ISEE Upper Level Quantitative : Data Analysis

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

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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.

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

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.

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

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 

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 

Possible Answers:

 is greater

and are equal

It is not possible to tell from the information given

 is greater

Correct answer:

 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 

 

Possible Answers:

 is greater

and are equal

is greater

It is not possible to tell from the information given

Correct answer:

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

 

Possible Answers:

and are equal

is greater

is greater

It is not possible to tell from the information given

Correct answer:

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 

 

Possible Answers:

It is not possible to tell from the information given

and are equal

 is greater

 is greater

Correct answer:

 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 

 

Possible Answers:

 is greater

 is greater

It is not possible to tell from the information given

and are equal

Correct answer:

 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?

Possible Answers:

Correct answer:

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

 

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

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

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