# Common Core: High School - Statistics and Probability : Evaluate Reports Based on Data: CCSS.Math.Content.HSS-IC.B.6

## Example Questions

### Example Question #1 : Evaluate Reports Based On Data: Ccss.Math.Content.Hss Ic.B.6

A high school decides to use a standardized test to evaluate the general knowledge of all of its students. Each grade contains 100 students and every grade takes the same exam. The scores were evaluated and the following box plots for each grade were created:

Based on this report, we can infer which of the following regarding the junior class?

The test scores are symmetrical

None of these

The test scores are bottom skewed

The test scores are top skewed

The test scores are uniform

The test scores are bottom skewed

Explanation:

We know that the scientific method starts with an observation of a phenomenon. Next, hypotheses are developed and tested using simulations and experiments. Once data are collected they can be used to make conclusions through statistical analysis. In this question, we are asked to analyze the distribution of comparative box plots.

First, let's look at how box plots are used to analyze data.

Box plots are broken into five main parts that create four primary regions. Each region contains a quarter of the data in the plot. The plot is initially broken into two regions using the following values: the minimum value, the maximum value, and the median or average of the set. Next, the minimum and median values are divided by the median of the lower half of the data or the first/lower quartile. Likewise, the median and the maximum values are divided by the median of the upper half of the data set or third/upper quartile. If the box is bigger, then there is a greater variance or spread in the data. Also, if the whiskers are very long, then the data possesses outliers.

Next, let's observe how data are distributed in box plots.

A uniform distribution indicates that all values are the same. A symmetrical distribution means that each box in the plot encompasses the same area; furthermore, each whisker (i.e. the line between Q3 and the Maximum as well as the line between Q1 and the Minimum) are the same length. This means that the data is evenly distributed and follows a normal or bell curve distribution. Box plots can also be skewed: either top or bottom skewed. When a plot is bottom or negatively skewed, the distance from the median to the minimum is greater than the distance from the median to the maximum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the bottom covers more area than the one closer to the top of the chart. In other words the data is being pulled to the negative end of the chart by outlying data points, while the positive points are clustered closer together at the top of the chart. On the other hand, a plot is top or positively skewed when the distance from the median to the maximum is greater than the distance from the median to the minimum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the top covers more area than the one closer to the bottom of the chart. In other words the data is being pulled to the positive end of the chart by outlying data points, while the negative points are clustered closer together at the bottom of the chart.

When data is analyzed in a box plot or chart, it can then be used to make conclusions on the experiment. These conclusions will either support or refute a hypothesis. It is important to note that hypothesis cannot be proven only support can be added for them or against them. Even scientific theories such as gravity are not proven: they are just supported by a wealth of experiments and knowledge.

Now, let's answer the question. When we look at the box plot for the juniors we can see that the distance from the median to the minimum is greater than the distance from the median to the maximum: therefore, the plot is bottom or negatively skewed.

### Example Question #2 : Evaluate Reports Based On Data: Ccss.Math.Content.Hss Ic.B.6

A high school decides to use a standardized test to evaluate the general knowledge of all of its students. Each grade contains 100 students and every grade takes the same exam. The scores were evaluated and the following box plots for each grade were created:

Based on this report we can infer which of the following regarding the junior class?

The test scores are bottom skewed

The test scores are symmetrical

The test scores are uniform

The test scores are top skewed

None of these

The test scores are bottom skewed

Explanation:

We know that the scientific method starts with the observation of a phenomenon. Next, hypotheses are developed and tested using simulations and experiments. Once data are collected they can be used to make conclusions through statistical analysis. In this question, we are asked to analyze the distribution of comparative box plots.

First, let's look at how box plots are used to analyze data.

Box plots are broken into five main parts that create four primary region. Each region contains a quarter of the data in the plot. The plot is broken into three initial regions: the minimum value, the maximum value, and the median or average of the set. Next the minimum and median are divided by the median of the lower half of the data or the first/lower quartile. Likewise the median and the maximum are divided by the median of the upper half of the data set or third/upper quartile. If the box is bigger, then there is a greater variance or spread in the data. Also, if the whiskers are very long, then the data possesses outliers.

Next, let's observe how data are distributed in box plots.

A uniform distribution indicates that all values are the same. A symmetrical distribution means that each box in the plot encompasses the same area; furthermore, each whisker (i.e. the line between Q3 and the Maximum as well as the line between Q1 and the Minimum) are the same length. This means that the data is evenly distributed and follows a normal or bell curve distribution. Box plots can also be skewed: either top or bottom skewed. When a plot is bottom or negatively skewed, the distance from the median to the minimum is greater than the distance from the median to the maximum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the bottom covers more area than the one closer to the top of the chart. In other words the data is being pulled to the negative end of the chart by outlying data points, while the positive points are clustered closer together at the top of the chart. On the other hand, a plot is top or positively skewed when the distance from the median to the maximum is greater than the distance from the median to the minimum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the top covers more area than the one closer to the bottom of the chart. In other words the data is being pulled to the positive end of the chart by outlying data points, while the negative points are clustered closer together at the bottom of the chart.

When data is analyzed in a box plot or chart, it can then be used to make conclusions on the experiment. These conclusions will either support or refute a hypothesis. It is important to note that hypothesis cannot be proven only support can be added for them or against them. Even scientific theories such as gravity are not proven: they are just supported by a wealth of experiments and knowledge.

Now, let's answer the question. When we look at the box plot for the juniors we can see that the distance from the median to the minimum is greater than the distance from the median to the maximum: therefore, the plot is bottom or negatively skewed.

### Example Question #31 : Making Inferences & Justifying Conclusions

A high school decides to use a standardized test to evaluate the general knowledge of all of its students. Each grade contains 100 students and every grade takes the same exam. The scores were evaluated and the following box plots for each grade were created:

Based on this report, we can infer which of the following regarding the sophomore class?

The test scores are uniform

The test scores are bottom skewed

The test scores are symmetrical

The test scores are top skewed

None of these

The test scores are bottom skewed

Explanation:

We know that the scientific method starts with an observation of a phenomenon. Next, hypotheses are developed and tested using simulations and experiments. Once data are collected they can be used to make conclusions through statistical analysis. In this question, we are asked to analyze the distribution of comparative box plots.

First, let's look at how box plots are used to analyze data.

Box plots are broken into five main parts that create four primary regions. Each region contains a quarter of the data in the plot. The plot is initially broken into two regions using the following values: the minimum value, the maximum value, and the median or average of the set. Next, the minimum and median values are divided by the median of the lower half of the data or the first/lower quartile. Likewise, the median and the maximum values are divided by the median of the upper half of the data set or third/upper quartile. If the box is bigger, then there is a greater variance or spread in the data. Also, if the whiskers are very long, then the data possesses outliers.

Next, let's observe how data are distributed in box plots.

A uniform distribution indicates that all values are the same. A symmetrical distribution means that each box in the plot encompasses the same area; furthermore, each whisker (i.e. the line between Q3 and the Maximum as well as the line between Q1 and the Minimum) are the same length. This means that the data is evenly distributed and follows a normal or bell curve distribution. Box plots can also be skewed: either top or bottom skewed. When a plot is bottom or negatively skewed, the distance from the median to the minimum is greater than the distance from the median to the maximum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the bottom covers more area than the one closer to the top of the chart. In other words the data is being pulled to the negative end of the chart by outlying data points, while the positive points are clustered closer together at the top of the chart. On the other hand, a plot is top or positively skewed when the distance from the median to the maximum is greater than the distance from the median to the minimum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the top covers more area than the one closer to the bottom of the chart. In other words the data is being pulled to the positive end of the chart by outlying data points, while the negative points are clustered closer together at the bottom of the chart.

When data is analyzed in a box plot or chart, it can then be used to make conclusions on the experiment. These conclusions will either support or refute a hypothesis. It is important to note that hypothesis cannot be proven only support can be added for them or against them. Even scientific theories such as gravity are not proven: they are just supported by a wealth of experiments and knowledge.

Now, let's answer the question. When we look at the box plot for the sophomores we can see that the distance from the median to the minimum is greater than the distance from the median to the maximum: therefore, the plot is bottom or negatively skewed.

### Example Question #32 : Making Inferences & Justifying Conclusions

A high school decides to use a standardized test to evaluate the general knowledge of all of its students. Each grade contains 100 students and every grade takes the same exam. The scores were evaluated and the following box plots for each grade were created:

Based on this report, we can infer which of the following regarding the senior class?

The test scores are uniform

The test scores are bottom skewed

The test scores are symmetrical

The test scores are top skewed

None of these

The test scores are top skewed

Explanation:

We know that the scientific method starts with an observation of a phenomenon. Next, hypotheses are developed and tested using simulations and experiments. Once data are collected they can be used to make conclusions through statistical analysis. In this question, we are asked to analyze the distribution of comparative box plots.

First, let's look at how box plots are used to analyze data.

Box plots are broken into five main parts that create four primary regions. Each region contains a quarter of the data in the plot. The plot is initially broken into two regions using the following values: the minimum value, the maximum value, and the median or average of the set. Next, the minimum and median values are divided by the median of the lower half of the data or the first/lower quartile. Likewise, the median and the maximum values are divided by the median of the upper half of the data set or third/upper quartile. If the box is bigger, then there is a greater variance or spread in the data. Also, if the whiskers are very long, then the data possesses outliers.

Next, let's observe how data are distributed in box plots.

A uniform distribution indicates that all values are the same. A symmetrical distribution means that each box in the plot encompasses the same area; furthermore, each whisker (i.e. the line between Q3 and the Maximum as well as the line between Q1 and the Minimum) are the same length. This means that the data is evenly distributed and follows a normal or bell curve distribution. Box plots can also be skewed: either top or bottom skewed. When a plot is bottom or negatively skewed, the distance from the median to the minimum is greater than the distance from the median to the maximum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the bottom covers more area than the one closer to the top of the chart. In other words the data is being pulled to the negative end of the chart by outlying data points, while the positive points are clustered closer together at the top of the chart. On the other hand, a plot is top or positively skewed when the distance from the median to the maximum is greater than the distance from the median to the minimum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the top covers more area than the one closer to the bottom of the chart. In other words the data is being pulled to the positive end of the chart by outlying data points, while the negative points are clustered closer together at the bottom of the chart.

When data is analyzed in a box plot or chart, it can then be used to make conclusions on the experiment. These conclusions will either support or refute a hypothesis. It is important to note that hypothesis cannot be proven only support can be added for them or against them. Even scientific theories such as gravity are not proven: they are just supported by a wealth of experiments and knowledge.

Now, let's answer the question. When we look at the box plot for the seniors we can see that the distance from the median to the minimum is less than the distance from the median to the maximum: therefore, the plot is top or positively skewed.

### Example Question #33 : Making Inferences & Justifying Conclusions

A high school decides to use a standardized test to evaluate the general knowledge of all of its students. Each grade contains 100 students and every grade takes the same exam. The scores were evaluated and the following box plots for each grade were created:

Based on this report, we can infer which of the following regarding the sophomore class?

The test scores are uniform

The test scores are bottom skewed

None of these

The test scores are symmetrical

The test scores are top skewed

The test scores are top skewed

Explanation:

We know that the scientific method starts with an observation of a phenomenon. Next, hypotheses are developed and tested using simulations and experiments. Once data are collected they can be used to make conclusions through statistical analysis. In this question, we are asked to analyze the distribution of comparative box plots.

First, let's look at how box plots are used to analyze data.

Box plots are broken into five main parts that create four primary regions. Each region contains a quarter of the data in the plot. The plot is initially broken into two regions using the following values: the minimum value, the maximum value, and the median or average of the set. Next, the minimum and median values are divided by the median of the lower half of the data or the first/lower quartile. Likewise, the median and the maximum values are divided by the median of the upper half of the data set or third/upper quartile. If the box is bigger, then there is a greater variance or spread in the data. Also, if the whiskers are very long, then the data possesses outliers.

Next, let's observe how data are distributed in box plots.

A uniform distribution indicates that all values are the same. A symmetrical distribution means that each box in the plot encompasses the same area; furthermore, each whisker (i.e. the line between Q3 and the Maximum as well as the line between Q1 and the Minimum) are the same length. This means that the data is evenly distributed and follows a normal or bell curve distribution. Box plots can also be skewed: either top or bottom skewed. When a plot is bottom or negatively skewed, the distance from the median to the minimum is greater than the distance from the median to the maximum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the bottom covers more area than the one closer to the top of the chart. In other words the data is being pulled to the negative end of the chart by outlying data points, while the positive points are clustered closer together at the top of the chart. On the other hand, a plot is top or positively skewed when the distance from the median to the maximum is greater than the distance from the median to the minimum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the top covers more area than the one closer to the bottom of the chart. In other words the data is being pulled to the positive end of the chart by outlying data points, while the negative points are clustered closer together at the bottom of the chart.

When data is analyzed in a box plot or chart, it can then be used to make conclusions on the experiment. These conclusions will either support or refute a hypothesis. It is important to note that hypothesis cannot be proven only support can be added for them or against them. Even scientific theories such as gravity are not proven: they are just supported by a wealth of experiments and knowledge.

Now, let's answer the question. When we look at the box plot for the sophomores we can see that the distance from the median to the minimum is less than the distance from the median to the maximum: therefore, the plot is top or positively skewed.

### Example Question #34 : Making Inferences & Justifying Conclusions

A high school decides to use a standardized test to evaluate the general knowledge of all of its students. Each grade contains 100 students and every grade takes the same exam. The scores were evaluated and the following box plots for each grade were created:

Based on this report, we can infer which of the following regarding the junior class?

None of these

The test scores are symmetrical

The test scores are uniform

The test scores are top skewed

The test scores are bottom skewed

The test scores are bottom skewed

Explanation:

We know that the scientific method starts with an observation of a phenomenon. Next, hypotheses are developed and tested using simulations and experiments. Once data are collected they can be used to make conclusions through statistical analysis. In this question, we are asked to analyze the distribution of comparative box plots.

First, let's look at how box plots are used to analyze data.

Box plots are broken into five main parts that create four primary regions. Each region contains a quarter of the data in the plot. The plot is initially broken into two regions using the following values: the minimum value, the maximum value, and the median or average of the set. Next, the minimum and median values are divided by the median of the lower half of the data or the first/lower quartile. Likewise, the median and the maximum values are divided by the median of the upper half of the data set or third/upper quartile. If the box is bigger, then there is a greater variance or spread in the data. Also, if the whiskers are very long, then the data possesses outliers.

Next, let's observe how data are distributed in box plots.

A uniform distribution indicates that all values are the same. A symmetrical distribution means that each box in the plot encompasses the same area; furthermore, each whisker (i.e. the line between Q3 and the Maximum as well as the line between Q1 and the Minimum) are the same length. This means that the data is evenly distributed and follows a normal or bell curve distribution. Box plots can also be skewed: either top or bottom skewed. When a plot is bottom or negatively skewed, the distance from the median to the minimum is greater than the distance from the median to the maximum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the bottom covers more area than the one closer to the top of the chart. In other words the data is being pulled to the negative end of the chart by outlying data points, while the positive points are clustered closer together at the top of the chart. On the other hand, a plot is top or positively skewed when the distance from the median to the maximum is greater than the distance from the median to the minimum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the top covers more area than the one closer to the bottom of the chart. In other words the data is being pulled to the positive end of the chart by outlying data points, while the negative points are clustered closer together at the bottom of the chart.

When data is analyzed in a box plot or chart, it can then be used to make conclusions on the experiment. These conclusions will either support or refute a hypothesis. It is important to note that hypothesis cannot be proven only support can be added for them or against them. Even scientific theories such as gravity are not proven: they are just supported by a wealth of experiments and knowledge.

Now, let's answer the question. When we look at the box plot for the juniors we can see that the distance from the median to the minimum is greater than the distance from the median to the maximum: therefore, the plot is bottom or negatively skewed.

### Example Question #35 : Making Inferences & Justifying Conclusions

A high school decides to use a standardized test to evaluate the general knowledge of all of its students. Each grade contains 100 students and every grade takes the same exam. The scores were evaluated and the following box plots for each grade were created:

Based on this report, we can infer which of the following regarding the junior class?

The test scores are bottom skewed

The test scores are top skewed

The test scores are symmetrical

None of these

The test scores are uniform

The test scores are top skewed

Explanation:

We know that the scientific method starts with an observation of a phenomenon. Next, hypotheses are developed and tested using simulations and experiments. Once data are collected they can be used to make conclusions through statistical analysis. In this question, we are asked to analyze the distribution of comparative box plots.

First, let's look at how box plots are used to analyze data.

Box plots are broken into five main parts that create four primary regions. Each region contains a quarter of the data in the plot. The plot is initially broken into two regions using the following values: the minimum value, the maximum value, and the median or average of the set. Next, the minimum and median values are divided by the median of the lower half of the data or the first/lower quartile. Likewise, the median and the maximum values are divided by the median of the upper half of the data set or third/upper quartile. If the box is bigger, then there is a greater variance or spread in the data. Also, if the whiskers are very long, then the data possesses outliers.

Next, let's observe how data are distributed in box plots.

A uniform distribution indicates that all values are the same. A symmetrical distribution means that each box in the plot encompasses the same area; furthermore, each whisker (i.e. the line between Q3 and the Maximum as well as the line between Q1 and the Minimum) are the same length. This means that the data is evenly distributed and follows a normal or bell curve distribution. Box plots can also be skewed: either top or bottom skewed. When a plot is bottom or negatively skewed, the distance from the median to the minimum is greater than the distance from the median to the maximum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the bottom covers more area than the one closer to the top of the chart. In other words the data is being pulled to the negative end of the chart by outlying data points, while the positive points are clustered closer together at the top of the chart. On the other hand, a plot is top or positively skewed when the distance from the median to the maximum is greater than the distance from the median to the minimum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the top covers more area than the one closer to the bottom of the chart. In other words the data is being pulled to the positive end of the chart by outlying data points, while the negative points are clustered closer together at the bottom of the chart.

When data is analyzed in a box plot or chart, it can then be used to make conclusions on the experiment. These conclusions will either support or refute a hypothesis. It is important to note that hypothesis cannot be proven only support can be added for them or against them. Even scientific theories such as gravity are not proven: they are just supported by a wealth of experiments and knowledge.

Now, let's answer the question. When we look at the box plot for the juniors we can see that the distance from the median to the minimum is less than the distance from the median to the maximum: therefore, the plot is top or positively skewed.

### Example Question #36 : Making Inferences & Justifying Conclusions

A high school decides to use a standardized test to evaluate the general knowledge of all of its students. Each grade contains 100 students and every grade takes the same exam. The scores were evaluated and the following box plots for each grade were created:

Based on this report, we can infer which of the following regarding the senior class?

The test scores are uniform

None of these

The test scores are bottom skewed

The test scores are symmetrical

The test scores are top skewed

The test scores are top skewed

Explanation:

We know that the scientific method starts with an observation of a phenomenon. Next, hypotheses are developed and tested using simulations and experiments. Once data are collected they can be used to make conclusions through statistical analysis. In this question, we are asked to analyze the distribution of comparative box plots.

First, let's look at how box plots are used to analyze data.

Box plots are broken into five main parts that create four primary regions. Each region contains a quarter of the data in the plot. The plot is initially broken into two regions using the following values: the minimum value, the maximum value, and the median or average of the set. Next, the minimum and median values are divided by the median of the lower half of the data or the first/lower quartile. Likewise, the median and the maximum values are divided by the median of the upper half of the data set or third/upper quartile. If the box is bigger, then there is a greater variance or spread in the data. Also, if the whiskers are very long, then the data possesses outliers.

Next, let's observe how data are distributed in box plots.

A uniform distribution indicates that all values are the same. A symmetrical distribution means that each box in the plot encompasses the same area; furthermore, each whisker (i.e. the line between Q3 and the Maximum as well as the line between Q1 and the Minimum) are the same length. This means that the data is evenly distributed and follows a normal or bell curve distribution. Box plots can also be skewed: either top or bottom skewed. When a plot is bottom or negatively skewed, the distance from the median to the minimum is greater than the distance from the median to the maximum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the bottom covers more area than the one closer to the top of the chart. In other words the data is being pulled to the negative end of the chart by outlying data points, while the positive points are clustered closer together at the top of the chart. On the other hand, a plot is top or positively skewed when the distance from the median to the maximum is greater than the distance from the median to the minimum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the top covers more area than the one closer to the bottom of the chart. In other words the data is being pulled to the positive end of the chart by outlying data points, while the negative points are clustered closer together at the bottom of the chart.

When data is analyzed in a box plot or chart, it can then be used to make conclusions on the experiment. These conclusions will either support or refute a hypothesis. It is important to note that hypothesis cannot be proven only support can be added for them or against them. Even scientific theories such as gravity are not proven: they are just supported by a wealth of experiments and knowledge.

Now, let's answer the question. When we look at the box plot for the seniors we can see that the distance from the median to the minimum is less than the distance from the median to the maximum: therefore, the plot is top or positively skewed.

### Example Question #37 : Making Inferences & Justifying Conclusions

A high school decides to use a standardized test to evaluate the general knowledge of all of its students. Each grade contains 100 students and every grade takes the same exam. The scores were evaluated and the following box plots for each grade were created:

Based on this report, we can infer which of the following regarding the sophomore class?

The test scores are symmetrical

The test scores are uniform

None of these

The test scores are bottom skewed

The test scores are top skewed

The test scores are bottom skewed

Explanation:

We know that the scientific method starts with an observation of a phenomenon. Next, hypotheses are developed and tested using simulations and experiments. Once data are collected they can be used to make conclusions through statistical analysis. In this question, we are asked to analyze the distribution of comparative box plots.

First, let's look at how box plots are used to analyze data.

Box plots are broken into five main parts that create four primary regions. Each region contains a quarter of the data in the plot. The plot is initially broken into two regions using the following values: the minimum value, the maximum value, and the median or average of the set. Next, the minimum and median values are divided by the median of the lower half of the data or the first/lower quartile. Likewise, the median and the maximum values are divided by the median of the upper half of the data set or third/upper quartile. If the box is bigger, then there is a greater variance or spread in the data. Also, if the whiskers are very long, then the data possesses outliers.

Next, let's observe how data are distributed in box plots.

A uniform distribution indicates that all values are the same. A symmetrical distribution means that each box in the plot encompasses the same area; furthermore, each whisker (i.e. the line between Q3 and the Maximum as well as the line between Q1 and the Minimum) are the same length. This means that the data is evenly distributed and follows a normal or bell curve distribution. Box plots can also be skewed: either top or bottom skewed. When a plot is bottom or negatively skewed, the distance from the median to the minimum is greater than the distance from the median to the maximum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the bottom covers more area than the one closer to the top of the chart. In other words the data is being pulled to the negative end of the chart by outlying data points, while the positive points are clustered closer together at the top of the chart. On the other hand, a plot is top or positively skewed when the distance from the median to the maximum is greater than the distance from the median to the minimum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the top covers more area than the one closer to the bottom of the chart. In other words the data is being pulled to the positive end of the chart by outlying data points, while the negative points are clustered closer together at the bottom of the chart.

When data is analyzed in a box plot or chart, it can then be used to make conclusions on the experiment. These conclusions will either support or refute a hypothesis. It is important to note that hypothesis cannot be proven only support can be added for them or against them. Even scientific theories such as gravity are not proven: they are just supported by a wealth of experiments and knowledge.

Now, let's answer the question. When we look at the box plot for the sophomores we can see that the distance from the median to the minimum is greater than the distance from the median to the maximum: therefore, the plot is bottom or negatively skewed.

### Example Question #38 : Making Inferences & Justifying Conclusions

A high school decides to use a standardized test to evaluate the general knowledge of all of its students. Each grade contains 100 students and every grade takes the same exam. The scores were evaluated and the following box plots for each grade were created:

Based on this report, we can infer which of the following regarding the junior class?

None of these

The test scores are top skewed

The test scores are bottom skewed

The test scores are uniform

The test scores are symmetrical

The test scores are top skewed

Explanation:

We know that the scientific method starts with an observation of a phenomenon. Next, hypotheses are developed and tested using simulations and experiments. Once data are collected they can be used to make conclusions through statistical analysis. In this question, we are asked to analyze the distribution of comparative box plots.

First, let's look at how box plots are used to analyze data.

Box plots are broken into five main parts that create four primary regions. Each region contains a quarter of the data in the plot. The plot is initially broken into two regions using the following values: the minimum value, the maximum value, and the median or average of the set. Next, the minimum and median values are divided by the median of the lower half of the data or the first/lower quartile. Likewise, the median and the maximum values are divided by the median of the upper half of the data set or third/upper quartile. If the box is bigger, then there is a greater variance or spread in the data. Also, if the whiskers are very long, then the data possesses outliers.

Next, let's observe how data are distributed in box plots.

A uniform distribution indicates that all values are the same. A symmetrical distribution means that each box in the plot encompasses the same area; furthermore, each whisker (i.e. the line between Q3 and the Maximum as well as the line between Q1 and the Minimum) are the same length. This means that the data is evenly distributed and follows a normal or bell curve distribution. Box plots can also be skewed: either top or bottom skewed. When a plot is bottom or negatively skewed, the distance from the median to the minimum is greater than the distance from the median to the maximum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the bottom covers more area than the one closer to the top of the chart. In other words the data is being pulled to the negative end of the chart by outlying data points, while the positive points are clustered closer together at the top of the chart. On the other hand, a plot is top or positively skewed when the distance from the median to the maximum is greater than the distance from the median to the minimum. Even though each box contains the same amount of the data (i.e. twenty-five percent), the box closer to the top covers more area than the one closer to the bottom of the chart. In other words the data is being pulled to the positive end of the chart by outlying data points, while the negative points are clustered closer together at the bottom of the chart.

When data is analyzed in a box plot or chart, it can then be used to make conclusions on the experiment. These conclusions will either support or refute a hypothesis. It is important to note that hypothesis cannot be proven only support can be added for them or against them. Even scientific theories such as gravity are not proven: they are just supported by a wealth of experiments and knowledge.

Now, let's answer the question. When we look at the box plot for the juniors we can see that the distance from the median to the minimum is less than the distance from the median to the maximum: therefore, the plot is top or positively skewed.