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ISEE Upper Level Quantitative : How to find range

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

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All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #631 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

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

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

Which is the greater quantity?

(a) The range of the data?

(b)

Possible Answers:

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(a) is greater

Correct answer:

(a) and (b) are equal

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 87 - 47 = 40 , which is the range.

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Example Question #1 : Range

Consider the set of numbers: $\left \{ 2,4,5,5,6,6,6,10,12\right \}$

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

Quantity B: The range of the set

Possible Answers:

The relationship cannot be determined from the information given.

The two quantities are equal.

Quantity B is greater.

Quantity A is greater.

Correct answer:

Quantity A is greater.

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 12-2=10 .

Quantity A is larger.

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Example Question #2 : Range

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

$\left \{ 2,4,7,8\right \}$

Possible Answers:

The median and the range are equal

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

The median is greater than the range

The range is greater than the median

Correct answer:

The range is greater than the median

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:

$Median=\frac{4+7}{2}=5.5$

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

$Range = Maximum\ Value-Minimum\ Value=8-2=6$

So the range is greater than the median.

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Example Question #1 : Range

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

$\left \{ 4,3,8,8\right \}$

Possible Answers:

The range is greater than the mean.

The mean is greater than the range.

The mean and the range are equal.

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

Correct answer:

The mean is greater than the range.

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:

$Mean = \frac{4+3+8+8}{4}=\frac{23}{4}=5.75$

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

$Range = Maximum\ Value-Minimum\ Value=8-3=5$

So the mean is greater than the range.

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Example Question #152 : Data Analysis And Probability

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

$\left \{ 1,1,1,2,2,2,2,3,3\right \}$

Possible Answers:

The range is greater than the mode.

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

The mode is greater than the range.

The range is equal to the mode.

Correct answer:

The range is equal to the mode.

Explanation:

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:

$Range = Maximum\ Value-Minimum\ Value=3-1=2$

So the range is equal to the mode.

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Example Question #153 : Data Analysis And Probability

Consider the following set of data:

$\left \{ 2,4,4,5,6,10 \right \}$

Compare (a) and (b) .

(a) : The sum of the median and the mean of the set

(b) : The range of the set

Possible Answers:

(a) is greater

(a) and (b) are equal

(b) is greater

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

Correct answer:

(a) is greater

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:

$Mean = \frac{2+4+4+5+6+10}{6}=\frac{31}{6}\approx 5.17$

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

$Median=\frac{4+5}{2}=4.5$

So we have:

$Median+Mean\approx 4.5+5.17\approx 9.67$

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

$Range = Maximum\ Value-Minimum\ Value=10-2=8$

Therefore (a) is greater than (b) .

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All ISEE Upper Level Quantitative Resources

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ISEE Upper Level Quantitative : How to find range

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #631 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #1 : Range

Example Question #2 : Range

Example Question #1 : Range

Example Question #152 : Data Analysis And Probability

Example Question #153 : Data Analysis And Probability

All ISEE Upper Level Quantitative Resources

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