A Missing Data Value From A Set Of Data Has A $z$-score Of -2.1. Fred Already Calculated The Mean And Standard Deviation To Be Μ = 43 \mu = 43 Μ = 43 And Σ = 2 \sigma = 2 Σ = 2 . What Was The Missing Data Value? Round The Answer To The Nearest

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Understanding the $z$-score formula

The $z$-score formula is used to calculate the number of standard deviations a data point is away from the mean. It is calculated as follows:

$$z = \frac{x - \mu}{\sigma}$$

where $x$ is the data point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Using the $z$-score formula to find the missing data value

We are given that the $z$-score is -2.1, the mean is 43, and the standard deviation is 2. We can plug these values into the $z$-score formula to solve for the missing data value.

$$-2.1 = \frac{x - 43}{2}$$

Solving for the missing data value

To solve for the missing data value, we can multiply both sides of the equation by 2 to get rid of the fraction.

$$-2.1 \times 2 = x - 43$$

$$-4.2 = x - 43$$

Isolating the missing data value

Next, we can add 43 to both sides of the equation to isolate the missing data value.

$$-4.2 + 43 = x$$

$$38.8 = x$$

Rounding the answer to the nearest integer

Since we are asked to round the answer to the nearest integer, we can round 38.8 to 39.

Conclusion

Therefore, the missing data value is 39.

Example use case

This problem can be used as an example of how to use the $z$-score formula to find a missing data value. It can also be used to demonstrate how to solve for a variable in an equation.

Step-by-step solution

1. Write down the $z$-score formula: $z = \frac{x - \mu}{\sigma}$
2. Plug in the given values: $-2.1 = \frac{x - 43}{2}$
3. Multiply both sides of the equation by 2: $-4.2 = x - 43$
4. Add 43 to both sides of the equation: $38.8 = x$
5. Round the answer to the nearest integer: $x = 39$

Common mistakes

• Forgetting to multiply both sides of the equation by 2
• Forgetting to add 43 to both sides of the equation
• Not rounding the answer to the nearest integer

Real-world applications

• Finding missing data values in a dataset
• Understanding how to use the $z$-score formula
• Solving for a variable in an equation

Future work

• Using the $z$-score formula to find the mean and standard deviation of a dataset
• Understanding how to use the $z$-score formula to find the probability of a data point being within a certain range
• Using the $z$-score formula to find the data point that is furthest away from the mean.
  

$$$$

Understanding the $z$-score formula

The $z$-score formula is used to calculate the number of standard deviations a data point is away from the mean. It is calculated as follows:

$$z = \frac{x - \mu}{\sigma}$$

where $x$ is the data point, $\mu$ is the mean, and $sigma$ is the standard deviation.

Using the $z$-score formula to find the missing data value

We are given that the $z$-score is -2.1, the mean is 43, and the standard deviation is 2. We can plug these values into the $z$-score formula to solve for the missing data value.

$$-2.1 = \frac{x - 43}{2}$$

Solving for the missing data value

To solve for the missing data value, we can multiply both sides of the equation by 2 to get rid of the fraction.

$$-2.1 \times 2 = x - 43$$

$$-4.2 = x - 43$$

Isolating the missing data value

Next, we can add 43 to both sides of the equation to isolate the missing data value.

$$-4.2 + 43 = x$$

$$38.8 = x$$

Rounding the answer to the nearest integer

Since we are asked to round the answer to the nearest integer, we can round 38.8 to 39.

Conclusion

Therefore, the missing data value is 39.

Example use case

This problem can be used as an example of how to use the $z$-score formula to find a missing data value. It can also be used to demonstrate how to solve for a variable in an equation.

Step-by-step solution

1. Write down the $z$-score formula: $z = \frac{x - \mu}{\sigma}$
2. Plug in the given values: $-2.1 = \frac{x - 43}{2}$
3. Multiply both sides of the equation by 2: $-4.2 = x - 43$
4. Add 43 to both sides of the equation: $38.8 = x$
5. Round the answer to the nearest integer: $x = 39$

Common mistakes

• Forgetting to multiply both sides of the equation by 2
• Forgetting to add 43 to both sides of the equation
• Not rounding the answer to the nearest integer

Real-world applications

• Finding missing data values in a dataset
• Understanding how to use the $z$-score formula
• Solving for a variable in an equation

Future work

• Using the $z$-score formula to find the mean and standard deviation of a dataset
• Understanding how to use the $z$-score formula to find the probability of a data point being within a certain range
• Using the $z$-score formula to find the data point that is furthest away from the mean.

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Q&A

Q: What is the $z$-score formula?

A: The $z$-score formula is used to calculate the number of standard deviations a data point is away from the mean. It is calculated as follows:

$$z = \frac{x - \mu}{\sigma}$$

where $x$ is the data point, $\mu$ is the mean, and $sigma$ is the standard deviation.

Q: How do I use the $z$-score formula to find a missing data value?

A: To use the $z$-score formula to find a missing data value, you need to plug in the given values into the formula and solve for the missing data value.

Q: What if I have a $z$-score of 0?

A: If you have a $z$-score of 0, it means that the data point is equal to the mean. In this case, you can use the formula $x = \mu$ to find the missing data value.

Q: What if I have a negative $z$-score?

A: If you have a negative $z$-score, it means that the data point is below the mean. In this case, you can use the formula $x = \mu - z \times \sigma$ to find the missing data value.

Q: What if I have a positive $z$-score?

A: If you have a positive $z$-score, it means that the data point is above the mean. In this case, you can use the formula $x = \mu + z \times \sigma$ to find the missing data value.

Q: How do I round the answer to the nearest integer?

A: To round the answer to the nearest integer, you can use the following rules:

• If the decimal part is less than 0.5, round down to the nearest integer.
• If the decimal part is greater than or equal to 0.5, round up to the nearest integer.

Q: What are some common mistakes to avoid when using the $z$-score formula?

A: Some common mistakes to avoid when using the $z$-score formula include:

• Forgetting to multiply both sides of the equation by 2
• Forgetting to add 43 to both sides of the equation
• Not rounding the answer to the nearest integer

Q: What are some real-world applications of the $z$-score formula?

A: Some real-world applications of the $z$-score formula include:

• Finding missing data values in a dataset
• Understanding how to use the $z$-score formula
• Solving for a variable in an equation

Q: What are some future work ideas for the $z$-score formula?

A: Some future work ideas for the $z$-score formula include:

• Using the $z$-score formula to find the mean and standard deviation of a dataset
• Understanding how to use the $z$-score formula to find the probability of a data point being within a certain range
• Using the $z$-score formula to find the data point that is furthest away from the mean.