### All ISEE Upper Level Quantitative Resources

## Example Questions

### 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:**

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:**

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

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

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

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 #21 : 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

(B) is greater

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

(A) is greater

**Correct answer:**

(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 #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

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 #121 : Data Analysis

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

**Possible Answers:**

(A) is greater

(A) and (B) are equal

(B) is greater

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

**Correct answer:**

(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 #32 : Mean

What is the average of the three numbers in the set below?

**Possible Answers:**

**Correct answer:**

The average is calculated by adding together the numbers in a set and dividing by the number of items:

### Example Question #121 : Data Analysis And Probability

The course average for a chemistry class is the mean of five test scores. Anne has scores so far; Barb has scores so far. Which is the greater quantity?

(a) The score Anne must make to average

(b) The score Barb must make to average

**Possible Answers:**

It is impossible to tell from the information given.

(a) is greater.

(b) is greater.

(a) and (b) are equal.

**Correct answer:**

(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 . This makes (b) greater.

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