ISEE Upper Level Quantitative : Mean
Study concepts, example questions & explanations for ISEE Upper Level Quantitative
All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #21 : How To Find Mean
Which one is greater:
It is not possible to tell from the information given
Mean of a data set 
So we have:
So the mean of the data set is greater than 
Example Question #22 : 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?
Start by writing out what you know. We know that four numbers had a mean of 21. That would look like this: 
Example Question #23 : 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
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(A) is greater
(B) is greater
(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
Example Question #24 : How To Find 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?
The lowest score is 5, so this is disregarded; the remaining seven are averaged by dividing their sum by seven:
Example Question #25 : How To Find 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?
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 #26 : How To Find 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
(A) is greater
It is impossible to determine which is greater from the information given
(B) is greater
(A) and (B) are equal
(A) and (B) are equal
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 #27 : How To Find 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 
(A) and (B) are equal
(B) is greater
It is impossible to determine which is greater from the information given
(A) is greater
(B) is greater
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 
Example Question #21 : 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
(A) is greater
(B) is greater
It is impossible to determine which is greater from the information given
(A) and (B) are equal
It is impossible to determine which is greater from the information given
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 #22 : 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
(B) is greater
(A) is greater
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(A) is greater
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 #612 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
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?
It is impossible to tell which is greater from the information given
(A) is greater
(A) and (B) are equal
(B) is greater
(B) is greater
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.
All ISEE Upper Level Quantitative Resources
