### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #1 : Mode

The data set below represents a class's scores on a recent math test. What is the mode score in the data set?

**Possible Answers:**

**Correct answer:**

The mode is simply the value that appears most often in a given data set. In this data set the value 77 appears three times. The value 68 appears twice. No other value appears more than once, which means 77 is the mode.

You may want to arrange the values in numerical order if it helps you see the repeating values, but it isn't required.

### Example Question #2 : Mode

Examine the data set . You are given that can be any integer from 1 to 10.

Which value(s) of would give the data set *no* mode?

**Possible Answers:**

Any integer from 1 to 10 except 5.

1, 3, 5, 7, or 9.

Only 5.

Any integer from 1 to 10.

This is impossible for any value of .

**Correct answer:**

Only 5.

The mode of a data set is the element that appears most frequently; a data set with no mode has all of its elements appear exactly once.

All of the integers from 1 to 10 except for 5 are known to appear in this data set at least once. If is equal to any of those integers, it is the only one repeated, and it is the mode. Only if can the set not have a repeated value. That makes this the correct choice.

### Example Question #3 : Mode

Give the mode(s) of the data set:

**Possible Answers:**

The data set has no mode.

**Correct answer:**

The mode of a data set is the element that appears most frequently. In this set, that element is , which appears three times. No other element appears more than twice.

### Example Question #4 : Mode

Give the mode(s) of the data set

**Possible Answers:**

The data set has no mode.

**Correct answer:**

The mode of a data set is the element that appears the most frequently. When two numbers both appear most frequently, there are two modes:

### Example Question #5 : Mode

Find the mode and the median of the frequency distribution shown in the following table:

**Possible Answers:**

**Correct answer:**

The mode is the value that appears most often or has more frequency which is in this problem. The total number of data values are . Since the number of values is odd, the median is the single middle value which is the value in this problem. So the median is .

### Example Question #6 : Mode

in the following set of data the mode is , what are the possible values for .

**Possible Answers:**

**Correct answer:**

The mode is the value that has more frequency in a given set of data than other values. Among the given frequencies in this problem, has the frequency of which is more than others. If is the mode, its frequency must be more than .

### Example Question #7 : Mode

The heights of the starting volleyball team for a high school are inches. Give the mode of this data set.

**Possible Answers:**

**Correct answer:**

The mode is the value that appears most often which is in this data set, because appears two times while all of the other values only appear one time.

### Example Question #8 : Mode

In the following set of scores find the mode:

**Possible Answers:**

**Correct answer:**

The mode is the value that appears most often or has more frequency in a given set of data. So in this problem, the mode is which occurs most frequently.

### Example Question #9 : Mode

Consider the data set . If the data set has only one mode, how many possible values of are there?

**Possible Answers:**

Infinitely many

**Correct answer:**

If then the value of is appears five times, more than any other element. This would give the set one mode.

If , then 4, 6, and the value of would appear three times each, more than any other element. This would give the set three modes.

If assumes any other value, then 4 and 6 would appear three times each, more than any other element. This would give the set two modes.

Therefore, there are only two values of that would give the set one mode.

### Example Question #10 : Mode

Consider the data set . For the data set to have exactly two modes, what are all of the possible choices of ?

**Possible Answers:**

**Correct answer:**

If , then the value of will occur in the set five times, more than any other element. This will give the set one mode.

If , then there will be three elements - - that occur three times, more than any other element. This will give the set three modes.

If is any other number, then there will be two elements - - that occur twice, more than any other number. This will give the set two modes.

Therefore, , and any other value of gives the set one mode.