There are several common measures of center and spread for a given data set. The most common measures of center are the mean and median. The mean represents the arithmetic average of a set and the median is the middlemost value. On the other hand, the most common measures of spread are the mean absolute deviation (MAD) and inter-quartile range (IQR).

The measures of center and spread vary for different sets of data. The mean and MAD are used together to analyze data presented in bar charts or histograms while the median and IQR are most commonly used for box and whisker plots
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Let's look at our data. We have the following pounds of brass for the five-month period starting in January:

First, let's plot this data on a bar graph.

Now, let's use the mean and MAD to calculate the center and spread of the data respectively.

The center should be calculated using the mean. The mean is the arithmetic average and is found by adding all of the values together and dividing by the number of values in the series.

Now, let's find the spread of the data using the MAD. The MAD describes how data varies about the mean. The MAD is calculated by finding out how much each data points deviates from the mean and dividing by the total number of values in the series.

First, let's find out how much each value varies from the mean by taking the absolute value of the mean minus each individual value.

Now, we need to add up these values and divide that total by the number of values in the series.

The MAD is the value that each individual number in the set deviates from the mean; therefore, it represents the spread of the series.

The correct answer for this problem is the following:

In order to solve this problem we need to make an inference. An inference is made using observations in prior knowledge. If we have multiple observations, then we can make better inferences. Let's develop our inference using the information provided for Joe and Melissa.

Joe obtained the following scores:

Let's tabulate this data into a histogram.

Let's find the mean of this data series. The mean is the arithmetic average of the data set. The mean is found by adding up the values and dividing the total by the number of values in the series.

Now let's calculate the standard deviation of the data series. The standard deviation for an entire population is found using the following formula:

First, we need to calculate how much each value deviates from the mean. We will do this by subtracting the mean from each value and squaring the difference.

Second, we will find the variance by adding up this values and dividing by the number of values in the series.

Last, the standard deviation equals the square root of the variance.

Now, we need to focus on Melissa's scores:

Let's tabulate this data into a histogram.

Let's find the mean of this data series. The mean is the arithmetic average of the data set. The mean is found by adding up the values and dividing the total by the number of values in the series.

Now let's calculate the standard deviation of the data series. The standard deviation for an entire population is found using the following formula:

First, we need to calculate how much each value deviates from the mean. We will do this by subtracting the mean from each value and squaring the difference.

Second, we will find the variance by adding up this values and dividing by the number of values in the series.

Last, the standard deviation equals the square root of the variance.

Now, let's review our data and calculations.

Given the information, we can see that Melissa's scores have a higher mean value and a smaller standard deviation for the set of values. This means that her scores are, on average, higher than Joe's and the vary less; therefore, we can predict that she will score higher on the test. Some may argue that Joe will score higher because of his on very high grade. It is true that he has the highest single grade between the two students; however, this is an outlier in the data. His lower mean score and higher tendency to vary between tests indicates that he will most likely not score higher than Melissa.

In order to solve this problem, we need to make an inference. An inference is made using observations in prior knowledge. If we have multiple observations, then we can make better inferences. Let's develop our inference using the information provided for Joe and Melissa.

Joe obtained the following scores:

Let's tabulate this data into a histogram.

Let's find the mean of this data series. The mean is the arithmetic average of the data set. The mean is found by adding up the values and dividing the total by the number of values in the series.

Now, let's calculate the standard deviation of the data series. The standard deviation for an entire population is found using the following formula:

First, we need to calculate how much each value deviates from the mean. We will do this by subtracting the mean from each value and squaring the difference.

Second, we will find the variance by adding up this values and dividing by the number of values in the series.

Last, the standard deviation equals the square root of the variance.

Now, we need to focus on Melissa's scores:

Let's tabulate this data into a histogram.

Let's find the mean of this data series. The mean is the arithmetic average of the data set. The mean is found by adding up the values and dividing the total by the number of values in the series.

Now, let's calculate the standard deviation of the data series. The standard deviation for an entire population is found using the following formula:

First, we need to calculate how much each value deviates from the mean. We will do this by subtracting the mean from each value and squaring the difference.

Second, we will find the variance by adding up this values and dividing by the number of values in the series.

Last, the standard deviation equals the square root of the variance.

Now, let's review our data and calculations.

Given the information, we can see that Melissa's scores have a higher mean value and a smaller standard deviation for the set of values. This means that her scores are—on average—higher than Joe's and they vary less; therefore, we can predict that she will score higher on the test. Some may argue that Joe will score higher because of his one very high grade. It is true that he has the highest single grade between the two students; however, this is an outlier in the data. His lower mean score and higher tendency to vary between tests indicates that he will most likely not score higher than Melissa.

In order to solve this problem we need to make an inference. An inference is made using observations in prior knowledge. If we have multiple observations, then we can make better inferences. Let's develop our inference using the information provided for Joe and Melissa.

Joe obtained the following scores:

Let's tabulate this data into a histogram.

Let's find the mean of this data series. The mean is the arithmetic average of the data set. The mean is found by adding up the values and dividing the total by the number of values in the series.

Now let's calculate the standard deviation of the data series. The standard deviation for an entire population is found using the following formula:

First, we need to calculate how much each value deviates from the mean. We will do this by subtracting the mean from each value and squaring the difference.

Second, we will find the variance by adding up this values and dividing by the number of values in the series.

Last, the standard deviation equals the square root of the variance.

Now, we need to focus on Melissa's scores:

Let's tabulate this data into a histogram.

Let's find the mean of this data series. The mean is the arithmetic average of the data set. The mean is found by adding up the values and dividing the total by the number of values in the series.

Now let's calculate the standard deviation of the data series. The standard deviation for an entire population is found using the following formula:

First, we need to calculate how much each value deviates from the mean. We will do this by subtracting the mean from each value and squaring the difference.

Second, we will find the variance by adding up this values and dividing by the number of values in the series.

Last, the standard deviation equals the square root of the variance.

Now, let's review our data and calculations.

Given the information, we can see that Melissa's scores have a higher mean value and a smaller standard deviation for the set of values. This means that her scores are, on average, higher than Joe's and the vary less; therefore, we can predict that she will score higher on the test. Some may argue that Joe will score higher because of his on very high grade. It is true that he has the highest single grade between the two students; however, this is an outlier in the data. His lower mean score and higher tendency to vary between tests indicates that he will most likely not score higher than Melissa.

In order to solve this problem, we need to make an inference. An inference is made using observations in prior knowledge. If we have multiple observations, then we can make better inferences. Let's develop our inference using the information provided for Joe and Melissa.

Joe obtained the following scores:

Let's tabulate this data into a histogram.

Let's find the mean of this data series. The mean is the arithmetic average of the data set. The mean is found by adding up the values and dividing the total by the number of values in the series.

Now, let's calculate the standard deviation of the data series. The standard deviation for an entire population is found using the following formula:

First, we need to calculate how much each value deviates from the mean. We will do this by subtracting the mean from each value and squaring the difference.

Second, we will find the variance by adding up this values and dividing by the number of values in the series.

Last, the standard deviation equals the square root of the variance.

Now, we need to focus on Melissa's scores:

Let's tabulate this data into a histogram.

Let's find the mean of this data series. The mean is the arithmetic average of the data set. The mean is found by adding up the values and dividing the total by the number of values in the series.

Now, let's calculate the standard deviation of the data series. The standard deviation for an entire population is found using the following formula:

First, we need to calculate how much each value deviates from the mean. We will do this by subtracting the mean from each value and squaring the difference.

Second, we will find the variance by adding up this values and dividing by the number of values in the series.

Last, the standard deviation equals the square root of the variance.

Now, let's review our data and calculations.

Given the information, we can see that Melissa's scores have a higher mean value and a smaller standard deviation for the set of values. This means that her scores are—on average—higher than Joe's and they vary less; therefore, we can predict that she will score higher on the test. Some may argue that Joe will score higher because of his one very high grade. It is true that he has the highest single grade between the two students; however, this is an outlier in the data. His lower mean score and higher tendency to vary between tests indicates that he will most likely not score higher than Melissa.

In order to solve this problem, we need to make an inference. An inference is made using observations in prior knowledge. If we have multiple observations, then we can make better inferences. Let's develop our inference using the information provided for Joe and Melissa.

Joe obtained the following scores:

Let's tabulate this data into a histogram.

Let's find the mean of this data series. The mean is the arithmetic average of the data set. The mean is found by adding up the values and dividing the total by the number of values in the series.

Now, let's calculate the standard deviation of the data series. The standard deviation for an entire population is found using the following formula:

First, we need to calculate how much each value deviates from the mean. We will do this by subtracting the mean from each value and squaring the difference.

Second, we will find the variance by adding up this values and dividing by the number of values in the series.

Last, the standard deviation equals the square root of the variance.

Now, we need to focus on Melissa's scores:

Let's tabulate this data into a histogram.

Let's find the mean of this data series. The mean is the arithmetic average of the data set. The mean is found by adding up the values and dividing the total by the number of values in the series.

Now, let's calculate the standard deviation of the data series. The standard deviation for an entire population is found using the following formula:

First, we need to calculate how much each value deviates from the mean. We will do this by subtracting the mean from each value and squaring the difference.

Second, we will find the variance by adding up this values and dividing by the number of values in the series.

Last, the standard deviation equals the square root of the variance.

Now, let's review our data and calculations.

Given the information, we can see that Melissa's scores have a higher mean value and a smaller standard deviation for the set of values. This means that her scores are—on average—higher than Joe's and they vary less; therefore, we can predict that she will score higher on the test. Some may argue that Joe will score higher because of his one very high grade. It is true that he has the highest single grade between the two students; however, this is an outlier in the data. His lower mean score and higher tendency to vary between tests indicates that he will most likely not score higher than Melissa.

In order to solve this problem, we need to make an inference. An inference is made using observations in prior knowledge. If we have multiple observations, then we can make better inferences. Let's develop our inference using the information provided for Joe and Melissa.

Joe obtained the following scores:

Let's tabulate this data into a histogram.

Let's find the mean of this data series. The mean is the arithmetic average of the data set. The mean is found by adding up the values and dividing the total by the number of values in the series.

Now, let's calculate the standard deviation of the data series. The standard deviation for an entire population is found using the following formula:

\textup{Standard Deviation}=\sqrt{\frac{\sum(x-\textup{mean})^2}{n}}

First, we need to calculate how much each value deviates from the mean. We will do this by subtracting the mean from each value and squaring the difference.

Second, we will find the variance by adding up this values and dividing by the number of values in the series.

Last, the standard deviation equals the square root of the variance.

Now, we need to focus on Melissa's scores:

Let's tabulate this data into a histogram.

Let's find the mean of this data series. The mean is the arithmetic average of the data set. The mean is found by adding up the values and dividing the total by the number of values in the series.

Now, let's calculate the standard deviation of the data series. The standard deviation for an entire population is found using the following formula:

First, we need to calculate how much each value deviates from the mean. We will do this by subtracting the mean from each value and squaring the difference.

Second, we will find the variance by adding up this values and dividing by the number of values in the series.

Last, the standard deviation equals the square root of the variance.

Now, let's review our data and calculations.

Given the information, we can see that Joe's scores have a higher mean value and a smaller standard deviation for the set of values. This means that his scores are—on average—higher than Melissa's and they vary less; therefore, we can predict that he will score higher on the test. Some may argue that Melissa will score higher because of his one very high grade. It is true that she has the highest single grade between the two students; however, this is an outlier in the data. Her lower mean score and higher tendency to vary between tests indicates that she will most likely not score higher than Joe.

In order to solve this problem, we need to make an inference. An inference is made using observations in prior knowledge. If we have multiple observations, then we can make better inferences. Let's develop our inference using the information provided for Joe and Melissa.

Joe obtained the following scores:

Let's tabulate this data into a histogram.

Let's find the mean of this data series. The mean is the arithmetic average of the data set. The mean is found by adding up the values and dividing the total by the number of values in the series.

Now, let's calculate the standard deviation of the data series. The standard deviation for an entire population is found using the following formula:

First, we need to calculate how much each value deviates from the mean. We will do this by subtracting the mean from each value and squaring the difference.

Second, we will find the variance by adding up this values and dividing by the number of values in the series.

Last, the standard deviation equals the square root of the variance.

Now, we need to focus on Melissa's scores:

Let's tabulate this data into a histogram.

Let's find the mean of this data series. The mean is the arithmetic average of the data set. The mean is found by adding up the values and dividing the total by the number of values in the series.

Now, let's calculate the standard deviation of the data series. The standard deviation for an entire population is found using the following formula:

First, we need to calculate how much each value deviates from the mean. We will do this by subtracting the mean from each value and squaring the difference.

Second, we will find the variance by adding up this values and dividing by the number of values in the series.

Last, the standard deviation equals the square root of the variance.

Now, let's review our data and calculations.

Given the information, we can see that Melissa's scores have a higher mean value and a smaller standard deviation for the set of values. This means that her scores are—on average—higher than Joe's and they vary less; therefore, we can predict that she will score higher on the test. Some may argue that Joe will score higher because of his one very high grade. It is true that he has the highest single grade between the two students; however, this is an outlier in the data. His lower mean score and higher tendency to vary between tests indicates that he will most likely not score higher than Melissa.

In order to solve this problem, we need to make an inference. An inference is made using observations in prior knowledge. If we have multiple observations, then we can make better inferences. Let's develop our inference using the information provided for Joe and Melissa.

Joe obtained the following scores:

Let's tabulate this data into a histogram.

Let's find the mean of this data series. The mean is the arithmetic average of the data set. The mean is found by adding up the values and dividing the total by the number of values in the series.

Now, let's calculate the standard deviation of the data series. The standard deviation for an entire population is found using the following formula:

First, we need to calculate how much each value deviates from the mean. We will do this by subtracting the mean from each value and squaring the difference.

Second, we will find the variance by adding up this values and dividing by the number of values in the series.

Last, the standard deviation equals the square root of the variance.

Now, we need to focus on Melissa's scores:

Let's tabulate this data into a histogram.

Let's find the mean of this data series. The mean is the arithmetic average of the data set. The mean is found by adding up the values and dividing the total by the number of values in the series.

Now, let's calculate the standard deviation of the data series. The standard deviation for an entire population is found using the following formula:

First, we need to calculate how much each value deviates from the mean. We will do this by subtracting the mean from each value and squaring the difference.

Second, we will find the variance by adding up this values and dividing by the number of values in the series.

Last, the standard deviation equals the square root of the variance.

Now, let's review our data and calculations.

Given the information, we can see that Joe's scores have a higher mean value and a smaller standard deviation for the set of values. This means that his scores are—on average—higher than Melissa's and they vary less; therefore, we can predict that he will score higher on the test. Some may argue that Melissa will score higher because of his one very high grade. It is true that she has the highest single grade between the two students; however, this is an outlier in the data. Her lower mean score and higher tendency to vary between tests indicates that she will most likely not score higher than Joe.