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). 

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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. 

Standard deviation is essentially the average distance from the mean of a group of numbers.  There are a number of steps in computing standard deviation, but the steps are not too complicated if you take them one at a 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.  Finally, find the square root of the result. 

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There are five steps to finding the standard deviation of a group of values. 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 minus one.  Finally, find the square root of the result.