How to find a missing value given the mean | Data and statistics | 6th grade | Khan Academy

Khan Academy
5 Feb 201505:02
EducationalLearning
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TLDRThe video script presents a problem-solving scenario involving a babysitter who has kept a record of the ages of six children they have babysat recently. Unfortunately, one age is obscured by a blue ink spill. However, the babysitter remembers that they calculated the mean age of the children as four. Using this information, the script guides viewers through a step-by-step process to determine the missing age. By adding the known ages, dividing by the number of children, and then multiplying by the total number of ages, the babysitter deduces that the missing age is three. This engaging narrative not only solves the mystery but also illustrates the practical application of calculating the mean in everyday situations.

Takeaways
  • ๐Ÿ“ The story begins with a babysitter who maintains a log of the children they babysit, including their ages.
  • ๐Ÿ” An issue arises when blue ink spills on the log, obscuring the age of one child.
  • ๐Ÿค” Initially, the babysitter is worried about losing valuable information due to the ink spill.
  • ๐Ÿงฎ The babysitter remembers calculating the mean age each time a new age was logged, which provides a clue to solving the problem.
  • ๐Ÿ”‘ The mean age of the six children is known to be four, which is a key piece of information for finding the missing age.
  • ๐Ÿง The babysitter encourages viewers to pause and attempt to solve the problem on their own before revealing the solution.
  • ๐Ÿ“Š The mean is calculated by summing all ages and dividing by the number of children, which in this case is six.
  • ๐Ÿง  By multiplying the mean by the number of children, the total sum of ages can be found, which helps in solving for the missing age.
  • ๐Ÿ”ข The known ages are added together, and the sum is used to find the missing age by subtracting it from the total calculated with the mean.
  • ๐ŸŽ‰ The missing age is determined to be three, which is found by subtracting the sum of known ages from the total calculated using the mean.
  • ๐Ÿ“Œ The story illustrates the importance of keeping accurate records and the utility of mean calculation in solving problems when information is incomplete.
Q & A

  • What is the primary concern of the babysitter in the transcript?

    -The babysitter is concerned about a blue ink spill that obscured the age of one of the children in their log.

  • How does the babysitter remember the ages of the children?

    -The babysitter remembers the ages by keeping a log and recalculating the mean age each time a new age is added.

  • What is the mean age of the six children according to the babysitter's log?

    -The mean age of the six children is four years old.

  • How does the babysitter use the mean to figure out the missing age?

    -The babysitter uses the mean by setting up an equation where the total of all ages divided by the number of children equals the mean, and then solving for the missing age.

  • What is the total of the known ages of the five children?

    -The total of the known ages of the five children is 21 (five plus two plus two plus four plus eight).

  • What mathematical operation is used to find the total of all ages?

    -The babysitter multiplies the mean by the number of children to find the total of all ages.

  • What is the formula for calculating the mean age?

    -The formula for calculating the mean age is the total sum of ages divided by the number of children.

  • What does the babysitter conclude is the missing age after solving the equation?

    -The babysitter concludes that the missing age is three years old.

  • How does the babysitter verify the missing age?

    -The babysitter verifies the missing age by subtracting the total of known ages from the product of the mean and the number of children.

  • What is the significance of the babysitter's method in solving for the missing age?

    -The method demonstrates a practical application of mean calculation in real-life scenarios and shows how to deal with missing data points.

  • Why is it important to keep a log of the ages of children when babysitting?

    -Keeping a log helps the babysitter to remember important details about the children they are caring for and can be useful for record-keeping and planning.

  • What advice does the video script give to the viewer?

    -The video script encourages the viewer to pause and attempt to solve the problem independently before revealing the solution.

Outlines
00:00
๐Ÿ” Solving for the Missing Age with Mean

The video script presents a problem-solving scenario where a babysitter has a log of children's ages but one age is obscured by ink. The babysitter recalls the mean age of the children, which is four. To find the missing age, the script guides the viewer through a mathematical process. It explains that the mean is calculated by summing all ages and dividing by the number of children. The script then demonstrates how to use the known mean and five of the six ages to calculate the missing age. By adding the known ages and dividing by the number of children, the script shows that the sum of the ages plus the missing age (represented as a question mark) equals the mean times the number of children. After simplification, it is determined that the missing age is three, completing the set of ages.

Mindmap
Keywords
๐Ÿ’กBabysitting business
The babysitting business refers to the activity of looking after children for a fee. In the video's context, it is the main character's occupation, which involves keeping a log of the children they babysit. This is central to the video's narrative as it sets up the scenario for the problem-solving exercise.
๐Ÿ’กLog
A log is a record or a register of information, in this case, the ages of the children being babysat. The babysitter uses a log to keep track of the children's ages, which becomes crucial when one of the ages is obscured by ink, leading to the main problem of the video.
๐Ÿ’กMean
The mean, often referred to as the average, is a measure of central tendency that is calculated by summing up all the values in a data set and then dividing by the number of values. In the video, the mean age of the children is known to be four, which becomes a key piece of information in solving for the missing age.
๐Ÿ’กTotal of ages
The total of ages refers to the sum of all the ages of the children that the babysitter has recorded. This is an important step in calculating the mean and is used to find the missing age by setting up an equation where the total of ages divided by the number of children equals the mean.
๐Ÿ’กData points
Data points are individual pieces of information in a data set. In the context of the video, the ages of the children represent the data points. The babysitter has six data points (ages), one of which is missing, and the video is about finding that missing data point.
๐Ÿ’กQuestion mark
The question mark is used symbolically to represent the unknown or missing piece of information. In the video, it stands for the missing age of one of the children. The process of solving for the question mark involves mathematical operations and is the main focus of the video's educational content.
๐Ÿ’กSolve
To solve means to find an answer or explanation for a problem. In the video, the babysitter needs to solve for the missing age, which is done by using the known mean and the ages of the other children to set up and solve an equation.
๐Ÿ’กBlue ink spill
The blue ink spill is the incident that causes the problem in the video. It obscures one of the ages in the babysitter's log, leading to the need to determine the missing age. This serves as the catalyst for the mathematical exercise presented in the video.
๐Ÿ’ก
๐Ÿ’กMultiplication
Multiplication is a mathematical operation where two numbers are multiplied together to give a product. In the video, it is used to simplify the equation by multiplying both sides by the number of data points, which helps in isolating the missing age.
๐Ÿ’กNumber of ages
The number of ages refers to the total count of age values being considered. In this video, it is six, as the babysitter is dealing with the ages of six children. This number is essential for calculating the mean and for setting up the equation to find the missing age.
๐Ÿ’กCancellation
Cancellation is a mathematical process where corresponding terms on both sides of an equation are eliminated to simplify the equation. In the script, it is used to simplify the equation after multiplying both sides by the number of ages, leading to the final step of solving for the missing age.
๐Ÿ’กMissing number
The missing number is the age of the child that was obscured by the blue ink spill. It is the ultimate answer that the babysitter seeks to find through the process described in the video. The term is central to the video's narrative as it represents the problem to be solved.
Highlights

The babysitter keeps a log of the ages of children they babysit.

An age is obscured by a blue ink spill, creating a puzzle to solve.

The babysitter recalls the mean age of the children, which is four.

The mean age is used to recalculate the total age of all children.

The formula for calculating the mean is explained.

A method to find the missing age using the mean and known ages is proposed.

The total of known ages is calculated to be 21.

The mean age is multiplied by the number of children to find the total age.

The missing age is solved by setting up an equation with the mean and total known ages.

The missing age is found to be three by solving the equation.

The process of solving for the missing age is demonstrated step by step.

The importance of keeping accurate records is highlighted.

The practical application of mean in solving real-world problems is shown.

The video encourages viewers to pause and attempt the problem themselves.

A clear explanation of how to manipulate the mean formula to find a missing value is provided.

The solution to the puzzle is reached by substituting known values into the formula.

The video concludes with the exciting revelation of the missing age.

Transcripts

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Mean CalculationBabysitting LogMissing DataMath ProblemAge CalculationRecord KeepingData RecoveryEducational ContentSolve PuzzleLogical ThinkingStatistical Analysis