ISEE Upper Level Math : Range

Study concepts, example questions & explanations for ISEE Upper Level Math

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Example Questions

Example Question #1 : Range

For tonight’s class reading, Erin was assigned to read Chapter 6, which begins on page 60 and ends on page 83. How many pages must Erin read tonight?

Possible Answers:

25

22

24

23

Correct answer:

24

Explanation:

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:

\displaystyle 83 - \displaystyle 60 \displaystyle =23

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.

Example Question #1 : How To Find Range

Consider the following set of scores from a math test. Give the range of the data.

 

\displaystyle \left \{ 88,72,61,84,77,79,93 \right \}

Possible Answers:

\displaystyle 31

\displaystyle 32

\displaystyle 33

\displaystyle 30

\displaystyle 35

Correct answer:

\displaystyle 32

Explanation:

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

 

\displaystyle Range=93-61=32

Example Question #111 : Data Analysis

In the following set of data, \displaystyle x has the smallest value. If the range of the data values is \displaystyle 26, give \displaystyle x.

\displaystyle \begin{matrix} Data \ Value & Frequency \\ 41 & 7\\ 33& 3\\35& 4\\x& 1 \end{matrix}

Possible Answers:

\displaystyle 12

\displaystyle 14

\displaystyle 20

\displaystyle 22

\displaystyle 15

Correct answer:

\displaystyle 15

Explanation:

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

 

\displaystyle 41-x=26\Rightarrow x=15

Example Question #1 : Range

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

\displaystyle \left.\begin{matrix} 4\\ 5\\ 6\\ 7\\ 8 \end{matrix}\right|\begin{matrix} \textrm{7 9}\; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \; \;\\ \textrm{4 4 7 7}\; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \\ \textrm{0 1 2 2 4 5 5 8 8 9}\\ \textrm{3 5 5 8}\; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \\ \textrm{4 7}\; \; \; \; \; \; \; \; \; \; \;\; \; \; \; \; \; \; \; \; \; \; \; \; \end{matrix}

What is the midrange of this data set?

Possible Answers:

\displaystyle 67

\displaystyle 64.5

\displaystyle 64

\displaystyle 65

Correct answer:

\displaystyle 67

Explanation:

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 \displaystyle \left (47 + 87 \right )\div 2 = 67, the midrange.

Example Question #112 : Data Analysis And Probability

What is the range of the following set of numbers?

\displaystyle 100, 98, 250, 78, 194, 207, 144

Possible Answers:

\displaystyle 172

\displaystyle 153

\displaystyle 144

\displaystyle 150

\displaystyle 250

Correct answer:

\displaystyle 172

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:

\displaystyle 78, 98, 100, 144, 194, 207, 250

\displaystyle 250 - 78 = 172

Thus, the range is 172.

Example Question #114 : Data Analysis

What is the range of the following 5 numbers?

\displaystyle 17, 13, 22, 6, 12

Possible Answers:

\displaystyle 15

\displaystyle 16

\displaystyle 13

\displaystyle 14

Correct answer:

\displaystyle 16

Explanation:

The range of a set is determined by subtracting the smallest number from the largest number:
\displaystyle range=22-6=16

Example Question #1 : How To Find Range

What is the range of the following series of numbers?

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

Possible Answers:

\displaystyle 40

\displaystyle 22

\displaystyle 16

\displaystyle 24

Correct answer:

\displaystyle 40

Explanation:

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:

\displaystyle range=47-7=40

Example Question #2 : How To Find Range

Find the range of the following data set:

\displaystyle 45,67,12,34,55,88,67,343,49

Possible Answers:

\displaystyle 84

\displaystyle 55

\displaystyle 331

\displaystyle 67

Correct answer:

\displaystyle 331

Explanation:

Find the range of the following data set:

\displaystyle 45,67,12,34,55,88,67,343,49

Begin by putting your numbers in increasing order:

\displaystyle 12,34,45,49,55,67,67,88,343

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

\displaystyle Range=343-12=331

So our answer is 331

Example Question #2 : Range

Find the range of the following data set:

\displaystyle 5,76,12,34,55,89,76,109,67,33,9

 

Possible Answers:

\displaystyle 51

\displaystyle 76

\displaystyle 55

\displaystyle 104

Correct answer:

\displaystyle 104

Explanation:

Find the range of the following data set:

\displaystyle 5,76,12,34,55,89,76,109,67,33,9

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

\displaystyle 5,9,12,33,34,55,67,76,76,89,109

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

\displaystyle 109-5=104

So, our answer is 104

Example Question #3 : How To Find Range

Find the range of the following data set:

\displaystyle 34,56,76,12,33,43,98,99,77,93,33

Possible Answers:

\displaystyle 33

\displaystyle 59

\displaystyle 87

\displaystyle 56

Correct answer:

\displaystyle 87

Explanation:

Find the range of the following data set:

\displaystyle 34,56,76,12,33,43,98,99,77,93,33

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

\displaystyle 12,33,33,34,43,56,76,77,93,98,99

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

\displaystyle 99-12=87

So our range is 87.

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