The median of an even numbered data set is the average of the central two numbers in a chronologically ordered data set from least to greatest.

The set of numbers are already from least to greatest.

Average the two center numbers.

The median is:  

Reorganize all the numbers from least to greatest.

The median for an even amount of numbers in the data set is the average of the two central numbers.

Average the two numbers.

The median is:  

Step 1:

To make this problem easier to solve, let's list out the Elo ratings from least to greatest.

Step 2:

Because there are an even amount of players, there will be two middle terms. We must take the average of the two middle terms in order to get an accurate median value.

Solution: 

The median in the number in the middle of the data set.

Arrange the data in numerical order.

  .

Therefore, the median is 21.

The correct answer is . It is regarded as the middle value, or the average of the two middle values of a data set. The first step in finding the median is ordering the data from least to greatest. 

From here, find the middle value. In this case, that is the ^th value, . 

Let's interpret the problem. One number is . Another is two times square root of  or . The last number is one less than  or . The sum is three which means the equation to set up is: . Let's solve for . 

 I want to have the square root on one side and the numbers and variable on the other.

 When  I square both sides, we get a quadratic equation. If I were to square the equation before, I still have a radical to get rid of.           

Remember when foiling, you multiply the numbers/variables that first appear in each binomial, followed by multiplying the outer most numbers/variables, then multiplying the inner most numbers/variables and finally multiplying the last numbers/variables.

 Let's factor out a  to reduce the quadratic.

 If I divide both sides by , I get:

 Remember, we need to find two terms that are factors of the c term that add up to the b term. We have: 

Solve for . 

We are not done as the problem asks for median of the set. If we plug in , we have:  or . Once we arrange in increasing order, we have . By checking, the sum is  and the middle number is . Let's check when  is . We have:  or . In increasing order we have . The answer may be 4, HOWEVER, it doesn't satisfy the problem as the sum should be  but instead we have . Therefore the correct answer to this problem 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 mode is the number that shows up more often than the others in a set of data.

If we put our data set in order we see:

98, 65, 85, 100, 76, 50, 88, 63, 70, 65, 70, 99, 82, 80, 78, 65, 94, 66

Becomes,

50, 63, 65, 65, 65, 66, 70, 70, 76, 78, 80, 82, 85, 88, 94, 98, 99, 100.

Therefore, 65 is the mode because it appears 3 times.

Arrange the set in numerical order: {2, 4, 5, 7, 7, 7, 9, 9, 10, 11, 11, 15, 19, 20}.

You can then chart the frequency of each value.

Value (Frequency)

2 (1)

4 (1)

5 (1)

7 (3)

9 (2)

10 (1)

11 (2)

15 (1)

19 (1)

20 (1)

From this you can see the most common value, which is the mode, is 7.

12 appears in the set most frequently, appearing three times; 19 is second in frequency, appearing twice. 10, 11, 18, and 20 appear once each.

The only number we can set  to to make two data values tie for appearing most frequently is 19; 12 and 19 would then each appear three times, and the others, once. If  is set to any other number, 12 would remain the most frequent data value.