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:

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

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

His median test score is .

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

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

Now, we will find the number in the middle.

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

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

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

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.

The divide the result by the number of values

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

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  her score on the final, then her course score will be

,

which simplifies to 

.

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

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

.

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

Alice's grade is a weighted mean in which her hourly tests have weight 1 and her final has weight 2. If we call  her final, then her term score will be 

,

which simplifies to 

.

Since she wants her score to be 90 or better, we solve this inequality:

Since it is established that 100 is the maximum score, Alice cannot achieve an average of 90 or more for the term.

The first step here, since you're working with the average (or mean), is to determine what is the sum of five test scores that will result in Eric earning at least a mean score of 90.

Start with the fact that he will need to make at least a 90 for his average score. Since you already have the average score, you're working backwards. You need to multiply 90 by 5 for the 5 test scores that will be used to get that average:

This tells you that the five scores - the four test scores and the final exam - will need to add up to at least 450 in total.

You know the four original test scores, so you can add those up:

So you know the four test scores add up to 365. To get an average of at least 90, the fifth score must bring that sum to at least 450. To find the minimum final exam test score, you subtract 365 from 450:

This tells you that Eric must score at least an 85 on the final exam to achieve an overall mean score of 90.

To calculate the average, find the sum of the total hours divided by the number of nights: