Common Core: High School - Statistics and Probability : Fit a Function to the Data: CCSS.Math.Content.HSS-ID.B.6a

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Example Question #1 : Fit A Function To The Data: Ccss.Math.Content.Hss Id.B.6a

Researchers study a group of thirty males. They collect data on their weight and the length of time it takes them to run one mile. The data was recorded in the following table:

Screen shot 2015 12 17 at 1.19.40 pm

Afterwards, the researchers plotted the point on a scatter plot and fit a trend line with an equation to the data.

Runners

Based on this data, estimate how long it will take a male that weighs 185 pounds to run a mile.

Possible Answers:

Correct answer:

Explanation:

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations. 

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x or y variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

Runners

First, let’s observe if we can make a prediction using the following data:

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 185 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 185 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Visualtrendline

From this information, we can make the prediction that a male of this weight should be able to run a mile in just under ten minutes.

Now, lets predict this value quantitatively using the equation of the line:

Plug in 185 for the x-coordinate.

Solve.

Round to two decimal places.

According to the data, we can predict that it would take a male 9.71 minutes for a 185 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

Example Question #2 : Fit A Function To The Data: Ccss.Math.Content.Hss Id.B.6a

Researchers study a group of thirty males. They collect data on their weight and the length of time it takes them to run one mile. The data was recorded in the following table:

Screen shot 2015 12 17 at 1.19.40 pm

Afterwards, the researchers plotted the data on a scatter plot and fit a trend line with an equation for the data.

Runners

Based on this data, estimate how long it will take a male that weighs 185 pounds to run a mile?

Possible Answers:

Correct answer:

Explanation:

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations. 

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

Runners

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 185 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 185 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Visualtrendline

From this information, we can make the prediction that a male of this weight should be able to run a mile in just under ten minutes.

Now, lets predict this value quantitatively using the equation of the line:

Plug in 185 for the x-coordinate.

Solve.

Round to two decimal places.

According to the data, we can predict that it would take a male 9.71 minutes for a 185 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

Example Question #2 : Fit A Function To The Data: Ccss.Math.Content.Hss Id.B.6a

Researchers study a group of thirty males. They collect data on their weight and the length of time it takes them to run one mile. The data was recorded in the following table:

Screen shot 2015 12 17 at 1.19.40 pm

Afterwards, the researchers plotted the data on a scatter plot and fit a trend line with an equation for the data.

Runners

Based on this data, estimate how long it will take a male that weighs 185 pounds to run a mile?

Possible Answers:

Correct answer:

Explanation:

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations. 

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

Runners

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 185 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 185 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Visualtrendline

From this information, we can make the prediction that a male of this weight should be able to run a mile in just under ten minutes.

Now, lets predict this value quantitatively using the equation of the line:

Plug in 185 for the x-coordinate.

Solve.

Round to two decimal places.

According to the data, we can predict that it would take a male 9.71 minutes for a 185 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

Example Question #3 : Fit A Function To The Data: Ccss.Math.Content.Hss Id.B.6a

Researchers study a group of thirty males. They collect data on their weight and the length of time it takes them to run one mile. The data was recorded in the following table:

 

 

Afterwards, the researchers plotted the data on a scatter plot and fit a trend line with an equation for the data.

Plot3.1

If the best fit line is  estimate how long it will take a male that weighs  pounds to run a mile?

Possible Answers:

Correct answer:

Explanation:

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations.

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

Plot3.1

 

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 125 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 125 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Plot3.2

Now, lets predict this value quantitatively using the equation of the line:

Plug in 125 for the x-coordinate.

Solve

Round to two decimal places.

According to the data, we can predict that it would take a male 9.94 minutes for a 125 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

 

Example Question #4 : Fit A Function To The Data: Ccss.Math.Content.Hss Id.B.6a

Researchers study a group of thirty males. They collect data on their weight and the length of time it takes them to run one mile. The data was recorded in the following table:

 

 

Afterwards, the researchers plotted the data on a scatter plot and fit a trend line with an equation for the data.

Plot4.1

If the best fit line is  estimate how long it will take a male that weighs  pounds to run a mile?

Possible Answers:

Correct answer:

Explanation:

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations.

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

Plot4.1 

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 205 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 205 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Plot4.2

Now, lets predict this value quantitatively using the equation of the line:

Plug in 205 for the x-coordinate.

Solve

Round to two decimal places.

According to the data, we can predict that it would take a male 8.61 minutes for a 205 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

Example Question #5 : Fit A Function To The Data: Ccss.Math.Content.Hss Id.B.6a

Researchers study a group of thirty males. They collect data on their weight and the length of time it takes them to run one mile. The data was recorded in the following table:

 

 

Afterwards, the researchers plotted the data on a scatter plot and fit a trend line with an equation for the data.

Plot2.1

If the best fit line is  estimate how long it will take a male that weighs  pounds to run a mile?

Possible Answers:

Correct answer:

Explanation:

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations.

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

Plot2.1

 

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 188 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 188 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Plot2.2

Now, lets predict this value quantitatively using the equation of the line:

Plug in 188 for the x-coordinate.

Solve

Round to two decimal places.

According to the data, we can predict that it would take a male 8.79 minutes for a 188 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

 

Example Question #6 : Fit A Function To The Data: Ccss.Math.Content.Hss Id.B.6a

Researchers study a group of thirty males. They collect data on their weight and the length of time it takes them to run one mile. The data was recorded in the following table:

 

Afterwards, the researchers plotted the data on a scatter plot and fit a trend line with an equation for the data.

Plot5.1

If the best fit line is  estimate how long it will take a male that weighs  pounds to run a mile?

Possible Answers:

Correct answer:

Explanation:

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations.

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

Plot5.1

 

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 197 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 197 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Plot5.2

Now, lets predict this value quantitatively using the equation of the line:

Plug in 197 for the x-coordinate.

Solve

Round to two decimal places.

According to the data, we can predict that it would take a male 8.77 minutes for a 197 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

 

Example Question #7 : Fit A Function To The Data: Ccss.Math.Content.Hss Id.B.6a

Researchers study a group of thirty males. They collect data on their weight and the length of time it takes them to run one mile. The data was recorded in the following table:

 

Afterwards, the researchers plotted the data on a scatter plot and fit a trend line with an equation for the data.

Plot6.1

If the best fit line is  estimate how long it will take a male that weighs 239 pounds to run a mile?

Possible Answers:

Correct answer:

Explanation:


When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations.

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

Plot6.1

 

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 239 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 239 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Plot6.2

Now, lets predict this value quantitatively using the equation of the line:

Plug in 239 for the x-coordinate.

Solve

Round to two decimal places.

According to the data, we can predict that it would take a male 10.64 minutes for a 239 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

 

Example Question #8 : Fit A Function To The Data: Ccss.Math.Content.Hss Id.B.6a

Researchers study a group of thirty males. They collect data on their weight and the length of time it takes them to run one mile. The data was recorded in the following table:

 

Afterwards, the researchers plotted the data on a scatter plot and fit a trend line with an equation for the data.

Plot7.1

If the best fit line is  estimate how long it will take a male that weighs 155 pounds to run a mile?

Possible Answers:

Correct answer:

Explanation:

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations.

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

Plot7.1

 

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 155 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 155 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Plot7.2

Now, lets predict this value quantitatively using the equation of the line:

Plug in 155 for the x-coordinate.

Solve

Round to two decimal places.

According to the data, we can predict that it would take a male 9.37 minutes for a 155 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

Example Question #9 : Fit A Function To The Data: Ccss.Math.Content.Hss Id.B.6a

Researchers study a group of thirty males. They collect data on their weight and the length of time it takes them to run one mile. The data was recorded in the following table: 

 

Afterwards, the researchers plotted the data on a scatter plot and fit a trend line with an equation for the data.

Plot8.1

If the best fit line is  estimate how long it will take a male that weighs  pounds to run a mile?

Possible Answers:

Correct answer:

Explanation:

When data are presented using a scatter plot that is fitted with a trend line, we can calculate estimations based on the association between variables. Several conditions must be met before one can use a scatter plot to make estimates off of correlations.

First, the points must possess some type of relationship between one another. This relationship can be positive or negative. Positive relationships occur when data move upwards from the left side to the right side of the graph; however, when the data slopes downward the relationship is negative. Second, we must identify if the relationship is strong or weak. A strong correlation exists when the data is clustered closer together and the trend line. On the other hand, a weak correlation occurs when data is spread apart from each other and the trend line. After we have evaluated these characteristics of the graph, we can use the scatter plot to make predictions.

How do we make predictions? Predictions are made using several methods: qualitative and quantitative observations. One can qualitatively use the associations present in the graph to make estimates based on spread, clustering, and the trend line’s position. Spread between points in a given area can provide a range of values for a given coordinate, while clustering of plots in a given area can give an average value for a given coordinate. On the other hand, the trend line can be used to estimate points by drawing lines that intersect from each axis. Last, we can quantitatively estimate a point using the equation of the trend line and solving for either the x- or y-variable.

Let’s work with these methods and solve the question.

First let’s observe if we can make a prediction using the following data:

Plot8.1

 

We can see that the data possesses a positive correlation: that is, as the runner’s weight increases then so does the time it takes them to run a mile. Also, we can see that the points are weakly to moderately clustered with one another and the trend line; therefore, we can use qualitative and quantitative means to estimate how fast a 141 pound male can run a mile.

Next, let’s make a qualitative estimate by drawing a line from 141 pounds on the x-axis to the trend line. Next, we will draw a line from that point to the y-axis. This will qualitatively estimate our value. Observe this method below:

Plot8.2

Now, lets predict this value quantitatively using the equation of the line:

Plug in 141 for the x-coordinate.

Solve

Round to two decimal places.

According to the data, we can predict that it would take a male 8.62 minutes for a 141 pound male to run a single mile.

Remember, we can also use this method to estimate the y-value of the data.

 

 

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