Based on Data Set 1 “Body Data” in Appendix B, males have pulse rates with a mean of 69.6 beats per minute and a standard deviation of 11.3 beats per minute. Is a male pulse rate of 50 beats per minute significantly low or significantly high? (All of these pulse rates are measured at rest.) Explain.
The Correct Answer and Explanation is :
To determine whether a male pulse rate of 50 beats per minute (bpm) is significantly low or high, we use the concept of z-scores. The z-score measures how many standard deviations a given value is from the mean and is calculated as:
[
z = \frac{x – \mu}{\sigma}
]
Where:
- ( x = 50 ) bpm (the observed value)
- ( \mu = 69.6 ) bpm (the mean)
- ( \sigma = 11.3 ) bpm (the standard deviation)
Step 1: Calculate the z-score
[
z = \frac{50 – 69.6}{11.3} = \frac{-19.6}{11.3} \approx -1.73
]
Step 2: Interpret the z-score
- A z-score of -1.73 means that a pulse rate of 50 bpm is 1.73 standard deviations below the mean.
- Typically, values that are more than 2 standard deviations from the mean (i.e., ( |z| > 2 )) are considered unusual or significantly low or high.
Since ( -1.73 ) is not quite below -2, a pulse rate of 50 bpm is lower than average but not considered significantly low. However, it is on the borderline and may still be of medical interest, depending on other factors such as symptoms, fitness level, or health conditions.
Conclusion
A resting pulse rate of 50 bpm for a male is low but not statistically significant in terms of standard deviation rules. However, in a real-world context, medical evaluation might still be required, especially if the individual experiences symptoms like dizziness or fatigue. On the other hand, athletes and physically active individuals often have lower resting pulse rates due to their enhanced cardiovascular efficiency.
Now, I will generate an image that visually represents this analysis, including the normal distribution curve and the z-score placement.
The image above illustrates the normal distribution of male pulse rates, highlighting the mean (69.6 bpm) and the given pulse rate (50 bpm). The red-shaded area represents the lower tail, indicating that 50 bpm is below the mean but not significantly low, as it is within 2 standard deviations.