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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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Example Questions

Example Question #1 : How To Find Range

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:

(a) is greater

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

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 #2 : How To Find 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:

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

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 #3 : How To Find Range

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

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

Possible Answers:

The range is greater than the median

The median and the range are equal

The median is greater than the range

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

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 #4 : How To Find Range

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

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

Possible Answers:

The mean and the range are equal.

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

The mean is greater than the range.

The range is greater than the mean.

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 #5 : How To Find Range

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:

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 greater than the mode.

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 #3 : How To Find Range

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:

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

(a) and (b) are equal

(a) is greater

(b) is greater

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 #1 : How To Find Range

Example Question #2 : How To Find Range

Example Question #3 : How To Find Range

Example Question #4 : How To Find Range

Example Question #5 : How To Find Range

Example Question #3 : How To Find Range

All ISEE Upper Level Quantitative Resources

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