Median - GMAT Quantitative Reasoning

Write the numbers in order from smallest to largest. The median is the middle number, which is 11.

The median of a dataset with an even number of elements is the arithmetic mean of the two elements that fall in the middle when the elements are arranged in ascending order. Since there are 100 elements and , this means the fiftieth-highest and fiftieth-lowest elements.

The median of a data set with an even number of elements is the mean of its two middle elements, when ranked. The set is already ranked, so just find the mean of middle elements and :

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:

The median of her current five scores is the third-highest, or 86. Even if she does not take the sixth examination, this median will stand, and even if her mean is less, she has already achieved a score of 86 or better.

The median of the original data set, which has nine elements, is the fifth-highest element; here it is 50. The median of a data set with eleven elements is its sixth-highest element; since one of the elements added is greater than 50 and one is less than 50, 50 becomes the sixth-highest element in the new set, and it remains the median.

Arrange the eight known values from least to greatest.

If the unknown positive integer is added to the set, then the median of the resulting nine-element set is the fifth-highest.

Case 1:

The fifth-highest element is then 37.

Case 2:

The fifth-highest element is then .

Case 3:

The fifth-highest element is then 50.

Therefore, it is possible for the median to be any integer from 37 to 50 inclusive.

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.

Arrange the elements in ascending order:

There are ten elements, so the median is the arithmetic mean of the fifth- and sixth-highest elements, which are . This mean is

The numbers in the "stem" of this display represent tens digits of the test scores, and the numbers in the "leaves" represent the units digits.

This stem-and-leaf display represents twenty scores, so the median is the arithmetic mean of the tenth- and eleventh-highest elements. These elements are 62 and 64, so the median is .

The numbers in the "stem" of this display represent tens digits of the test scores, and the numbers in the "leaves" represent the units digits.

This stem-and-leaf display represents twenty scores. The first quartile is the median of the lower half, or the lower ten scores. This is the arithmetic mean of the fifth- and sixth-lowest scores. Both of these scores are the same, however - 57. Therefore, 57 is the first quartile.

In order to find the median, we first have to order the data points from lowest to highest. This would be-

.

Since we have an even number of data points, the median is the mean average of the middle two numbers, .

Hence our answer is

We start by sorting the ages from youngest to oldest:

19 21 23 24 25 29 33 37 38 42 43 47 48 53 68

The median is the number in the middle position, we have fifteen numbers so the middle position in this set is the 8th position (we get 7 numbers on each side of the 8th number)

37 is at the 8th position, therefore 37 is the median age.

To find the median, let's rewrite the list in ascending order:

5, 5, 9, 10, 12, 14, 22, 27, 39

The median is the midpoint value such that half of the values are lower than the median and the other half of the values are higher than the median.

The median is 12.

The range is the difference between the highest and the lowest number in the list. The range is: 39-5=34

The difference between the range and the median is 22.

To find the median, sort the numbers from smallest to largest:

59, 65, 67, 73, 73, 73, 76, 80, 80, 83, 85, 94, 98

The median is the middle value in a list of numbers, it is the number separating the higher half of a data sample or a list of numbers from the lower half.

The median of the grades is 76.

The mode is the value occurring most often. The most occurring value in the list of numbers given is 73. So, the mode is 73.

The median of a set of data is the entry located exactly in the middle when the entries are arranged in increasing order. If there are an odd number of entries arranged in increasing order, the median will be the middle entry. If there are an even number of entries arranged in increasing order, the median will be the average of the middle two entries. Our first step, then, is to arrange the given set in increasing order:

Now that our set is in order from least to greatest, we can see that the value of 6 is located exactly in the middle of the set, so this is the median.

The median of a set of data is the entry located directly in the middle when the entries are arranged in increasing order. The first step, then, is to arrange the given set of data in increasing order:

Because we have an even number of entries, we can see that no entry is located directly in the middle. When this is the case, the median is the average of the middle two entries, which gives us:

To find the median, sort the numbers and determine which one is in the middle.

Since splits the middle, is your median.

The median is the middle number when the numbers are sorted from smallest to largest. Since they are already sorted, the answer is .