First we need to find . We know that the mean of a set of data is given by the sum of the data, divided by the total number of values in the set. So we can write:

Now we have:

If there are an odd number of values in a data set, the median is the middle value. First we need to put the numbers in order:

So the median is .

The mode of a set of data is the value which occurs most frequently which is in this problem (it is not dependent on in this problem). So the mean is also equal to .

We know that the mean of a set of data is given by the sum of the data, divided by the total number of values in the set. So we can write:

So we have:

If there are an odd number of values in a data set, the median is the middle value. First we need to put the numbers in order:

So the median is also .

The seven elements are already arranged in ascending order, so we need to look at the value occurring in the middle - that is, the fourth position. This element is 26.

If , then the mean of the data set is the sum of the eight elements divided by eight:

The median of the data set, however, depends on the values of  and , as can be demonstrated using two cases.

Case 1: 

The data set is then 

and the median is the mean of the two middle values. Since both middle values are 35, the median is 35.

Case 2:  and 

The data set is then 

and the median is the mean of the two middle values. They are 25 and 35, so the median is 

In the first case, the median is greater than the mean; in the second case, the mean is greater than the median. Therefore, the information is insufficient.

The median of a data set with an even number of elements is the mean of the middle two numbers, assuming the elements are arranged in order; since the data set has eight elements, the median will be the mean of the fourth-lowest element and the fourth-highest element.

If  and , the data set becomes ; if  and , the data set becomes . In both data sets, the middle two elements are 25 and 35, making both medians equal to . The quantities are equal.

Note: You don't need to do the last step and actually find the median. As long as you know that the two medians are the same, you've answered the question!

The first step is to reorder the set, , in order from smallest to largest. 

The mode (which occurs most often) is 3.3, so . 

The median is the middle number in the set (which is 6.8, having 3 numbers to its right and 3 to its left in the ordered list), so . 

The mean (or average) is , so 

Therefore, . 

To find her average grade for the class, we need to multiply Mary's test scores by their corresponding weights and then add them up.

The five quizzes were each worth 10%, or 0.1, of her grade, and the midterm and final were both worth 25%, or 0.25.

average = (0.1 * 89) + (0.1 * 74) + (0.1 * 84) + (0.1 * 92) + (0.1 * 90) + (0.25 * 92) + (0.25 * 91) = 88.95 = 89. 

Looking at the answer choices, they are all spaced 2 percentage points apart, so clearly the closest answer choice to 88.95 is 89.

The median of the set is the fifth-highest value, which is 70; this is also the mode, being the most commonly occurring element.

The mean is the sum of the elements divided by the number of them. This is

The midrange is the mean of the least and greatest elements, This is 

The midrange is the greatest of the four.

The mean of the data set is the sum of the elements divided by 5:

The median of the data set is the middle value when the values are arranged in ascending order, which here is the third-highest value. This is 79.

The mean exceeds the median by