### All ISEE Middle Level Quantitative Resources

## Example Questions

### Example Question #1 : Mode

Kali decided to keep a log of how much money she spent on lunch at school each day for three weeks. Her data included the following numbers:

Week 1: $2.50, $3.00, $2.75, $3.00, $2.50

Week 2: $3.00, $2.50, $2.75, $2.50, $3.00

Week 3: $2.50, $2.75, $2.50, $3.00, $2.50

What is the mode of this data?

**Possible Answers:**

$

$

$

$

$

**Correct answer:**

$

In order to find mode, we must determine which number occurs most often in the data set. In this particular set, $ occurs times, $ occurs times, and $ occurs times. Since $ occurs the most often, it is the mode for this set of data.

### Example Question #1 : Mode

Which measure of central tendency would you use to find the term that is most occuring?

**Possible Answers:**

Range

Mode

Interquartile Range

Median

Mean

**Correct answer:**

Mode

Mode is the number that occurs most often, so that is the correct answer. Median is the middle number, while mean is the average of the set. Range is the difference between the greatest and least numbers.

### Example Question #1 : Mode

Give the mode of the data set

**Possible Answers:**

The data set has no mode.

**Correct answer:**

The data set has no mode.

No element in the data set appears more than once; for an element to have a mode, that element must appear at least twice. The set has no mode.

### Example Question #1 : Mode

Which is the greater quantity?

(A) The mode of the data set

(B) The median of the data set

**Possible Answers:**

(B) is greater

(A) and (B) are equal

It is impossible to determine which is greater from the information given

(A) is greater

**Correct answer:**

(B) is greater

Arrange the elements in ascending order.

The mode of the set is the element that appears most frequently, which here is 15.

The median of the set is the element that appears in the middle, which here is 19.

(B) is greater.

### Example Question #2 : Mode

Which is the greater quantity?

(A) The number of modes of the data set

(B)

**Possible Answers:**

(A) and (B) are equal

(A) is greater

It is impossible to determine which is greater from the information given

(B) is greater

**Correct answer:**

(B) is greater

The mode of a data set is the element that appears most frequently. The given data set has no repeated elements; it is considered to have *no* modes. (B) is greater.

### Example Question #2 : How To Find Mode

Consider the data set

Which of the following elements replaces the box to make 30 the mode of the data set?

**Possible Answers:**

None of the other responses is correct.

**Correct answer:**

None of the other responses is correct.

Regardless of what value replaces the box, 40 will still be the most frequently appearing element in the set (four times, more than any other element) - that is, 40 will be the mode.

### Example Question #3 : How To Find Mode

Consider the data set

Which of the following elements replaces the box to make 40 the mode of the data set?

(A)

(B)

(C)

**Possible Answers:**

Only (A) is correct.

(A), (B), and (C) are all correct.

Only (B) is correct.

None of (A), (B), or (C) are correct.

Only (C) is correct.

**Correct answer:**

(A), (B), and (C) are all correct.

Regardless of what value replaces the box, 40 will still be the most frequently appearing element in the set (four times, more than any other element). By definition, that makes 40 the mode.

### Example Question #3 : Mode

Which is the greater quantity?

(A) The number of modes of the data set

(B)

**Possible Answers:**

It is impossible to determine which is greater from the information given

(A) is greater

(B) is greater

(A) and (B) are equal

**Correct answer:**

(B) is greater

Arrange the data set in ascending order.

18 appears three times; 65 and 79 appear two times each; therefore, 18 is the only mode, and (B) is greater.

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