Since it's in increasing order, let's have some scenarios. Let's say  are both , then that means  at can be  with  maxing out its value up to  with  maxing its value. That leaves  must be  with  maxing out its value and  being in a range of  with  maxing its value and not violating the set. Now, lets say  are respectively, this leaves  only being  and  being  as well. Let's find the range of . If  were both , that means the median of them is . If  are both , that means the median of them is .  is highest median of both  and  is the lowest median of . We need to find a number in the answer choices that fit this description. Answer is 

Cubic numbers are numbers taken to the third power. The first six cubic numbers are:  or . 

Since, the numbers are inceasing, count the numbers in the set. There are six. Then divide six by two. We do this because we will split the number set in half. Because six does divide evenly into two, this means we can't easily determine the median. Since six divided by two is three, we are going to eliminate three numbers from leftmost in number set toward the right direction and three numbers from rightmost in number set toward the left direction. The last number crossed out in both direction are  and . To find the middle number, just add both numbers and divide by two.

 That.s the final answer.

When finding the median, you are looking for the middle number. Always arrange the numbers in ascending order. Since, the numbers are inceasing, count the numbers in the set. There are five. Then divide five by two. We do this because we will split the number set in half. Because five doesn't divide evenly into two, this means we can easily determine the median. Since five divided by two is , we are going to eliminate two numbers from leftmost in number set toward the right direction and two numbers from rightmost in number set toward the left direction. The only number left is  and therefore is the right answer. 

When finding the median, you are looking for the middle number. Always arrange the numbers in ascending order. Since, the numbers are not in inceasing order, let's arrange it. It should look like: . Now, let's count the numbers in the set which is seven. Then divide seven by two. We do this because we will split the number set in half. Because seven doesn't divide evenly into two, this means we can easily determine the median. Since seven divided by two is , we are going to eliminate three numbers from leftmost in number set toward the right direction and three numbers from rightmost in number set toward the left direction. The only number left is  and therefore is the right answer. 

When finding the median, you are looking for the middle number. Always arrange the numbers in ascending order. Since, the numbers are inceasing, count the numbers in the set. There are six. Then divide six by two. We do this because we will split the number set in half. Because six does divide evenly into two, this means we can't easily determine the median. Since six divided by two is three, we are going to eliminate three numbers from leftmost in number set toward the right direction and three numbers from rightmost in number set toward the left direction. The last number crossed out in both direction are  and . To find the middle number, just add both numbers and divide by two.

 That's the final answer.

When finding the median, you are looking for the middle number. Always arrange the numbers in ascending order. Since, the numbers are not in order, lets arrange them.

The new set is

.

Then, we count the numbers in the set. There are six. Then divide six by two. We do this because we will split the number set in half. Because six does divide evenly into two, this means we can't easily determine the median. Since six divided by two is three, we are going to eliminate three numbers from leftmost in number set toward the right direction and three numbers from rightmost in number set toward the left direction. The last number crossed out in both direction are  and . To find the middle number, just add both numbers and divide by two.

 That's the final answer.

When finding the median, you are looking for the middle number. Always arrange the numbers in ascending order. Since, the numbers are not increasing, let's organize it.

The new set is

.

Remember, for negative numbers, the bigger the negative value, the smaller the number is since it's further away in the number line. Now, let's count the numbers in the set. There are six. Then divide six by two. We do this because we will split the number set in half. Because six does divide evenly into two, this means we can't easily determine the median. Since six divided by two is three, we are going to eliminate three numbers from leftmost in number set toward the right direction and three numbers from rightmost in number set toward the left direction. The last number crossed out in both direction are  and . To find the middle number, just add both numbers and divide by two.

 That's the final answer.

Let's look at each statement. 

I. Always search for the middle number

This is false, because what happens if the number set is jumbled. To find median, it's important to oragnize in increasing or decreasing order.

II. Always arrange in increasing or decreasing order before searching for the middle number

As explained in statement one explanation, this is true.

III. Once arranged, if the set has an even number, just take the two middle numbers and subtract them and divide by two

This s false, because once there is an even number set, you need to ADD the middle numbers and divide it by two. Essentially, the new value represents the middle of the set.

IV. Once arranged, if the set has an even number, just take the two middle numbers and add them and divide by two

This is true based on statement three explanation. 

The set is already in increasing order. We have six numbers in the set and we need to ensure the set will have a median of . When there is an even number in the set, we need to take the two middle numbers by adding them then dividing by two. The two middle numbers represent  and .  Let's set up an equation.

.

The numerator represents the two middle numbers being added and divided by the denominator. If we multiply both sides by  we get the sum of the variables to be . So we need to find the sum of  and  to be . The only choices are ,  and , . However, ,  doesn't work because  is bigger than both  and  and thus changing the median. ,  is good because both of the values are les than  but greater than . 

The set is already in increasing order. We have six numbers in the set and we need to ensure the set will have a median of . When there is an even number in the set, we need to take the two middle numbers by adding them then dividing by two. The two middle numbers represent  and .  Let's set up an equation.

.

The numerator represents the two middle numbers being added and divided by the denominator. If we multiply both sides by , and subtract  on both sides, we get  to be . Finally, to find , we need a number that is greater than or equal to  and less than or equal to . Answer ,  satisfies all conditions.