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

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

Which is the greater quantity?

(a) The range of the data?

(b)

Possible Answers:

(b) is greater

(a) and (b) are equal

(a) is greater

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, which is the range.

Example Question #1 :Range

Consider the set of numbers:

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.

Quantity B is greater.

The two quantities are equal.

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.

Quantity A is larger.

Example Question #2 :Range

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

Possible Answers:

The median is greater than the range

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

The range is greater than the median

The median and the range are equal

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:

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

So the range is greater than the median.

Example Question #3 :Range

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

Possible Answers:

The range is greater than the mean.

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

The mean is greater than the range.

The mean and the range are equal.

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:

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

So the mean is greater than the range.

Example Question #4 :Range

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

Possible Answers:

The mode is greater than the range.

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

The range is greater than the mode.

范围等于模式。

Correct answer:

范围等于模式。

Explanation:

The mode of a set of data is the value which occurs most frequently which isin this problem.

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

So the range is equal to the mode.

Example Question #1 :How To Find Range

Consider the following set of data:

Compareand.

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

: The range of the set

Possible Answers:

is greater

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

andare equal

is greater

Correct answer:

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:

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:

Thereforeis greater than.

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