Mean - ISEE Upper Level Quantitative Reasoning
Card 1 of 152
Alice's numeric grade in her physics class is determined by four equally weighted hourly tests and a final, weighted twice as much as an hourly test. The highest score possible on each is 100.
Going into finals week, Alice's hourly test scores are 76, 85, 82, and 87. What must Alice make on her final, at minimum, in order to average 90 or more for the term?
Alice's numeric grade in her physics class is determined by four equally weighted hourly tests and a final, weighted twice as much as an hourly test. The highest score possible on each is 100.
Going into finals week, Alice's hourly test scores are 76, 85, 82, and 87. What must Alice make on her final, at minimum, in order to average 90 or more for the term?
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Alice's grade is a weighted mean in which her hourly tests have weight 1 and her final has weight 2. If we call 
her final, then her term score will be
,
which simplifies to
.
Since she wants her score to be 90 or better, we solve this inequality:
Since it is established that 100 is the maximum score, Alice cannot achieve an average of 90 or more for the term.
Alice's grade is a weighted mean in which her hourly tests have weight 1 and her final has weight 2. If we call
which simplifies to
Since she wants her score to be 90 or better, we solve this inequality:
Since it is established that 100 is the maximum score, Alice cannot achieve an average of 90 or more for the term.
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Sally's numeric grade in her economics class is determined by four equally weighted hourly tests, a midterm weighted twice as much as an hourly test, and a final weighted three times as much as an hourly test. The highest score possible on each is 100.
Going into finals week, Sally's hourly test scores are 89, 85, 84, and 87, and her midterm score is 93. What must Sally make on her final at minimum in order to average 90 or more for the term?
Sally's numeric grade in her economics class is determined by four equally weighted hourly tests, a midterm weighted twice as much as an hourly test, and a final weighted three times as much as an hourly test. The highest score possible on each is 100.
Going into finals week, Sally's hourly test scores are 89, 85, 84, and 87, and her midterm score is 93. What must Sally make on her final at minimum in order to average 90 or more for the term?
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Sally's grade is a weighted mean in which her hourly tests have weight 1, her midterm has weight 2, and her final has weight 3. If we call 
her score on the final, then her course score will be
,
which simplifies to
.
Since Sally wants at least a 90 average for the term, we can set up and solve the inequality:
Sally must score at least 93 on the final.
Sally's grade is a weighted mean in which her hourly tests have weight 1, her midterm has weight 2, and her final has weight 3. If we call
which simplifies to
Since Sally wants at least a 90 average for the term, we can set up and solve the inequality:
Sally must score at least 93 on the final.
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Fred's course average in French class is the average of the best five of his six hourly test scores. Going into finals week, Fred has scores of 78, 77, 84, 89, and 72. How much, at minimum, must Fred score on his sixth test in order to make an average of 80 or better for the term?
Fred's course average in French class is the average of the best five of his six hourly test scores. Going into finals week, Fred has scores of 78, 77, 84, 89, and 72. How much, at minimum, must Fred score on his sixth test in order to make an average of 80 or better for the term?
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If Fred does not take the sixth test or gets a 0 on it, he will receive the average of his first five tests. This is
.
Since he can only improve his class grade by taking the sixth test, Fred is already assured of an average of 80 or better.
If Fred does not take the sixth test or gets a 0 on it, he will receive the average of his first five tests. This is
Since he can only improve his class grade by taking the sixth test, Fred is already assured of an average of 80 or better.
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The mean of six numbers is 77. What is their sum?
The mean of six numbers is 77. What is their sum?
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The mean of six numbers is their sum divided by 6, so the sum is the mean multiplied by 6. This is:
The mean of six numbers is their sum divided by 6, so the sum is the mean multiplied by 6. This is:
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Eric has taken four tests in his English class. His scores on the tests are 94, 87, 95, and 89. The upcoming final exam will be weighted as much as each of the previous four tests. What is the lowest score Eric can get on the final exam and still have a mean score of no less than 90?
Eric has taken four tests in his English class. His scores on the tests are 94, 87, 95, and 89. The upcoming final exam will be weighted as much as each of the previous four tests. What is the lowest score Eric can get on the final exam and still have a mean score of no less than 90?
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The first step here, since you're working with the average (or mean), is to determine what is the sum of five test scores that will result in Eric earning at least a mean score of 90.
Start with the fact that he will need to make at least a 90 for his average score. Since you already have the average score, you're working backwards. You need to multiply 90 by 5 for the 5 test scores that will be used to get that average:
This tells you that the five scores - the four test scores and the final exam - will need to add up to at least 450 in total.
You know the four original test scores, so you can add those up:
So you know the four test scores add up to 365. To get an average of at least 90, the fifth score must bring that sum to at least 450. To find the minimum final exam test score, you subtract 365 from 450:
This tells you that Eric must score at least an 85 on the final exam to achieve an overall mean score of 90.
The first step here, since you're working with the average (or mean), is to determine what is the sum of five test scores that will result in Eric earning at least a mean score of 90.
Start with the fact that he will need to make at least a 90 for his average score. Since you already have the average score, you're working backwards. You need to multiply 90 by 5 for the 5 test scores that will be used to get that average:
This tells you that the five scores - the four test scores and the final exam - will need to add up to at least 450 in total.
You know the four original test scores, so you can add those up:
So you know the four test scores add up to 365. To get an average of at least 90, the fifth score must bring that sum to at least 450. To find the minimum final exam test score, you subtract 365 from 450:
This tells you that Eric must score at least an 85 on the final exam to achieve an overall mean score of 90.
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Consider the time Becky spends doing homework each night. What is the average number of hours Becky spends on homework each night (consider only Monday-Thursday)?
Monday: 3.2 hours
Tuesday: 1.1 hours
Wednesday: 2.7 hours
Thursday: 0.9 hours
Consider the time Becky spends doing homework each night. What is the average number of hours Becky spends on homework each night (consider only Monday-Thursday)?
Monday: 3.2 hours
Tuesday: 1.1 hours
Wednesday: 2.7 hours
Thursday: 0.9 hours
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To calculate the average, find the sum of the total hours divided by the number of nights:
To calculate the average, find the sum of the total hours divided by the number of nights:
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The mean of the following numbers is 
. Solve for 
.
The mean of the following numbers is
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The mean is determined by dividing the sum of the values by the total number of values:
The mean is determined by dividing the sum of the values by the total number of values:
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David's course score in a chemistry course is the mean of five tests. He has scored 
and 
. What must he score on the fifth test to be assured of a course score of 
?
David's course score in a chemistry course is the mean of five tests. He has scored
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Let 
be the minimum fifth test score. Then the average of the scores is
.
, the minimum score David needs.
Let
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A gymnastics meet has seven judges. After each routine, each judge assigns a merit-based score from 0 to 10; a contestant's score for the routine is the mean of all the judges' scores except for the highest and the lowest.
The seven judges individually assigned the following scores to one of Donna's routines: 
. What is Donna's score, rounded to the nearest tenth?
A gymnastics meet has seven judges. After each routine, each judge assigns a merit-based score from 0 to 10; a contestant's score for the routine is the mean of all the judges' scores except for the highest and the lowest.
The seven judges individually assigned the following scores to one of Donna's routines:
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The highest and lowest scores, 
and 
, are tossed out, so Donna's score is the mean of the five that remain.
The highest and lowest scores,
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The heights of a football team's members are 
and 
inches. Find the mean of the heights.
The heights of a football team's members are
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The mean is the sum of all the data values divided by the number of values. So we can write:
The mean is the sum of all the data values divided by the number of values. So we can write:
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The mean of five numbers is 
. Give their sum.
The mean of five numbers is
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The mean of five numbers is equal to their sum divided by 
, or as a formula we can write:
Where:
is the mean of a data set, 
indicates the sum of the data values 
, and 
is the number of data values. So we can write:
The mean of five numbers is equal to their sum divided by
Where:
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The sum of 
numbers is 
. Find the mean in terms of 
. (
is a real number)
The sum of
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The mean of eight numbers is equal to their sum divided by 
or as a formula we can write:
The mean of eight numbers is equal to their sum divided by
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The sum of a set of values is 
. If the mean of the data set is 
, give the number of values in the set.
The sum of a set of values is
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Mean of the scores can be calculated as:
Where:
is the mean of a data set, indicates the sum of the data values , and is the number of data values. So we can write:
Mean of the scores can be calculated as:
Where:
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The mean of 
test scores is 
. When the 
student takes the test, the mean goes down by two points. Give the 
score.
The mean of
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The total of 
test scores is 
. The mean of the total scores for 
students would be:
Where:
is the mean of a data set, 
indicates the sum of the data values 
and 
is the number of data values. So we can write:
The total of
Where:
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The sum of 
test scores is 
. When the 
student takes the test and gets a score of 
, how does the mean change?
The sum of
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The mean is the sum of the data values divided by the number of values or as a formula we have:
Where:
is the mean of a data set, 
indicates the sum of the data values 
and 
is the number of data values. The total of 
test scores is 
; the mean of the scores is:
When the 
student takes the test the sum of scores would be 
and the new mean of the scores is:
The mean is the sum of the data values divided by the number of values or as a formula we have:
Where:
When the
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The sum of 
test scores is 
. When the 
student takes the test, the mean of the scores does not change. Give the score of the 
student.
The sum of
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The mean is the sum of the data values divided by the number of values or as a formula we have:
Where:
is the mean of a data set, indicates the sum of the data values and is the number of data values. So we have:
When the 
student takes the test the mean of the score does not change. Let:
student score. So we can write:
That means the 
student should get the score of 
which is equal to the initial mean in order to get the same value for the new mean.
The mean is the sum of the data values divided by the number of values or as a formula we have:
Where:
When the
That means the
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What is the mean of the following numbers?
What is the mean of the following numbers?
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The mean is equal to the sum of the values divided by the total number of values (
).
The mean is equal to the sum of the values divided by the total number of values (
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What is the median of the following set?
What is the median of the following set?
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The median is the middle number in a set when the numbers are ordered from smallest to largest. The first step is to rearrange the numbers from smallest to largest.
Given that there are 5 items in this set, the median will be the third number (which is the middle number. That number is 4, the correct answer.
The median is the middle number in a set when the numbers are ordered from smallest to largest. The first step is to rearrange the numbers from smallest to largest.
Given that there are 5 items in this set, the median will be the third number (which is the middle number. That number is 4, the correct answer.
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What is the mean of the set below?
What is the mean of the set below?
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The first step to finding the mean is to convert the set to integers.
This simplifies to:
The mean is determined by adding together the numbers in a set and then dividing by the total number of items in that set. This gives us:
The first step to finding the mean is to convert the set to integers.
This simplifies to:
The mean is determined by adding together the numbers in a set and then dividing by the total number of items in that set. This gives us:
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Find the mean of the following data set:
Find the mean of the following data set:
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Find the mean of the following data set:
To find the mean, we need to add up all our numbers, and then divide by the number of terms.
In this case, we have nine terms, so we will divide by nine.
So, our answer is 84
Find the mean of the following data set:
To find the mean, we need to add up all our numbers, and then divide by the number of terms.
In this case, we have nine terms, so we will divide by nine.
So, our answer is 84
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