How to find range - ISEE Upper Level Quantitative Reasoning

Quantity A: The median (middle number) is , and the mode (most common number) is , so the sum of the two numbers is .

Quantity B: The range is the smallest number subtracted from the largest number, which is .

Quantity A is larger.

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

The range of a data set is the difference of the high and low values. The highest value represented is 87 (7 is the last "leaf" in the bottom, or, 8, row); the low value is 47 (7 is the first "leaf" in the top, or, 4, row). The difference is , which is the range.

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:

The median is the average of the two middle values of a set of data with an even number of values. So we have:

So we have:

The range is the difference between the lowest and the highest values. So we have:

Therefore is greater than .

The median is the average of the two middle values of a set of data with an even number of values. So we have:

The range is the difference between the lowest and the highest values. So we have:

So the range is greater than the median.

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:

The range is the difference between the lowest and the highest values. So we have:

So the mean is greater than the range.

The mode of a set of data is the value which occurs most frequently which is in this problem.

The range is the difference between the lowest and the highest values. So we have:

So the range is equal to the mode.

Erin will start reading on page 60 and will stop reading on page 83.

If you subtract these two numbers, you will get the number of pages between 60 and 83:

-

However, this subtraction does not include the first page read - page 60. Consider a similar, more simpler case: reading from pages 1 to 3. There are three pages read there: 1, 2, and 3. If you subtract, you get an answer of 2, which leaves you one page short of what you actually read.

So when you subtract 60 from 83, it gives you the pages between those two markers. You need to add on one more page to get your total page count - that is, to include page 60.

Therefore, Erin will read 24 pages.

Reorder the numbers from smallest to largest:

7, 14, 19, 22, 30, 31, 47

The range is the difference between the largest and smallest values:

The range is a measure of spread. It is the difference between the largest and the smallest data values. So we get:

The range is a measure of spread. It is the difference between the largest and the smallest data values. So we can write:

To determine the range, first order the numbers in order from least to greatest. Then, find the difference between the greatest number and the least number:

Thus, the range is 172.

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

The midrange of a data set is the arithmetic mean of its greatest and least values, which, in this case, are 47 and 87. Their arithmetic mean is , the midrange.

The range of a set is determined by subtracting the smallest number from the largest number:

Find the range of the following data set:

Begin by putting your numbers in increasing order:

Next, find the range by subtracting our first number from our last number:

So our answer is 331

Find the range of the following data set:

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

Now, find the difference between our largest and smallest terms:

So, our answer is 104

Find the range of the following data set:

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

Next, our range will just be the difference between the greatest and least terms.

So our range is 87.

Find the range of the following data set:

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

Now, find the difference between our first and last terms.

So, our range is 82.

To find the range of a data set, we will find the smallest and the largest number. Then, we will find the difference of those two numbers.

So, given the set

we can see the smallest number is 2 and the largest number is 9. Now, we will find the difference. To find the difference, we will simply subtract the two numbers. So,

Therefore, the range of the data set is 7.

To find the range of a data set, we will find the smallest and the largest number within the set, then we will find the difference.

So, given the set

we can see the smallest number is 1 and the largest number is 10. Now, we will find the difference. To find the difference, we will subtract the two numbers. So, we get

Therefore, the range of the data set is 9.

In order to find the range, you will need to first find the smallest and largest number in the set.

For this set of numbers, the smallest number is , and the largest number is .

To find the range, take the difference of these two numbers: