ISEE Upper Level Quantitative : Data Analysis and Probability
Study concepts, example questions & explanations for ISEE Upper Level Quantitative
All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #121 : Data Analysis And Probability
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 #122 : Data Analysis And Probability
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 #123 : Data Analysis And Probability
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
(B) is greater
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(A) is greater
(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 #124 : Data Analysis And Probability
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 
(B) is greater
(A) and (B) are equal
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 #125 : Data Analysis And Probability
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
It is impossible to determine which is greater from the information given
(A) and (B) are equal
(A) is greater
(B) is greater
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 #126 : Data Analysis And Probability
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
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(A) is greater
(B) is greater
(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 #127 : Data Analysis And Probability
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?
(A) is greater
(A) and (B) are equal
It is impossible to tell which is greater from the information given
(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.
Example Question #31 : How To Find Mean
In the first round of a gymnastics competition, six judges scored Rhonda's routine as follows:
In the second round, eight judges scored her routine as follows:
In each round, 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 remaining scores.
Which is the greater quantity?
(A) Rhonda's first round score
(B) Rhonda's second round score
(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
Rhonda's highest and lowest scores in the first round were 10 and 5, so her score in the first round was the mean of the scores
This is the sum of the four scores divided by four, or
Rhonda's highest and lowest scores in the second round were 10 and 6, so her score in the first round was the mean of the scores
This is the sum of the six scores divided by six, or
(A) is greater.
Example Question #128 : Data Analysis And Probability
What is the average of the three numbers in the set below?
The average is calculated by adding together the numbers in a set and dividing by the number of items:
Example Question #33 : How To Find Mean
The course average for a chemistry class is the mean of five test scores. Anne has scores 
(a) The score Anne must make to average
(b) The score Barb must make to average
It is impossible to tell from the information given.
(a) is greater.
(b) is greater.
(a) and (b) are equal.
(b) is greater.
The only real comparison that needs to be made is between the two students' totals; the one with the lesser total needs a greater score to average .
(a) Anne's total:
(b) Barb's total:
Barb has fewer points so she needs more points to average 
All ISEE Upper Level Quantitative Resources
