Median - Algebra II

List the numbers in ascending order: 2,3,4,4,6,8,9,11,13,15,16

The median is the middle number, or 8.

To find the median of a set of values, simply place the numbers in order and find the value that is exactly "in the middle." Here, we can place the test scores in ascending order to get , , , , . (Descending order would work just as well.) The median is the middle value, . Make sure you don't confuse median with mean (average)! To get the mean value of this set, you would find the sum of the test scores and then divide by the number of values.

To find the median, first you arrange the numbers in order from least to greatest.

Then you count how many numbers you have and divide that number by two. In this case 12,15,16,21,22,32,93,108= 8 numbers.

So

Then starting from the least side of the numbers count 4 numbers till you reach the median number of

Then starting from the greatest side count 4 numbers until you reach the other median number of

Finally find the mean of the two numbers by adding them together and dividing them by two

to find the median number of .

The mean is just the average of all the test scores, which is found by adding up the scores and dividing by the number of scores (). This gives as the mean. The mode is the score which occurs most frequently. In this case, the mode is . The median, the middle score of the sequence, is .

Let's think of this list of numbers:

2, 4, 6, ...

Where does it end? The first 5 even numbers goes to 10. That means that the last number in the first 20 will be the number 40. So the question is, "Where is the middle?" Well, this is an even number of values, so there is no actual middle. What we have to do, then is find the 10th and the 11th numbers and take their average. The 10th number is easy, based on what we just said. If the 5th is 10, then the 10th is 20. The 11th will just be two more than that, namely 22. To calculate the median, we just have to find the average of those two numbers:

If you prefer to write out the full list:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40

To answer this question, you need to know the first ten prime numbers! Remember, prime numbers are all of the integers that are divisible only by themselves and by 1. They do not include 1. So, our list is:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

The median is the "middle value." There is no proper "middle" since we have an even number of values. We need to take the 5th and the 6th elements (the middle two values) and average them. The 5th term is 11 and the 6th is 13; therefore, the median is:

The easiest way to do this is first to find the total number of flowers:

Now, the median element is the "middle" term. To find the middle, you can divide 21 by 2:

Since you have an odd number of elements, you unsurprisingly get a fraction. This means that there 10 items to the left of the median and 10 to its right. The 11th term is your median. Now, your group of flowers looks like this:

1-12: 10 inches

13-17: 12 inches

18-21: 15 inches

The 11th item is going to be in that first group, meaning that the median is 10 inches.

If you prefer to write out all of the terms, it will be:

10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 15, 15, 15, 15

The first thing to do is figure out which stalk is in the "middle." Since there are an even number of stalks, there is no exact middle; there are 500 on one side and 500 on the other. This means that the 500th and the 501st are the median. These will have to be averaged.

Now, we need to determine the height of these two stalks. Consider the pattern given:

1st stalk: 10 feet

2nd stalk: 20 feet

3rd stalk: 30 feet

4th stalk: 40 feet

You should see the pattern that emerges for this problem. Each stalk is 10 times that stalk's place in the row. This means that the 500th stalk will be:

The 501st stalk will be:

The average of these two numbers is:

5005 feet is the median.

The median in a data set is the number that lies directly in the middle. To determine the median, first list the numbers in ascending order:

Then, count in from both sides to find the number that lies directly in the middle. Therefore the correct answer is "median".

First, arrange all of the data in numerical order: .

Then locate the middle number by using the formula

, which gives you the location of the median in the ordered data set and where is the number of terms in the data set.

Here, there are 11 terms.

So,

Therefore, our number is the one in the list, which is .

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 five numbers in the set, however, we need to add another number to ensure the set will have a median of . This will make the set have six numbers. When there is an even number in the set, we need to take the two middle numbers by adding them then dividing by two. Let's say this number is . Let's setup 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, is . Make sure this answer doesn't violate the set. is less than but greater than , so therefore is the correct answer.

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.