Median - GMAT Quantitative

The median of an odd number of data values is the middle valie when the scores are arranged in descending order. Since the scores are arranged, the middle score, and the median, is .

The median of an odd number of data values is the middle valie when the scores are arranged in descending order. Since the scores are arranged, the middle score, and the median, is .

There are nine elements, so the median is the fifth-highest element. For this fifth-highest element to be 70, first of all, 70 must be in the set; since none of the known elements are equal to 70, then one of the two unknowns must be 70.

Assume without loss of generality that . Then four of the elements are already known to be less than 70. Since four elements must be greater than or equal to 70, must be one of them.

Therefore, the correct choice is that one must be equal to 70 and the other must be greater than or equal to 70.

The median of an odd number of data values is the middle valie when the scores are arranged in descending order. Since the scores are arranged, the middle score, and the median, is .

There are nine elements, so the median is the fifth-highest element. For this fifth-highest element to be 70, first of all, 70 must be in the set; since none of the known elements are equal to 70, then one of the two unknowns must be 70.

Assume without loss of generality that . Then four of the elements are already known to be less than 70. Since four elements must be greater than or equal to 70, must be one of them.

Therefore, the correct choice is that one must be equal to 70 and the other must be greater than or equal to 70.

The median of an even number of data values is the arithmetic mean of the middle two when the scores are arranged in descending order. Here, the scores are in descending order, and the middle two scores are and , so the median is their arithmetic mean, or .

The data set can be arranged from least to greatest as follows:

The median of a data set with eight elements is the mean of its fourth-highest and fourth-lowest elements, which are and . Add and divide by two:

There are nine elements, so the median is the fifth-highest element. For this fifth-highest element to be 70, first of all, 70 must be in the set; since none of the known elements are equal to 70, then one of the two unknowns must be 70.

Assume without loss of generality that . Then four of the elements are already known to be less than 70. Since four elements must be greater than or equal to 70, must be one of them.

Therefore, the correct choice is that one must be equal to 70 and the other must be greater than or equal to 70.

There are nine elements, so the median is the fifth-highest element. For this fifth-highest element to be 70, first of all, 70 must be in the set; since none of the known elements are equal to 70, then one of the two unknowns must be 70.

Assume without loss of generality that . Then four of the elements are already known to be less than 70. Since four elements must be greater than or equal to 70, must be one of them.

Therefore, the correct choice is that one must be equal to 70 and the other must be greater than or equal to 70.

There are nine elements, so the median is the fifth-highest element. For this fifth-highest element to be 70, first of all, 70 must be in the set; since none of the known elements are equal to 70, then one of the two unknowns must be 70.

Assume without loss of generality that . Then four of the elements are already known to be less than 70. Since four elements must be greater than or equal to 70, must be one of them.

Therefore, the correct choice is that one must be equal to 70 and the other must be greater than or equal to 70.

The median of an odd number of data values is the middle valie when the scores are arranged in descending order. Since the scores are arranged, the middle score, and the median, is .

There are nine elements, so the median is the fifth-highest element. For this fifth-highest element to be 70, first of all, 70 must be in the set; since none of the known elements are equal to 70, then one of the two unknowns must be 70.

Assume without loss of generality that . Then four of the elements are already known to be less than 70. Since four elements must be greater than or equal to 70, must be one of them.

Therefore, the correct choice is that one must be equal to 70 and the other must be greater than or equal to 70.

The median of an odd number of data values is the middle valie when the scores are arranged in descending order. Since the scores are arranged, the middle score, and the median, is .

The median of an even number of data values is the arithmetic mean of the middle two when the scores are arranged in descending order. Here, the scores are in descending order, and the middle two scores are and , so the median is their arithmetic mean, or .

The median of an odd number of data values is the middle valie when the scores are arranged in descending order. Since the scores are arranged, the middle score, and the median, is .

The median of an even number of data values is the arithmetic mean of the middle two when the scores are arranged in descending order. Here, the scores are in descending order, and the middle two scores are and , so the median is their arithmetic mean, or .

The median of an even number of data values is the arithmetic mean of the middle two when the scores are arranged in descending order. Here, the scores are in descending order, and the middle two scores are and , so the median is their arithmetic mean, or .

The median of an even number of data values is the arithmetic mean of the middle two when the scores are arranged in descending order. Here, the scores are in descending order, and the middle two scores are and , so the median is their arithmetic mean, or .

The data set can be arranged from least to greatest as follows:

The median of a data set with eight elements is the mean of its fourth-highest and fourth-lowest elements, which are and . Add and divide by two: