How to find range

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ISEE Upper Level Quantitative Reasoning › How to find range

Questions 1 - 10
1

Examine this stem-and-leaf diagram for a set of data:

Which is the greater quantity?

(a) The range of the data?

(b)

(a) and (b) are equal

(a) is greater

(b) is greater

It is impossible to tell from the information given

Explanation

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.

2

Consider the following set of data:

Compare and .

: The sum of the median and the mean of the set

: The range of the set

is greater

is greater

and are equal

It is not possible to compare the mean and the mode based on the information given.

Explanation

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 .

3

Find the range of the following data set:

Explanation

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.

4

Use the following data set to answer the question:

Find the range.

Explanation

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 number.

So, given the set

we can see the smallest number is 5 and the largest number is 17.

Now, we will find the difference. To find the difference, we will subtract the two number. We get

Therefore, the range of the data set is 12.

5

What is the range of the following set of numbers?

Explanation

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.

6

In the following set of data compare the median and the range:

The range is greater than the median

The median is greater than the range

The median and the range are equal

It is not possible to compare the mean and the mode based on the information given

Explanation

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.

7

Find the range of the following data set:

Explanation

Find the range of the following data set:

To find the range, first put the numbers in increasing order

Next, find the difference between our first and last terms

Thus, our range is 87 because there is a "distance" of 87 between our biggest and smallest terms.

8

Find the range of the following data set:

Explanation

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.

9

Consider the set of numbers:

Quantity A: The sum of the median and mode of the set

Quantity B: The range of the set

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Explanation

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.

10

In the following set of data compare the mean and the range:

The mean is greater than the range.

The range is greater than the mean.

The mean and the range are equal.

It is not possible to compare the mean and the mode based on the information given

Explanation

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.

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