### All ISEE Upper Level Quantitative Resources

## Example Questions

### Example Question #111 : Data Analysis And Probability

Katie's grade in her Shakespeare class is the mean of her best five test scores out of six tests taken.

Her test scores are .

Which is the greater quantity?

(a) Katie's grade

(b)

**Possible Answers:**

It is impossible to tell from the information given.

(a) is greater.

(b) is greater.

(a) and (b) are equal.

**Correct answer:**

(a) is greater.

Take the sum of all of her test scores except for her lowest and divide that by the number of test scores included.

### Example Question #11 : How To Find Mean

Consider the following set of numbers:

Quantity A: Median of the set

Quantity B: Mean of the set

**Possible Answers:**

Quantity A is greater.

The relationship cannot be determined from the information given.

The two quantities are equal.

Quantity B is greater.

**Correct answer:**

Quantity B is greater.

The median of the set of numbers is determined by arranging the numbers in numerical order and finding the middle number. In this case there are two middle numbers, and , so we find the average of those numbers, which gives us .

The mean is found by dividing the sum of elements by the number of elements in the set:

Quantity B is larger.

### Example Question #11 : How To Find Mean

Compare and :

The average of

The average of

**Possible Answers:**

It is not possible to determine which quantity is greater.

The two quantities are equal.

The quantity of is greater than

The quantity of is greater than

**Correct answer:**

The quantity of is greater than

The average of a list of terms can be found as follows:

So we can write:

So is greater than

### Example Question #11 : How To Find Mean

Which one is greater:

The mean of the data set

The mean of the data set

**Possible Answers:**

is greater

and are equal

It is not possible to tell from the information given

is greater

**Correct answer:**

is greater

Mean of a data set is the sum of the data set values divided by the number of data:

So we have:

So the mean of the first data set is greater.

### Example Question #12 : How To Find Mean

Which one is greater:

The mean of the data set

**Possible Answers:**

is greater

and are equal

is greater

It is not possible to tell from the information given

**Correct answer:**

and are equal

Mean of a data set is the sum of the data set values divided by the number of data:

So we have:

### Example Question #13 : How To Find Mean

Which is greater:

The mean of the data set

**Possible Answers:**

and are equal

is greater

is greater

It is not possible to tell from the information given

**Correct answer:**

is greater

Mean of a data set is the sum of the data set values divided by the number of data:

So we have:

So the mean of the data set is greater than

### Example Question #17 : Mean

Which one is greater:

The mean of the data set

**Possible Answers:**

It is not possible to tell from the information given

and are equal

is greater

is greater

**Correct answer:**

is greater

Mean of a data set is the sum of the data set values divided by the number of data:

So we have:

So the mean of the data set is smaller than .

### Example Question #21 : Mean

Which one is greater:

The mean of the data set

**Possible Answers:**

is greater

is greater

It is not possible to tell from the information given

and are equal

**Correct answer:**

is greater

Mean of a data set is the sum of the data set values divided by the number of data:

So we have:

So the mean of the data set is greater than .

### Example Question #21 : How To Find Mean

A set of four numbers has a mean of 21. If one more number was added and the new mean was 20, what was the number that was added?

**Possible Answers:**

**Correct answer:**

Start by writing out what you know. We know that four numbers had a mean of 21. That would look like this: . Therefore, we can determine what the sum of the four numbers was by soliving for x. The sum is 84. If we know that info, we can make a new equation for the new mean, which looks like this: . Since we don't know what the new number is, we can just call it x. Solve this proportion to get your missing number. then yields x as 16.

### Example Question #22 : How To Find Mean

You are given the following data set:

Which of the following is the greater quantity?

(A) The mean of the data set

(B) The median of the data set

**Possible Answers:**

(B) is greater

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

(A) and (B) are equal

(A) is greater

**Correct answer:**

(B) is greater

The mean of the data set is the sum of the elements divided by the quantity - eight, in this case:

The median of the data set is the value in the middle - or, since there is an even number of elements, it is the mean of the fourth-highest and the fourth-lowest elements. We arrange the elements in ascending order:

The median is the arithmetic mean of 18 and 19:

(B) is the greater quantity

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