In order to solve this problem, we need to discuss probabilities. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:

Let's use a simple example: the rolling of a die. We want to know the probability of rolling a one. We know that the sample space is six because there are six sides or outcomes to the die. Also, we know that there is only a single side with a value of one; therefore,

Now, let's convert this into a percentage:

Probabilities expressed in fraction form will have values between zero and one. One indicates that an event will definitely occur, while zero indicates that an event will not occur. Likewise, probabilities expressed as percentages possess values between zero and one hundred percent where probabilities closer to zero are unlikely to occur and those close to one hundred percent are more likely to occur.

Now, we will start by constructing a table. The question presents data associated with two different types of variables: grade level and class. There are four grade levels (i.e. freshman, sophomores, juniors, and seniors) and four elective science classes (i.e. astronomy, ecology, physics, and chemistry). We need to make a table that has four rows and four columns. Next, we can input the data contained in the table. Last we will add up each row and column in order to gain totals for each variable. If you have done this properly, then you should have created a table similar to the following:

After, the two-way table has been constructed you can then use it to solve the question: what is the probability that a senior will take astronomy?

First, we need to create the following ratio: number seniors planning to take the astrology class to the total number of seniors.

Substitute values using the table and solve.

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: