Take the sum of all of her test scores except for her lowest and divide that by the number of test scores included.

$\displaystyle \frac{ 81+ 89+ 82 + 83+ 80 }{5} = \frac{415}{5} = 83 > 81.5$

The median of the set of numbers is determined by arranging the numbers in numerical order and finding the middle number. In this case there are two middle numbers, $\displaystyle 18$ and $\displaystyle 20$, so we find the average of those numbers, which gives us $\displaystyle 19$.

The mean is found by dividing the sum of elements by the number of elements in the set: 

$\displaystyle \frac{20+35+7+12+73+12+18+31}{8}=26$

Quantity B is larger.

The average of a list of terms can be found as follows:

$\displaystyle Average=\frac{Sum\ of\ Terms}{Number\ of\ Terms}$

So we can write:

$\displaystyle A=\frac{4+5+10+12+14}{5}=\frac{45}{5}=9$

$\displaystyle B=\frac{4+5+10+14}{4}=8.25$

So $\displaystyle A$ is greater than $\displaystyle B$

Mean of a data set $\displaystyle x_{1},x_{2}, ..., x_{n}$ is the sum of the data set values divided by the number of data:

$\displaystyle Mean=\frac{x_{1}+x_{2}+...+x_{n}}{n}$

So we have:

$\displaystyle Mean = \frac{\frac{1}{3}+\frac{2}{3}+1+\frac{4}{3}+\frac{5}{3}}{5}=\frac{\frac{1+2+3+4+5}{3}}{5}=\frac{15}{15}=1$

Mean of a data set $\displaystyle x_{1},x_{2}, ..., x_{n}$ is the sum of the data set values divided by the number of data:

$\displaystyle Mean=\frac{x_{1}+x_{2}+...+x_{n}}{n}$

So we have:

$\displaystyle Mean = \frac{3+2+1+\frac{1}{2}+\frac{1}{3}}{5}=\frac{\frac{18+12+6+3+2}{6}}{5}=\frac{41}{30}=1\tfrac{11}{30}$

So the mean of the data set is greater than $\displaystyle 1$

Start by writing out what you know. We know that four numbers had a mean of 21. That would look like this: $\displaystyle \frac{x}{4}=21$. Therefore, we can determine what the sum of the four numbers was by soliving for x. The sum is 84. If we know that info, we can make a new equation for the new mean, which looks like this: $\displaystyle \frac{84+x}{5}=20$. Since we don't know what the new number is, we can just call it x. Solve this proportion to get your missing number. $\displaystyle 84+x=100$ then yields x as 16.

The mean of the data set is the sum of the elements divided by the quantity - eight, in this case:

$\displaystyle (13 + 17 + 12 + 18 + 19 + 22 + 21 + 23) \div 8$

$\displaystyle = 145\div 8 = 18.125$

The median of the data set is the value in the middle - or, since there is an even number of elements, it is the mean of the fourth-highest and the fourth-lowest elements. We arrange the elements in ascending order:

$\displaystyle 12, 13, 17, 18, 19, 21, 22, 23$

The median is the arithmetic mean of 18 and 19:

$\displaystyle (18+19) \div 2 = 37 \div 2 = 18.5$

(B) is the greater quantity