# ISEE Upper Level Quantitative : Data Analysis

## 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?

(b)

It is impossible to tell from the information given.

(a) is greater.

(b) is greater.

(a) and (b) are equal.

(a) is greater.

Explanation:

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

Quantity A is greater.

The relationship cannot be determined from the information given.

The two quantities are equal.

Quantity B is greater.

Quantity B is greater.

Explanation:

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

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

The quantity of  is greater than

Explanation:

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

is greater

and are equal

It is not possible to tell from the information given

is greater

is greater

Explanation:

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

is greater

and are equal

is greater

It is not possible to tell from the information given

and are equal

Explanation:

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

and are equal

is greater

is greater

It is not possible to tell from the information given

is greater

Explanation:

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

It is not possible to tell from the information given

and are equal

is greater

is greater

is greater

Explanation:

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

is greater

is greater

It is not possible to tell from the information given

and are equal

is greater

Explanation:

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?

Explanation:

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

(B) is greater

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

(A) and (B) are equal

(A) is greater

(B) is greater

Explanation:

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