GRAPHING
A scatterplot is a type of graph where corresponding values from a set of data are placed as points on a coordinate plane. A relationship between the points is sometimes shown to be positive, negative, strong, or weak. Sometimes a scatterplot shows that there is no relationship at all. Aside from finding relationships, scatterplots are useful in predicting values based on the relationship that was revealed.
Take a look at this scatterplot to the left.
You can see that there is a relationship between the independent and dependent values of the chart. The relationship is moving up to the right and therefore is a positive correlation.
Let’s look at how you can examine these relationships.
What happens to people’s heating bills as the temperature outside goes up?
You might imagine that as the temperature outside goes up, people’s heating bills go down because they use their heaters less. As one variable goes up, the other goes down. This is a negative relationship or a negative correlation.
What happens to the gasoline consumption in a vehicle as the miles traveled goes up?
You might imagine that as the miles traveled in a car go up, the amount of gasoline consumed also goes up. So, as one variable goes up, the other goes up, too. This is a positive relationship or a positive correlation.
What happens to the number of accidents as the number of blue cars increases on the road?
You can imagine that there would be no relationship. While one variable goes up, the other may go up, down, or stay the same; the number of accidents is independent of the number of blue cars. This oftentimes occurs, too. This is an example of no relationship or no correlation.
These three trends, positive, negative, and no relationship are evident on scatterplots. This is what they look like:
Take a look at this scatterplot to the left.
You can see that there is a relationship between the independent and dependent values of the chart. The relationship is moving up to the right and therefore is a positive correlation.
Let’s look at how you can examine these relationships.
What happens to people’s heating bills as the temperature outside goes up?
You might imagine that as the temperature outside goes up, people’s heating bills go down because they use their heaters less. As one variable goes up, the other goes down. This is a negative relationship or a negative correlation.
What happens to the gasoline consumption in a vehicle as the miles traveled goes up?
You might imagine that as the miles traveled in a car go up, the amount of gasoline consumed also goes up. So, as one variable goes up, the other goes up, too. This is a positive relationship or a positive correlation.
What happens to the number of accidents as the number of blue cars increases on the road?
You can imagine that there would be no relationship. While one variable goes up, the other may go up, down, or stay the same; the number of accidents is independent of the number of blue cars. This oftentimes occurs, too. This is an example of no relationship or no correlation.
These three trends, positive, negative, and no relationship are evident on scatterplots. This is what they look like:
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POSITIVE RELATIONSHIP
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NEGATIVE RELATIONSHIP
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NO RELATIONSHIP
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This is a positive relationship. As the x-values increase, the y-values increase. Some points may not follow an exact pattern but the overall trend, the general tendency or movement, is clearly from the lower left to the upper right of the plot.
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This is a negative relationship. In this case, as the x-values increase, the y-values decrease. You may argue that the slope is not as steep which is true. However, the general tendency is evident. This graph moves from the upper left to the lower right.
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At times, like the one shown above, there is no relationship between variables. The scatterplots of these situations will show no trend. In other words, there seems to be no definite pattern with the points; you cannot see any particular direction that they take.
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Scatterplots are as useful for finding a relationship between variables as they are for making predictions. Here, you will make a trend line, or a line that best describes the data on a scatterplot, in order to estimate unknown outputs for given inputs.
A trend line is a straight line that best represents the points on a scatterplot. The trend line may go through some points but need not go through them all. The trend line is used to show the pattern of the data. This trend line may show a positive trend or a negative trend. However, if there is no relationship, then no trend line can be adequately drawn.
Your trend line is your best approximation of the pattern of the data.
A trend line is a straight line that best represents the points on a scatterplot. The trend line may go through some points but need not go through them all. The trend line is used to show the pattern of the data. This trend line may show a positive trend or a negative trend. However, if there is no relationship, then no trend line can be adequately drawn.
Your trend line is your best approximation of the pattern of the data.
This text was adapted from CK12.com. It is licensed under the Creative Commons (CC BY-NC 3.0)
Bar chart vs. Scatterplot |
The line on this graph is the trend line; it is the line that best describes the data. About half of the points should be on either side of the line. You may notice that outliers are practically ignored when a trend line is drawn. This trend line goes from the lower left to the upper right and shows a positive relationship.
You can also see that the trend line also goes off of the chart as it is an arrow and thus continues in the same direction. Therefore, you could use a chart like this one to predict the trend. It is likely that the trend will continue to go up. |
So far the examples we have seen are all scatterplot graphs. But sometimes a scatterplot graph isn't as useful as a bar graph. There are specific times when you should use a scatterplot and times when you should use a bar graph. The difference depends on the type of data you are graphing.
Scatterplots are used to graph continuous data. Continuous data is when there is a range in data points that are possible. Because there is a range in values there are no district categories. Normally scatterplot data has numbers. For example, temperature is a good example of something that has a range of data possible. It is possible to have a temperature of 30 degrees or a temperature of 31 degrees. It is also possible to have a temperature of 30.6 degrees. If you could measure in more precise detail then your data is probably continuous. Height is another example of continuous data. What can be confusing is that sometimes continuous data isn't a number. For example, hair color is not related to a number. However, you could have blonde hair or brunette hair, or any shade of hair in-between. As there are shades in-between you would graph hair color on a scatterplot.
On the other hand, bar graphs are normally used when you have discontinuous data. Discontinuous data has distinct values/categories and there are no in-between values. Discontinuous data tends to be qualitative, or not having a number. For example, sex is discontinuous, you are either a boy or a girl. If you were graphing the number of slices of pizza eaten for boys vs. girls you would use a bar graph. However, sometimes discontinuous data can be numbers. For example, you could be looking at the shoe size vs. the number of shoes sold. In this case you would use a bar chart because even though shoe size comes in numbers (7, 8, 9.5) you can't have an in-between size. It isn't possible to buy a shoe size 7.8. On the other hand, foot length is continuous and would be graphed on a scatterplot because you foot could be 7.6 inches or 7.7 inches, etc.
Here are some other examples of data and if it is continuous or discontinuous.
Scatterplots are used to graph continuous data. Continuous data is when there is a range in data points that are possible. Because there is a range in values there are no district categories. Normally scatterplot data has numbers. For example, temperature is a good example of something that has a range of data possible. It is possible to have a temperature of 30 degrees or a temperature of 31 degrees. It is also possible to have a temperature of 30.6 degrees. If you could measure in more precise detail then your data is probably continuous. Height is another example of continuous data. What can be confusing is that sometimes continuous data isn't a number. For example, hair color is not related to a number. However, you could have blonde hair or brunette hair, or any shade of hair in-between. As there are shades in-between you would graph hair color on a scatterplot.
On the other hand, bar graphs are normally used when you have discontinuous data. Discontinuous data has distinct values/categories and there are no in-between values. Discontinuous data tends to be qualitative, or not having a number. For example, sex is discontinuous, you are either a boy or a girl. If you were graphing the number of slices of pizza eaten for boys vs. girls you would use a bar graph. However, sometimes discontinuous data can be numbers. For example, you could be looking at the shoe size vs. the number of shoes sold. In this case you would use a bar chart because even though shoe size comes in numbers (7, 8, 9.5) you can't have an in-between size. It isn't possible to buy a shoe size 7.8. On the other hand, foot length is continuous and would be graphed on a scatterplot because you foot could be 7.6 inches or 7.7 inches, etc.
Here are some other examples of data and if it is continuous or discontinuous.
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Continuous data:
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Discontinuous Data:
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