# ISEE Middle Level Quantitative : How to find range

## Example Questions

### Example Question #1 : How To Find Range

Which is the greater quantity?

(A) The midrange of the data set

(B) The midrange of the data set

It is impossible to determine which is greater from the information given

(A) and (B) are equal

(A) is greater

(B) is greater

(A) is greater

Explanation:

The midrange of a data set is the mean of its least and greatest elements. The midrange of the first data set is ; that of the second data set is . (A) is greater.

### Example Question #2 : How To Find Range

Set  is defined as:

Set  is made by doubling the values in set .

What is the range of values in set ?

Explanation:

To find the range of a set of numbers, you do not even have to put them in order.  You merely need to subtract the smallest value from the largest.  Given the way of constructing set  by doubling set 's values, the largest and smallest values in  will directly correlate to the same in set :

Smallest:

Largest:

Therefore, the range  is:

### Example Question #3 : How To Find Range

The members of set  are defined as the values for:

For values of  between  and .

What is the range of set ?

Explanation:

To find the range of a set of numbers, you do not even have to put them in order. You merely need to subtract the smallest value from the largest. Given the way that we construct set  from the function , we merely need to use that function to find the smallest and largest values. Luckily, that is pretty easy for this question. The smallest will be  and the largest will be

Smallest:

Largest:

Therefore, the range  is:

### Example Question #4 : How To Find Range

Set  is defined as:

The members of set  are defined by the function:

, where  is a member of set .

So, for instance, set T contains  because for , we get:

What is the range of set ?

Explanation:

We first need to determine the members of set . Using our function, we will get:

Our largest value is , and our smallest value is ; therefore, the range is

### Example Question #5 : How To Find Range

Given the below set of numbers find the range:

Explanation:

Range for a set of data is defined as the difference between the biggest and smallest number.

First we find the biggest number which is 15, we then subtract the smallest number in this set which is negative 2 as shown below:

Remember, when subtracting a negative number we must add the numbers.

### Example Question #6 : How To Find Range

Given the below set of numbers, find the range:

Explanation:

In order to find the range, we must subtract the smallest number from the biggest number.

We must convert the fractions to have a common denominator which is 10.

Therefore, the range of this set is

.

### Example Question #7 : How To Find Range

Given the below set of numbers, find the range:

Explanation:

In order to find the range, we must subtract the smallest number from the biggest number.

We must convert the fractions to have a common denominator which is 10.

Therefore, the range of this set is

.