The systolic blood pressures of sample of 40 women have a mean of 110.8 mm Hg and a standard deviation of 17.1 mm Hg. The highest systolic blood pressure measurement in this sample is 181 mm Hg. In this context, is a systolic blood pressure of 181 mm Hg “unusual”? Answer 1 Question 9



To determine if a systolic blood pressure of 181 mm Hg is "unusual," we can use the concept of **z-scores**. A z-score tells us how many standard deviations a particular value is from the mean. Generally, a z-score beyond \(\pm 2\) is considered unusual, and a z-score beyond \(\pm 3\) is considered very unusual.

### Z-Score Calculation
The z-score is calculated using the following formula:

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

Where:
- \(X\) is the value in question (181 mm Hg in this case).
- \(\mu\) is the mean (110.8 mm Hg).
- \(\sigma\) is the standard deviation (17.1 mm Hg).

Substituting the values:

\[
z = \frac{181 - 110.8}{17.1} \approx \frac{70.2}{17.1} \approx 4.1
\]

### Interpretation
A z-score of 4.1 means that 181 mm Hg is 4.1 standard deviations above the mean. Since this is well beyond the usual cutoff of 2 or even 3 standard deviations, we can conclude that a systolic blood pressure of 181 mm Hg is indeed **very unusual** in this context.

**Answer 1 Question 9:** Yes, a systolic blood pressure of 181 mm Hg is "unusual."

Would you like any more details or have any further questions?

Here are five related questions to consider:

1. What might be the clinical implications of such an unusual systolic blood pressure?
2. How would the interpretation change if the standard deviation were larger?
3. What proportion of the sample would typically fall within 2 standard deviations of the mean?
4. How does the z-score help in comparing different data points across different distributions?
5. What other statistical methods can be used to identify outliers in a dataset?

**Tip:** In real-world applications, identifying unusual data points using z-scores is a common technique for detecting outliers that might require further investigation.

Explore whether a systolic blood pressure of 181 mm Hg is unusual using statistical analysis. Learn about z-scores, mean, and standard deviation in this context. Suitable for advanced high school students and beyond.

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