The resting heart rates for a sample of 15 students are recorded in the following stemplot.
Heart Rates
\begin{tabular}{l|lllll}
5 & 5 & & & & \\
6 & 3 & & & & \\
6 & 5 & 9 & 9 & 9 & 9 \\
7 & 0 & 1 & 3 & 3 & 4 \\
7 & 5 & 6 & 7 & &
\end{tabular}
What is the mean resting heart rate for this sample?
A. 66.0 beats per minute
B. 69.0 beats per minute
C. 69.9 beats per minute
D. 70.0 beats per minute
Key: [tex]7 \mid 5=75[/tex] beats per minute
Answer (1)
List the heart rates: 55, 63, 65, 69, 69, 69, 69, 70, 71, 73, 73, 74, 75, 76, 77.
Calculate the sum: 55 + 63 + 65 + 69 + 69 + 69 + 69 + 70 + 71 + 73 + 73 + 74 + 75 + 76 + 77 = 1048 .
Divide the sum by 15: 15 1048 = 69.8666... .
Round to one decimal place: 69.9 beats per minute.
Explanation
Understand the stemplot and the data The stemplot provides a visual representation of the resting heart rates of 15 students. Each row represents a 'stem' (the tens digit), and the 'leaves' (the ones digits) show the individual heart rates. The key 7∥5 = 75 beats per minute helps us interpret the data.
List all heart rates First, let's list all the heart rates from the stemplot: 55, 63, 65, 69, 69, 69, 69, 70, 71, 73, 73, 74, 75, 76, 77.
Calculate the sum of heart rates Next, we need to calculate the sum of all these heart rates: 55 + 63 + 65 + 69 + 69 + 69 + 69 + 70 + 71 + 73 + 73 + 74 + 75 + 76 + 77 = 1048 .
Divide the sum by the number of students Now, we divide the sum by the number of students (15) to find the mean: 15 1048 = 69.86666666666666 .
Round to one decimal place and conclude Finally, we round the result to one decimal place, which gives us 69.9. Therefore, the mean resting heart rate for this sample is 69.9 beats per minute.
Examples
Understanding mean heart rates can be useful in various real-world scenarios. For instance, a fitness tracker company might analyze the average heart rate of its users to provide personalized workout recommendations. Similarly, healthcare professionals can use mean heart rates to assess the overall cardiovascular health of a population or to evaluate the effectiveness of a new medication. By comparing the mean heart rate of different groups, researchers can gain insights into the impact of lifestyle factors on heart health.
