Describing Patterns in Scatter Plots
Basics on the topic Describing Patterns in Scatter Plots
Title: Scatter Plot
Scatter Plot Introduction
A scatter plot is a type of graph that shows the relationship, or association, between two different sets of data, which we call bivariate data. By looking at a scatter plot, we can see patterns such as how the data points cluster, if there are any unusual points (outliers), and whether the relationship is positive, negative, linear, or nonlinear.
Understanding Scatter Plot
A scatter plot helps us see if there's a link between two variables. For example, it can show if one thing increases, does the other thing tend to increase too? This is a positive association. Or if one decreases as the other increases, that's a negative association. When the points don't show any obvious pattern, we say there's no association. If the points make a straight line, that's a linear association. If they form a curve, it's a nonlinear association.
Scatter Plot Example
Example Problem:
Create a scatter plot for the following data that shows the number of hours students studied and their test scores:
| Hours Studied | Test Score |
|---|---|
| 1 | 50 |
| 2 | 60 |
| 3 | 65 |
| 4 | 70 |
| 5 | 80 |
Solution:
- Draw a graph with two axes: horizontal for hours studied and vertical for test scores.
- Mark each pair of values as a point on the graph.
- Observe the pattern that the points make.
Scatter Plot - Guided Practice
Scatter Plot - Your Turn!
Example Problem:
Plot the following data on a scatter plot:
| Hours Studied | Test Score |
|---|---|
| 1 | 80 |
| 2 | 78 |
| 3 | 75 |
| 4 | 70 |
| 5 | 65 |
Scatter Plot Summary
Scatter plots are a useful way to visualize the relationship between two variables. By plotting bivariate data and analyzing the pattern of points, we can determine if there is an association—whether it's positive, negative, linear, or nonlinear. Understanding scatter plots can help us make predictions and find trends in the data.
Transcript Describing Patterns in Scatter Plots
Kai is getting excited, but also nervous about his first keytar performance in front of hundreds of people. Let's rewind time first and learn more about, describing patterns in scatter plots to discover different relationships in the events leading up to the big day. To review, a 'scatter plot' is graph that displays the relationship between two sets of data. We can find patterns between the x and y values that define their relationship and make predictions. The relationship has a positive association, when both the x and y values increase. For example, the more time you spend exercising, the more calories you burn. The relationship has a negative association when the x value increases, and the y value decreases. For example as the temperature outside increases, hot chocolate sales decrease. No association means that the x and y values have no relationship. For example, age has no effect on the number of siblings you have. Some scatter plots have 'outliers', which is a point that does not fit the pattern. Clusters are data points that form a group. Let's get back to Kai's big keytar performance! Leading up to the big day, Kai practiced weekly. Each week, he recorded the hours he practiced as the x variable, and compared that to his weekly assessment score y. This scatter plot shows the relationship between the number of hours Kai practiced and the score on his weekly assessment. Let's describe any patterns we see in this scatter plot. This scatter plot has a positive association, you can see the points are trending upward, and as the x value increases, the y value also increases. There is also one outlier in this graph when Kai practiced for five hours, his score was less than twenty-five percent and this one does not fit the pattern. This scatter plot also happens to have a cluster of points. What has Kai learned from this pattern? The more he practices, the higher his assessment score will be. On the day of the performance, Kai along with the band, will ride a bus to the performance. The drive is over twenty miles, and this scatter plot shows the relationship between the miles driven and the amount of gas left. This scatter plot shows a negative association since the points show a downward pattern. There are no outliers or clusters. The relationship is that as the x value or miles driven increases, the y value or gallons of gas in the tank decreases. When the bus ran out of gas, they stopped at a gas station. During the stop, the band members took a survey and made a scatter plot showing the relationship between their ages x, and the number of snacks they packed y. Pause the video here and identify the pattern of ages to snacks. There is no association between the ages and snacks. Also, there are no outliers or clusters. This means that how old you are has no effect on how many snacks are packed for a bus ride. To summarize, a scatter plot displays a relationship between two data sets which we can then analyze. The relationships can either be positive, negative or have no association. We can also identify outliers and clusters in a scatter plot to help us learn more about the data. Oh! Shhhh, get ready, here comes Kai!
