When the data points on the scatter plot lie close to a line, the scatter plot shows a linear association.
C
Can you see any relationship between the data? How can you use it to predict the value?
A
B
Example Solution:
The scatter plot shows a positive linear association. There are no clusters or outliers.
C
About 70 units
Practice makes perfect
A scatter plot is a graph that shows the associations between two data sets. Let's start by looking at the given table.
Time (h)
8
19
16
40
34
8
40
19
34
Units Produced
20
41
28
60
49
28
63
40
58
We want to create a scatter plot of number of units produced over time. First, we need to represent the data as ordered pairs (x,y), where x is the time and y is the number of units produced.
cc
(8,20) & (8,28) & (16,28) (19,40) & (19,41) & (34,49) (34,58) & (40,60) & (40,63)
Now, we can graph the ordered pairs on a coordinate plane.
We want to interpret the scatter plot from Part A. To do so, we can start by reviewing different patterns of associations that can be shown using scatter plots.
Notice that we can use the shape of the distribution of a scatter plot to determine the type of the association. Let's now look at the scatter plot from Part A!
We can see that the points lie close to a line. As the time increases, the number of unit produced also increases. This means that the slope of the line is positive. Therefore, the scatter plot shows a positive linear association. Next, let's recall some important definitions.
Outlier
Cluster
An outlier is a data point that is set off from the other data points.
A cluster is a group of points that lie close together.
With these definitions in mind, we can finally make some conclusions about the outliers and clusters in our graph.
There are no outliers
There are no clusters.
Note that clusters and outliers are found by observing a graph. Therefore, they are subjective and a different observer can interpret the graph differently. Our solution is just an example solution.
We want to make a conjecture about the number of units produced in 50 hours. To do so, we can follow the pattern until the x-value on the scatter plot from Part A is equal to 50. Let's do it!
We can see on the diagram that in 50 hours we can produce around 70 units. Notice that this is only our expectation based on the given data, and the real value could be different.
