How To Find The Missing Value Given The Mean - Chemistry Test Scores and Statistics

The Organic Chemistry Tutor
13 Oct 202309:10
EducationalLearning
32 Likes 10 Comments

TLDRThe video explains how to calculate the score needed on a future exam to achieve a desired overall test average. It starts with an example problem of a student needing to score a 98 on her 5th exam to obtain a 90 average with her previous scores of 82, 89, 85, and 96. It then derives a formula to directly calculate the score needed on a future exam to achieve a target average given the previous scores. This formula is demonstrated by figuring out the score another student needs on his 7th exam to obtain an 80 average given his previous 6 scores.

Takeaways
  • ๐Ÿ˜€ To find a missing value when given the mean, set up an equation equating the mean to the sum of the values divided by the number of values
  • ๐Ÿ‘ Use the known mean, number of values, and given values in the equation to solve for the missing value
  • โœ๏ธ An easier way is to multiply both sides of the equation by the number of values to eliminate the denominator
  • ๐Ÿ’ก To calculate the score needed on a future exam to reach a target average, use: score = (number of exams) x (desired average) - (sum of existing scores)
  • ๐Ÿ“ This equation can be expanded to any number of existing exam scores by continuing to subtract those scores
  • โž• Use this equation to easily calculate the score needed on a future exam when aiming for a certain test average
  • ๐Ÿ”ข Plug in the number of total exams, desired average test score, and scores from exams already taken
  • ๐Ÿงฎ The result will be the score needed on the next exam to achieve that average test score
  • ๐Ÿ† This method streamlines determining what grade you need on an upcoming test to get your desired class average
  • โœ… Applying this technique helps take the guesswork out of what score you need to earn on a future exam
Q & A

  • What is the formula used to calculate the mean or average test score?

    -The formula is Mean = Sum of all the X values / Total number of X values (n)

  • What information is provided in the word problem about Kristen's test scores?

    -Kristen received scores of 82, 89, 85, and 96 on her first four chemistry exams. We need to find what score she needs on the fifth exam to have an average test score of 90.

  • How do you calculate the score Kristen needs on her fifth exam to get an average of 90?

    -Set up an equation: 90 = (82 + 89 + 85 + 96 + X5) / 5. Solve the equation to find X5 = 98. So Kristen needs a 98 on her fifth exam.

  • What is the equation derived to directly calculate the score needed on a future exam?

    -Xn = (Number of total exams) * (Desired average) - (Sum of scores on previous exams)

  • How would you modify the equation if you wanted to find the score needed on a 7th exam rather than a 5th exam?

    -X7 = (Number of total exams) * (Desired average) - (X1 + X2 + X3 + X4 + X5 + X6)

  • What were the scores Jim had received on his first 6 exams?

    -Jim's scores on the first 6 exams were: 76, 83, 69, 78, 85, 84

  • What average test score does Jim want to achieve?

    -Jim wants to achieve an average test score of 80 across all his exams.

  • What score does Jim need on his 7th exam to get his desired 80 average?

    -Using the equation, Jim needs a score of 85 on his 7th exam to get an 80 average.

  • What is the benefit of the derived equation for finding a needed test score?

    -The benefit is it provides a direct way to calculate the score needed on a future exam to achieve a desired test average, without needing to write out the full mean calculation each time.

  • How could this method apply for a student wanting a different average, like 90 for an A grade?

    -The student would just modify the desired average parameter in the equation to 90 instead of 80. The rest of the method would remain the same to calculate the score needed on the next exam.

Outlines
00:00
๐Ÿ˜€ How to calculate a missing value to obtain a desired average score

This paragraph explains how to calculate a missing test score in order to achieve a desired average test score. It provides an example where Kristen has scores of 82, 89, 85, and 96 on her first 4 chemistry exams, and needs to determine what score is required on the 5th exam to obtain an average of 90. The method involves setting up an equation where the mean/average multiplied by the number of exams equals the sum of all the scores. After solving, Kristen needs a 98 on her 5th exam to achieve the 90 average.

05:01
๐Ÿ˜€ Formula to easily calculate required score for a future exam

This paragraph derives a formula to easily calculate the score needed on a future exam to achieve a desired test average, without needing to write out the full equation each time. The formula is: Score_needed = Number_of_exams * Desired_average - Sum of existing scores. An example applies this to calculate the score Jim needs on his 7th exam to obtain an 80 average given his existing 6 scores.

Mindmap
Keywords
๐Ÿ’กmean
The mean, also called the average, is calculated by adding all the number values and dividing the sum by the total count. In the video, the mean refers to the average test score that Kristen wants to achieve, which is 90. Calculating the mean helps determine what Kristen needs to score on her next exam to reach that average.
๐Ÿ’กmissing value
The missing value refers to the unknown score that Kristen needs to get on her 5th exam. Finding this missing value based on the desired mean/average is the main focus of the word problem presented in the video.
๐Ÿ’กcross multiply
Cross multiplication is a mathematical technique used to solve certain types of equations and word problems. In the context of this video, cross multiplication could have been used as an alternative method to solve for the missing score value.
๐Ÿ’กequation
An equation is a mathematical statement where one expression is set equal to another. Several equations are presented in the video, including the formula for calculating mean/average. Equations help model the mathematical relationships and are manipulated to solve for unknowns like the missing score.
๐Ÿ’กsubtract
Subtraction is a key arithmetic operation carried out multiple times in the video to solve the word problem. Values from the first 4 exam scores are subtracted from the total sum of scores multiplied by 5 exams to isolate the missing 5th exam score.
๐Ÿ’กcalculator
A calculator is a tool used to perform mathematical computations. In the video, a calculator helps add the first 4 exam scores, make subtractions, and determine the final missing score value.
๐Ÿ’กformula
A formula refers to a set procedure for solving a particular mathematical problem. The video introduces formulas for calculating mean/average as well as for directly calculating the next exam score needed to achieve a target average.
๐Ÿ’กscore
In the context of this video, a score refers to the numeric grade Kristen received on each of her chemistry exams. The scores are used in the formulas to determine the missing value or score needed to obtain the desired average test score.
๐Ÿ’กsolve
To solve a mathematical problem means to find its solution. The video demonstrates step-by-step how to solve for the missing score value needed to achieve the target average test score.
๐Ÿ’กaverage
Average means the same as mean. It refers to the central tendency of a set of numbers calculated by summing the values and dividing by the count. The video explains how to calculate average and how to determine a missing value to obtain a desired average.
Highlights

To find a missing value given the mean, write equations setting the mean equal to the sum of the values divided by the number of values.

The formula for the mean is the sum of the x values divided by n, where n is the number of values.

To find a missing value, set up an equation with the mean, known values, and unknown value, then solve for the unknown.

To easily calculate the score needed on a future exam, use the formula: Score = (Number of Exams) x (Desired Average) - (Sum of Current Exam Scores)

The equation can be expanded to any number of exam scores by continuing to subtract all the previous scores.

By using the formula, you can quickly calculate the score needed on an exam to reach a target overall average.

The formula simplifies the process of determining what grade is required to achieve a desired average test score.

Kristen needs a 98 on her next exam to achieve an average score of 90 across her first 5 exams.

Jim needs an 85 on his 7th exam to have an 80 average across all his exams so far.

The formula works for any number of exam scores and allows calculating the needed score for a target average.

Calculating averages is useful for determining what final exam score you need to get your desired grade.

The process can be applied to calculate a missing value needed to achieve a target mean.

The formula simplifies figuring out the score needed on a future exam to reach your target average.

By plugging in values, you can quickly calculate the exact score needed on an upcoming exam.

The method streamlines determining what grade you need to get your desired final course average.

Transcripts

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