ISEE Upper Level Quantitative : How to find mean

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

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Example Questions

Example Question #11 : Mean

John's grade in his economics class is the mean of his best five test scores out of the six tests he takes.

John's first five test scores are:

Which is the greater quantity?

(a) The lowest score John must take to achieve a score of at least a score of  for the term

(b) 

Possible Answers:

(a) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

(b) is greater.

Correct answer:

(b) is greater.

Explanation:

John's current point sum is .

Even if John achieves a score lower than  on his sixth test, he will have at least  points and a minimum mean of at least . He can even score zero points on his last test and keep his average above what he wants, making (b) greater.

Example Question #12 : Mean

A student's grade in Professor Jackson's Shakespeare class is the mean of his or her four best test scores out of five. 

Craig and his brother Jerry have been in a friendly competition to see who can get the best grade in the class. 

Craig outscored Jerry on the first test by 9 points and on the fifth test by 5 points. Jerry outscored Craig by 6 points on the second test and by 8 points on the fourth. Their scores were identical on the third.

Which is the greater quantity? 

(a) Craig's grade 

(b) Jerry's grade

Possible Answers:

It is impossible to tell from the information given.

(b) is greater.

(a) and (b) are equal.

(a) is greater.

Correct answer:

It is impossible to tell from the information given.

Explanation:

This question cannot be answered. 

Let  stand for Jerry's total score after his lowest test is thrown out.

We need to compare the sums after the lowest test for each student is disregarded, since each will be divided by the four tests. But it is not known which test will be thrown out for each student. 

If, for example, the first test is thrown out for both Craig and Jerry, Craig's total will be

,

and Jerry's score will be higher.

If the second test is thrown out for both Craig and Jerry, Craig's total will be

,

and Craig's score will be higher.

Example Question #11 : Mean

A student's grade in Professor Kalton's abstract algebra class is the mean of his or her five test scores. 

Philip outscored Kellie on the first test by 8 points and on the second test by 5 points. They scored the same on the third test. Kellie outscored Philip by 7 points on the fourth test and by 6 points on the fifth.

Which is the greater quantity? 

(a) Philip's grade 

(b) Kellie's grade

Possible Answers:

(a) and (b) are equal.

It is impossible to tell from the information given.

(a) is greater.

(b) is greater.

Correct answer:

(a) and (b) are equal.

Explanation:

You do not need to take the two means; just compare the sums, since each will be divided by 5.

Let  be Kellie's total points. Then since Philip outscored Kellie by 8 points and 5 points on two tests and scored fewer than Kellie by 7 points and 6 points on two tests, Philip's score is 

.

Philip and Kellie scored the same number of points, making their mean test scores the same.

Example Question #591 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

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 #13 : Mean

Compare and :

 

The average of 

The average of

Possible Answers:

The two quantities are equal.

It is not possible to determine which quantity is greater.

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:

It is not possible to tell from the information given

and are equal

is greater

 is greater

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 #16 : Mean

Which is greater:

 

The mean of the data set

 

Possible Answers:

It is not possible to tell from the information given

is greater

is greater

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 #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 .

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