given aset of real numbers "x"with amean of 81 and std of 130,adata point withavalu of 250 can be reliably considereble?

To determine whether a data point with a value of 250 can be reliably considered in the context of the given data set, we typically assess how far it deviates from the mean in terms of standard deviations (using the **z-score**).

### Step-by-Step Calculation:

Given:
- Mean (\(\mu\)) = 81
- Standard deviation (\(\sigma\)) = 130
- Data point (\(x\)) = 250

The formula for the **z-score** is:

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

Substituting the values:

\[
z = \frac{250 - 81}{130} = \frac{169}{130} \approx 1.3
\]

### Interpretation of the Z-Score:
- A **z-score of 1.3** means that the data point is 1.3 standard deviations away from the mean.
- In general, data points within ±2 standard deviations are typically considered normal in many contexts (depending on the distribution), while values beyond ±3 standard deviations might be considered unusual or outliers.

Since a z-score of 1.3 is within 2 standard deviations from the mean, the value of 250 can be considered within a typical range for this data set, though it is on the higher end.

### Conclusion:
The data point 250 can be considered **reliably** part of the data set, but it is somewhat higher than the average, lying about 1.3 standard deviations away from the mean.

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Would you like more details or have any questions?

Here are five related questions to expand on this:
1. What does it mean if a data point has a very high z-score?
2. How would the interpretation change if the z-score was closer to 2 or 3?
3. What are the implications of using different confidence levels in statistical analysis?
4. How does skewness in the data affect the reliability of a data point?
5. What methods can be used to test for outliers in a data set?

**Tip:** Z-scores help standardize data and compare values from different distributions or units.

Given a set of real numbers 'x' with a mean of 81 and a standard deviation of 130, can a data point with a value of 250 be reliably considered?

Find out if a data point of 250 can be reliably considered in a data set with a mean of 81 and a standard deviation of 130. This solution explains the use of the z-score formula and the interpretation of standard deviations in a normal distribution. Suitable for students in Grades 10-12.

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