### All ISEE Upper Level Quantitative Resources

## Example Questions

### Example Question #1 : Range

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:**

It is impossible to tell from the information given

(a) and (b) are equal

(a) is greater

(b) is greater

**Correct answer:**

(a) and (b) are equal

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 #2 : How To Find 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 two quantities are equal.

The relationship cannot be determined from the information given.

Quantity B is greater.

Quantity A is greater.

**Correct answer:**

Quantity A is greater.

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 #1 : How To Find Range

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

**Possible Answers:**

The median and the range are equal

The median is greater than the range

The range is greater than the median

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

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 #2 : Range

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

**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 range is greater than the mean.

The mean is greater than the range.

**Correct answer:**

The mean is greater than the range.

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 #1 : Range

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

**Possible Answers:**

The mode is greater than the range.

The range is greater than the mode.

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

The range is equal to the mode.

**Correct answer:**

The range is equal to the mode.

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:

So the range is equal to the mode.

### Example Question #4 : Range

Consider the following set of data:

Compare and .

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

: The range of the set

**Possible Answers:**

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

and are equal

is greater

is greater

**Correct answer:**

is greater

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:

Therefore is greater than .

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