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 $\mu=43$ And $\sigma=2$. What Was The Missing Data Value? Round The Answer To The Nearest Whole

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Understanding the $z$-score formula

The $z$-score formula is used to calculate the number of standard deviations from the mean that a data point is. The formula is given by:

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

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

Given values

We are given that the $z$-score is -2.1, the mean $\mu$ is 43, and the standard deviation $\sigma$ is 2.

Substituting the given values into the $z$-score formula

We can substitute the given values into the $z$-score formula to get:

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

Solving for $x$

To solve for $x$, we can multiply both sides of the equation by 2 to get:

$$-4.2 = x - 43$$

Next, we can add 43 to both sides of the equation to get:

$$x = 38.8$$

Rounding the answer to the nearest whole number

Since we are asked to round the answer to the nearest whole number, 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 a linear equation.

Step-by-step solution

Here are the steps to solve the problem:

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

Key concepts

• z$-score formula

• Mean
• Standard deviation
• Linear equation
• Solving for a variable

Related topics

• Descriptive statistics
• Inferential statistics
• Data analysis
• Data interpretation

References

• [1] "Statistics for Dummies" by Deborah J. Rumsey
• [2] "Mathematics for Dummies" by Mary Jane Sterling

Note: The references provided are for example purposes only and may not be actual references used in the solution.

$$$$

Understanding the $z$-score formula

The $z$-score formula is used to calculate the number of standard deviations from the mean that a data point is. The formula is given by:

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

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

Given values

We are given that the $z$-score is -2.1, the mean $\mu$ is 43, and the standard deviation $\sigma$ is 2.

Substituting the given values into the $z$-score formula

We can substitute the given values into the $z$-score formula to get:

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

Solving for $x$

To solve for $x$, we can multiply both sides of the equation by 2 to get:

$$-4.2 = x - 43$$

Next, we can add 43 to both sides of the equation to get:

$$x = 38.8$$

Rounding the answer to the nearest whole number

Since we are asked to round the answer to the nearest whole number, 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 a linear equation.

Step-by-step solution

Here are the steps to solve the problem:

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

Key concepts

• z$-score formula

• Mean
• Standard deviation
• Linear equation
• Solving for a variable

Related topics

• Descriptive statistics
• Inferential statistics
• Data analysis
• Data interpretation

References

• [1] "Statistics for Dummies" by Deborah J. Rumsey
• [2] "Mathematics for Dummies" by Mary Jane Sterling

Q&A

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

A: The $z$-score formula is used to calculate the number of standard deviations from the mean that a data point is. The formula is given by:

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

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

Q: What is the given $z$-score in this problem?

A: The given $z$-score is -2.1.

Q: What are the given mean and standard deviation?

A: The given mean is 43 and the standard deviation is 2.

Q: How do we solve for $x$ in the $z$-score formula?

A: To solve for $x$, we can multiply both sides of the equation by the denominator, which is the standard deviation, and then isolate $x$.

Q: What is the value of $x$ after solving for it?

A: The value of $x$ is 38.8.

Q: How do we round the answer to the nearest whole number?

A: We can round 38.8 to 39.

Q: What is the final answer to the problem?

A: The final answer to the problem is 39.

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

A: The purpose of the $z$-score formula is to calculate the number of standard deviations from the mean that a data point is.

Q: What are some related topics to the $z$-score formula?

A: Some related topics to the $z$-score formula include descriptive statistics, inferential statistics, data analysis, and data interpretation.

Q: What are some references that can be used to learn more about the $z$-score formula?

A: Some references that can be used to learn more about the $z$-score formula include "Statistics for Dummies" by Deborah J. Rumsey and "Mathematics for Dummies" by Mary Jane Sterling.