Let the final test score.

The average is given by .

Solve by cross multiplying to get .

Then subtract from both sides to get . 

First, convert the weighted percents to decimals.

Next, multiply each score by the weight.

Finally, sum all of the weighted scores.

The mean is the sum of the numbers divided by their count:

To find the median, order the set from smallest to largest:

When there are two numbers in the middle, find the average of those numbers:

The average is the sum of the data divided by the total number of data points.

Let final score.

Simplify so the equation to solve becomes .

Cross multiplying we get .

Then subtract from both sides and divide by to get .

The interquartile range of a set of scores is the difference between the third and first quartile - that is, the difference between the 75th and 25th percentiles. The 75th percentile is between 78 and 86, so, if 41 is subtracted from those numbers, the upper and lower bounds of the 25th percentile can be found.

Of our choices, only 40 falls in this range.

The sample space, or total possible outcomes, when rolling two six-sided dice is .

Ways to get what you want:

So there are ways to get a .

So the probability becomes

First, put the data set in order from smallest to largest:

which is the middle number in the data set.

which is the average of the two middle numbers of the lower half of the data set.

which is the average of the two middle numbers of the upper half of the data set.

Thus the interquartile range is

Note, the range of the data set is given by the largest number minus the smallest number, or

Variation measures the average difference between values within a group.  The process is not complicated but there are four steps that can take time.  First, find the mean of the values.  Second, subtract the mean from the first value and square the result.  Do this for all remaining values.  Third, add these results together.  Fourth, divide this value by the number of values in the group minus one (in this case, there are four days). 

1:

2:

3:

4:

Note that to find the standard deviation, we would simply take one additional step of finding the square root of the variance. 

There are four steps to finding the variance of values within a group.  First, find the mean of the values.  Second, subtract the mean from the first value and square the result.  Do this for all remaining values.  Third, add these results together.  Fourth, divide the result  by the number of values in the group minus one (in this case, there are seven days, so you must divide by six).  

This question illustrates the close relationship between the concepts of variance and standard deviation.  We can find variance even though we do not know the values in the population if we know the standard deviation.  Simply square the standard deviation to find the variance.