Reorder all the numbers from smallest to largest.

$\displaystyle a=[3,19,2,10] = [2,3,10,19]$

Since there are four numbers in this set, we will average the second and third number in the set to find the median.

$\displaystyle \frac{3+10}{2} = \frac{13}{2}=6\frac{1}{2}$

The median is $\displaystyle 6\frac{1}{2}$.

The median of a set of numbers is the number that falls in the middle of the set. 

If we reorder the numbers from least to greatest, we get:

$\displaystyle 40, 41, 42, 42, 43, 51, 55$

The number that falls in the middle of this set is the fourth number, which is $\displaystyle 42$. 

To solve, simply find the middle number. Since the numbers are already ordered from smallest to largest, we can easily do this. 7 numbers means the 4th one from either end will be the middle. Thus, our answer is 17.

The median is the number that falls in the middle of a set of numbers when they are placed in order from least to greatest. 

With an odd number of numbers in this set, you always have one of the values in the set as your median (as opposed to the average of the two middle values when you have an even number of numbers in a set). Therefore, because all of the numbers in this set are integers, you cannot have 24.5 as the median 

The mean is the sum of the data values divided by the number of values or as a formula we have:

$\displaystyle \bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}$

Where:

$\displaystyle \bar{x}$ is the mean of a data set, $\displaystyle \sum$ indicates the sum of the data values $\displaystyle x_{i}$ and $\displaystyle n$ is the number of data values. So we can write:

$\displaystyle \bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}=\frac{(64+78+76+80+82+83+75+x)}{8}$

$\displaystyle \Rightarrow \bar{x}=\frac{538+x}{8}=78\Rightarrow 538+x=78\times 8$

$\displaystyle \Rightarrow 538+x=624\Rightarrow x=624-538=86\ in$

In order to find the median, the data must first be ordered:

$\displaystyle \left \{ 64,75,76,78,80,82,83,86 \right \}$

Since the number of values is even, the median is the mean of the two middle values. So we get:

$\displaystyle Median=\frac{78+80}{2}=79\ in$

In order to answer this question, we need to add each column up and see what column is the largest.

$\displaystyle \begin{tabular}{ccccccc} ~&1&2&3&4&5&6\\ \hline MidWest& 10 & 30 &40 & 60 & 100 &24\\ South& 11&45&54&65&90&34\\ East Coast& 56& 23 & 32 & 99 & 10 &56\\ \hline Totals& 77&98& 126&224& 200& 114 \end{tabular}$

It looks like that the $\displaystyle 4^{\text{th}}$ 2 month period has the most college graduates.

We know that the median is the middle number in a group of numbers. Therefore, the median of five numbers will be the 3rd largest number. Since one of the numbers is unknown, we need to solve for it.

We can set up the equation,

$\displaystyle 7 + 3 + 20 + 14 + x = 50$

After we solve for x, we learn that,

$\displaystyle x = 6$

Therefore our five numbers, in order, are 3, 6, 7, 14, and 20. The median number, which is the middle number and the 3rd largest in a group of 5 numbers, is 7. 

To find the median, one must arrange all the heights from the lowest to the highest value and then pick the middle value.

All values: 64 69 60 70 74 72 55 52 58

In order from lowest: 52 55 58 60 64 69 70 72 74

Median: 64