How to find median - ISEE Upper Level Quantitative Reasoning

(a) The mean of nine elements is , so, if is their sum, and . The sum of the new data set is . Since the new set has elements, its mean is .

(b) The median of the nine elements is , so, when they are ranked, the fifth-highest element is . Since is less than and is greater than , when they are added to the set, is the sixth-highest of eleven elements, which is the median.

Therefore, both are equal to .

(a) Since each element of the old set is increased by 5, the sum of the elements is increased by . This increases the mean by , to 55.

(b) The median of the old set is the mean of the sixth- and seventh-highest elements. Since each element of the old set is increased by 5, these elements remain the sixth- and seventh-highest elements; their sum is increased by 10, and their mean is increased by 5, to 55.

The mean and the median of the new set are equal.

If four of the elements are greater than 50 and four are less than 50, then the fifth-highest element, which is the median of a nine-element set, must be 50.

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.

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, .

The median of nine (an odd number) integers is the one in the middle when the numbers are arranged in ascending order; in this case, it is the fifth lowest. Since the nine integers are consecutive, the greatest integer is four more than the median, or .

We know that the numbers should be arranged in ascending order to find the median. When the number of values is odd, the median is the single middle value. In this question we have consecutive integers with the median of . So the median is the number in the rearranged data set. Since the integers are consecutive, the smallest integer is five less than the median or it is equal to .

There are data values altogether. When the number of values is even, the median is the mean of the two middle values. So in this problem the median is the mean of the and largest values. So we can write:

So:

There are data values altogether. When the number of values is even, the median is the mean of the two middle values. So in this problem the median is the mean of the and largest values. So we can write:

So:

To determine the median of a set of numbers, you first need to order them from least to greatest:

Since there is an odd number of scores, the median is the score that falls exactly in the middle of the new list. Thus, the median is 88.

To determine the median of a set of numbers, you first need to order them from least to greatest:

Since there is an even amount of numbers, the median is determined by finding the average of the two numbers in the middle - 36 and 44.

Thus, the median is 40.

The "stem" of this data set represents the tens digits of the data values; the "leaves" represent the units digits.

There are 22 elements, so the median is the arithmetic mean of the eleventh- and twelfth-highest elements, which are 64 and 65, the middle two "leaves". Their mean is .

The median is the center number when the data points are listed in ascending or descending order. To find the median, reorder the values in numerical order:

In this problem, the middle number, or median, is the third number, which is

The first step towards solving for the set, is to reorder the numbers from smallest to largest.

This gives us:

The median is equal to middle number in s a set. In since this set has 6 numbers, which is even, the average of the middle two numbers is the mean. The average can be found using the equation below:

Find the median of the following data set:

Begin by putting your numbers in increasing order:

Next, identify the median by choosing the middle value:

So, our answer is 55

Find the median of the following data set:

Let's begin by rearranging our terms from least to greatest:

Now, the median will be the middle term:

Find the median of the following data set:

First, let's put our terms in increasing order:

Now, we can find our median simply by choosing the middle term.

So, 56 is our median.

Find the median of the following data set:

First, let's put our terms in ascending order.

Now, our median will simply be the term which is in the middle.

So, our median is 67

To find the median of a data set, we will first arrange the numbers in ascending order. Then, we will locate the number in the center of the data set.

So, given the data set

we will arrange the numbers in ascending order. To do that, we will arrange them from smallest to largest. So, we get

Now, we will locate the number in the center of the data set.

We can see that it is 6.

Therefore, the median of the data set is 6.