and the temperature showed no correlation.
If there is a correlation between the two sets of data on a scatter plot, then a straight line can be drawn so that the
plotted points are either on the line or very close to it. This line is called theline of best fit. A line of best fit is
drawn on a scatter plot so that it joins as many points as possible and shows the general direction of the data. When
constructing the line of best fit, it is also important to keep, approximately, an equal number of points above and
below the line. To determine where the line of best fit should be drawn, a piece of spaghetti can easily be rolled
across the graph with the plotted points still being visible.
Returning to the scatter plot that shows the relationship between shoe sizes and the height of children, a line of best
fit can be drawn to define this relationship.
In a later lesson, we will determine the equation of this line manually and by using technology.