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Part 1

Body and exam measurements were collected from 300 subjects. The pulse rates from 100 males have a mean of 

70.670.6 

beats per minute and a standard deviation of 

11.911.9 

beats per minute. Use the range rule of thumb for identifying significant values to identify the limits separating values that are significantly low or significantly high. Is a pulse rate of 

110.0110.0 

beats per minute significantly​ low, significantly​ high, or​ neither? (All of these pulse rates are measured at​ rest.) Explain.

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Part 1

Significantly low values are 

enter your response here 

beats per minute or lower.

​(Type an integer or a decimal. Do not​ round.)

The **range rule of thumb** helps identify significantly low or high values by using the mean and standard deviation. According to this rule, values that are more than **2 standard deviations** away from the mean are considered significant.

### Formula for Limits:
- **Significantly low values** are calculated as:
  \[
  \text{Low Limit} = \text{Mean} - 2 \times \text{Standard Deviation}
  \]
  
- **Significantly high values** are calculated as:
  \[
  \text{High Limit} = \text{Mean} + 2 \times \text{Standard Deviation}
  \]

### Given Data:
- Mean pulse rate \( \mu = 70.6 \, \text{beats per minute} \)
- Standard deviation \( \sigma = 11.9 \, \text{beats per minute} \)

Let's calculate the low and high limits.

#### 1. Low Limit:
\[
\text{Low Limit} = 70.6 - 2 \times 11.9 = 70.6 - 23.8 = 46.8 \, \text{beats per minute}
\]

#### 2. High Limit:
\[
\text{High Limit} = 70.6 + 2 \times 11.9 = 70.6 + 23.8 = 94.4 \, \text{beats per minute}
\]

### Conclusion:
- Significantly low values are **46.8 beats per minute** or lower.
- Significantly high values are **94.4 beats per minute** or higher.

### Is a pulse rate of 110 beats per minute significant?
Since 110 beats per minute is greater than 94.4, it is considered **significantly high** according to the range rule of thumb.

Would you like further explanation or additional details?

Here are 5 questions to expand this topic:
1. How does the range rule of thumb compare to z-scores for identifying outliers?
2. What other statistical methods can be used to detect significant values?
3. How would you interpret a pulse rate significantly lower than 46.8?
4. Can the range rule of thumb be applied to data that is not normally distributed?
5. How would the limits change if the sample size was larger or smaller?

**Tip:** The range rule of thumb is a quick and intuitive way to detect outliers, but it works best for data that is approximately normal in distribution.

Body and exam measurements were collected from 300 subjects. The pulse rates from 100 males have a mean of 70.6 beats per minute and a standard deviation of 11.9 beats per minute. Use the range rule of thumb for identifying significant values to identify the limits separating values that are significantly low or significantly high. Is a pulse rate of 110.0 beats per minute significantly low, significantly high, or neither? (All of these pulse rates are measured at rest.)

This problem demonstrates how to use the range rule of thumb to determine significantly high or low pulse rates. With a mean pulse rate of 70.6 bpm and a standard deviation of 11.9 bpm, learn how to calculate the limits and analyze whether a pulse rate of 110 bpm is significantly high. Suitable for students in Grades 9-12.

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