To find the median of a data set, we will first arrange the numbers in ascending order.  Then, we will find the number in the middle of the data set.

So, given the Math test scores

$\displaystyle 98, 95, 82, 80, 76, 83, 92, 90, 85$

we will first arrange them in ascending order.  To do that, we will arrange them from smallest to largest  So, we get

$\displaystyle 76, 80, 82, 83, 85, 90, 92, 95, 98$

Now, we will find the number in the middle of the set. 

$\displaystyle 76, 80, 82, 83, {\color{Red} 85}, 90, 92, 95, 98$

Therefore, the median of the set of Math test scores is 85.

Find the median of the following data set:

$\displaystyle 44,65,12,33,99,12,55,44,65,12,79$

To find the median, first put the numbers in increasing order

$\displaystyle 12,12,12,33,44,44,55,65,65,79,99$

Now, identify the median by choosing the middle term

$\displaystyle 12,12,12,33,44,{\color{Green} 44},55,65,65,79,99$

In this case, it is 44, because 44 is in the middle of all our terms.

The median is the number that is in the middle of an ordered list. Start by putting the numbers in ascending order:

$\displaystyle 80, 88, 92, 94, 95, 97$

Since we have an even number of test scores, the median will be the number that is in between the middle two numbers.

In this case, the median will have to be between 92 and 94.

The number that is exactly between these two numbers is $\displaystyle 93$.

Remember that the median is the middle number of a data set when the data is sorted in numerical order.

Start by putting the numbers in ascending order:

$\displaystyle 58, 58, 65, 69$

Now, because there is an even number of test scores, the median will be in between the middle two numbers, $\displaystyle 58$ and $\displaystyle 65$.

Take the average of these two numbers to find the number that is exactly in the middle.

$\displaystyle \frac{58+65}{2}=61.5$

His median test score is $\displaystyle 61.5$.

To find the median of a data set, we will first arrange the numbers in ascending order.  Then, we will find the number in the middle of the set.  So, given the data set

$\displaystyle 99, 95, 84, 99, 81, 97, 79, 86$

We will arrange them in ascending order (from smallest to largest).  We get

$\displaystyle 79, 80, 81, 84, 86, 95, 97, 99, 99$

Now, we will find the number in the middle.

$\displaystyle 79, 80, 81, 84, {\color{Red} 86}, 95, 97, 99, 99$

We can see that it is 86.

Therefore, the median of the data set of test scores is 86.

To find the median of a data set, we will first arrange the data set in ascending order. Then, we will find the number that is located in the middle of the set.

So, given the set

$\displaystyle 5, 4, 7, 6, 9, 6, 2, 6, 9$

we will arrange the set in ascending order (from smallest to largest). We get

$\displaystyle 2, 4, 5, 6, 6, 6, 7, 9, 9$

Now, we will locate the number in the middle of the set. 

$\displaystyle 2, 4, 5, 6, {\color{Red} 6}, 6, 7, 9, 9$

We can see that it is 6.  

Therefore, the median of the data set is 6.

To find the mean, first sum up all the values.

$\displaystyle \small \sum \left \{ 70,89,67,77,92,83,67,75\right \}=620$

The divide the result by the number of values

$\displaystyle \small 620\div8=77.5$

The mean of six numbers is their sum divided by 6, so the sum is the mean multiplied by 6. This is:

$\displaystyle 77 \times 6 = 462$

Sally's grade is a weighted mean in which her hourly tests have weight 1, her midterm has weight 2, and her final has weight 3. If we call $\displaystyle x$ her score on the final, then her course score will be

$\displaystyle \frac{89 + 85 + 84 + 87 + 2 \cdot 93 + 3x}{1 + 1 + 1 + 1 + 2 + 3}$,

which simplifies to 

$\displaystyle \frac{89 + 85 + 84 + 87 + 186 + 3x}{9} = \frac{3x + 531}{9}$.

Since Sally wants at least a 90 average for the term, we can set up and solve the inequality:

$\displaystyle \frac{3x + 531}{9} \geq 90$ 

$\displaystyle \frac{3x + 531}{9} \cdot 9 \geq 90 \cdot 9$

$\displaystyle 3x + 531 \geq 810$

$\displaystyle 3x + 531-531 \geq 810-531$

$\displaystyle 3x \geq 279$

$\displaystyle 3x \div 3 \geq 279 \div 3$

$\displaystyle x \geq 93$

Sally must score at least 93 on the final.

If Fred does not take the sixth test or gets a 0 on it, he will receive the average of his first five tests. This is

$\displaystyle \frac{78 + 77 + 84+ 89 + 72}{5} =\frac{400}{5} = 80$.

Since he can only improve his class grade by taking the sixth test, Fred is already assured of an average of 80 or better.