https://file.aiquickdraw.com/mathbot/file/1725942032257w8u7p59e.jpg

To find and interpret the z-score for the given data value, we can use the z-score formula:

\[
z = \frac{X - \mu}{\sigma}
\]

where:
- \( X \) is the data value,
- \( \mu \) is the mean, and
- \( \sigma \) is the standard deviation.

From the image:
- The data value \( X = 269 \),
- The mean \( \mu = 190 \),
- The standard deviation \( \sigma = 23 \).

Now let's calculate the z-score.

\[
z = \frac{269 - 190}{23}
\] 

Let me compute this.The z-score is \( 3.43 \), meaning the value 269 is 3.43 standard deviations above the mean.

Do you want further details or explanations?

Here are 5 related questions to explore:
1. How do you interpret a z-score in different contexts?
2. What does it mean if the z-score is negative?
3. How can z-scores help in comparing data points from different datasets?
4. What is the relationship between z-scores and percentiles?
5. How would you calculate a z-score for a population vs a sample?

**Tip:** A higher absolute z-score indicates a data point is further from the mean.

The value 269 in a dataset with mean 190 and standard deviation 23. Find the z-score and interpret it.

Learn how to find and interpret the z-score for the value 269 in a dataset with a mean of 190 and a standard deviation of 23. This problem demonstrates key statistical concepts like the z-score formula. Suitable for students in Grades 9-12.

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