Had Sally scored 65 or less on her fifth test, that would have been the dropped score, and her final score would have been the mean of 90, 80, 65, and 70. This is the sum of the scores divided by four:

Since Sally's mean was greater than this (78), it can be deduced that her fifth score was better than 65, and that the 65 was dropped. Therefore, (A) is greater.

A mean is calculated by takng the sum of the elements and dividing by the number of elements.

The mean of the seven scores is

.

The lowest score is a 6; the highest is a 9, so the five scores remaining are 

.

The mean of the five scores is

.

Therefore (B) is greater.

Rhonda's highest and lowest scores in the first round were 10 and 5, so her score in the first round was the mean of the scores

.

This is the sum of the four scores divided by four, or

.

Rhonda's highest and lowest scores in the second round were 10 and 6, so her score in the first round was the mean of the scores

.

This is the sum of the six scores divided by six, or

.

(A) is greater.

The average is calculated by adding together the numbers in a set and dividing by the number of items: 

The only real comparison that needs to be made is between the two students' totals; the one with the lesser total needs a greater score to average .

(a) Anne's total: 

(b) Barb's total: 

Barb has fewer points so she needs more points to average . This makes (b) greater.

The median of the set is the fifth-highest value, which is ; 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 mode of a data set is the element that appears most frequently.

The data set has ten elements - one 2, one 3, three 4's, two 7's, one 9, one 10, and an element of unknown value.

If that unknown element is 4, then there will be four 4's, and two or fewer of any other value, making 4 the only mode.

If that unknown element is 7, then there will be three 4's, three 7's, and one of each of the other elements, making 4 and 7 the modes.

If the unknown element is any other integer, then there will be three 4's and no more than two of any other element, making 4 the only mode.

The correct choice is therefore any integer other than 7.

The mode of a data set is the element that appears most frequently.

Two values of the data set, 2 and 9, are known to appear twice; the others appear exactly once. 

If  is 6, 7, or 8, this does not change, and 2 and 9 are both modes.

If  is 1, 3, 4, 5, or 10, then three different values appear twice, and 2, 9, and the choice of  are the three modes.

If  is 2 or 9, then that number appears three times, the other number appears twice, and all others appear once. That makes the choice of  the only mode.

This makes the correct choice 2 or 9.

The mode of a data set is the element that appears most frequently.

The data set has ten elements - one 2, one 3, three 4's, two 7's, one 9, one 10, and an element of unknown value. 

If that unknown element is 7, there are two modes of the set, 4 and 7, which would occur three times each, as opposed to the other elements, which would appear once each.

If that unknown element is any other integer, then the only mode of the data set is 4, which would occur three times, as opposed to the other elements, which would appear once or twice each.

The correct choice is that this impossible.

(a) The median of a data set with ten elements is the arithmetic mean of the fifth-highest and sixth-highest elements. These elements are 13 and 15, so the median is 

(b) The mode of a data set is the element that occurs most frequently. Since 13 is the only repeated element, it is the mode.

This makes (a) the greater quantity.