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 #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 #22 : 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 : 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:

(A) and (B) are equal

(A) is greater

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

(B) 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

Example Question #23 : Mean

Eight judges scored Geri's gymnastics routine as follows:

The lowest score is disregarded to account for possible bias on the part of the judges. Geri's score is the mean of the scores that remain.

What is Geri's score, to the nearest tenth?

Possible Answers:

Correct answer:

Explanation:

The lowest score is 5, so this is disregarded; the remaining seven are averaged by dividing their sum by seven:

Example Question #23 : Mean

Eight judges scored Donna's gymnastics routine as follows:

The highest and lowest scores are disregarded to account for possible bias on the part of the judges. Donna's score is the mean of the scores that remain.

What is Donna's score, to the nearest tenth?

Possible Answers:

Correct answer:

Explanation:

The highest and lowest scores are 10 and 5, so these are disregarded; the remaining six are averaged by dividing their sum by six:

Example Question #25 : Mean

Seven judges scored Donna's gymnastics routine as follows:

The same seven judges scored Karen's routine as follows:

The highest and lowest scores are removed to account for possible bias on the part of the judges, and each gymnast is awarded the mean of the five remaining scores. 

Which is the greater quantity?

(A) Donna's score

(B) Karen's score

Possible Answers:

(A) is greater

(B) is greater

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

(A) and (B) are equal

Correct answer:

(A) and (B) are equal

Explanation:

The highest and lowest score in both lists is 5 and 9, respectively; when these are removed from both lists, the scores become

Donna: 

Karen: 

Each mean is calculated by adding the scores and dividing by five: 

Donna: 

Karen: 

The means - their scores - are equal.

Example Question #24 : Mean

A data set has six known quantities and two unknown quantities, as follows:

Which is the greater quantity?

(A) The mean of the data set if 

(B) The mean of the data set if   

Possible Answers:

(A) and (B) are equal

(B) is greater

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

(A) is greater

Correct answer:

(B) is greater

Explanation:

The mean of a data set is the sum of its elements divided by the number of elements. Since in both cases the sum is divided by six, it suffices to compare the sums of the elements.

 

Since  is greater in choice (B) than in choice (A), this sum, and, subsequently, the mean, is greater in choice (B).

Example Question #28 : Mean

Julie's final score in psychology is calculated by taking the mean of the best five of her six test scores. Julie received a final score of 85. Her first four test scores were 85, 98, 78, 80, and 84. Which is the greater quantity?

(A) Her sixth test score

(B) 75

Possible Answers:

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

(A) and (B) are equal

(A) is greater

(B) is greater

Correct answer:

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

Explanation:

The mean of Julie's first five test scores is

.

Since Julie's final score is 85, it can be deduced that Julie's fifth test score was the one that was dropped, so it must have been less than or equal to the least of the first five scores, 78. However, no further information can be determined; the score may have been greater than, less than, or equal to 75.

Example Question #29 : Mean

Sally's final score in economics is calculated by taking the mean of the best four of her five test scores. Sally received a final score of 78. Her first four test scores were 90, 80, 65, and 70. Which is the greater quantity?

(A) Her fifth test score

(B) 65

Possible Answers:

(A) and (B) are equal

(A) is greater

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

(B) is greater

Correct answer:

(A) is greater

Explanation:

Had Sally scored 65 or less on her fifth test, that would have been the dropped score, and her final score would have been the mean of 90, 80, 65, and 70. This is the sum of the scores divided by four:

Since Sally's mean was greater than this (78), it can be deduced that her fifth score was better than 65, and that the 65 was dropped. Therefore, (A) is greater.

Example Question #26 : Mean

Seven judges scored Sally's gymnastics routine as follows:

The highest and lowest scores are removed to account for possible bias on the part of the judges.

Which is the greater quantity?

(A) The mean of the seven scores?

(B) The mean of the five scores that remain after the highest score and the lowest score are removed?

Possible Answers:

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

(A) is greater

(A) and (B) are equal

(B) is greater

Correct answer:

(B) is greater

Explanation:

A mean is calculated by takng the sum of the elements and dividing by the number of elements.

The mean of the seven scores is

.

The lowest score is a 6; the highest is a 9, so the five scores remaining are 

.

The mean of the five scores is

.

Therefore (B) is greater.

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