Question

Aqua Running Aqua running has been suggested as a method of cardiovascular conditioning for injured athletes and others who want a low-impact aerobics program. A study reported in the Journal of Sports Medicine investigated the relationship between exercise cadence and heart rate by measuring the heart rates of 20 healthy volunteers at a cadence of 48 cycles per minute (a cycle consisted of two steps). \({ }^{10}\) The data are listed here: $$\begin{array}{rrrrrrrrrr}87 & 109 & 79 & 80 & 96 & 95 & 90 & 92 & 96 & 98 \\\101 & 91 & 78 & 112 & 94 & 98 & 94 & 107 & 81 & 96\end{array}$$ Construct a stem and leaf plot to describe the data. Discuss the characteristics of the data distribution.

Short answer

Question: Based on the stem and leaf plot created for the heart rate data during aqua running exercise, describe the characteristics of the data distribution. Answer: The data distribution in the stem and leaf plot shows that the heart rate values are positively skewed, with the majority of values concentrated around the 90-98 range. The dataset has a moderate variability, with a range of 34 between the lowest and highest heart rate values.

Step-by-step solution

Organize the data in ascending order

First, let's organize the heart rate values in ascending order: 78, 79, 80, 81, 87, 90, 91, 92, 94, 94, 95, 96, 96, 96, 98, 98, 101, 107, 109, 112

Create the stem and leaf plot

Now, we create a stem and leaf plot with the stems representing the tens digits and the leaves representing the ones digits. Here is the plot: $$ \begin{array}{c|l} 7 & 89 \\ 8 & 01279 \\ 9 & 24666788 \\ 10 & 17 \\ 11 & 29 \\ \end{array} $$

Analyze the data distribution

From the stem and leaf plot, we can observe the following characteristics: 1. Shape: The heart rate values are not symmetrically distributed. They are positively skewed, having more values in the lower range (70s and 80s) and fewer values in the higher range (100s and 110s). 2. Central tendency: The majority of the heart rate values are concentrated around 90-98 range, which indicates the central tendency is around that range. 3. Variability: The heart rate values have a range of 112 - 78 = 34. This means that there is a relatively moderate variability in the data. This information shows that while the majority of heart rates are within a similar range, there are outliers that could influence the overall data distribution. Overall, the stem and leaf plot gives us a clear and immediately understandable visualization of the heart rate data for aqua running exercisers.

Key concepts

Data Distribution

Data distribution refers to the way data values are spread out over a range. It provides insights into how often each value or range of values occurs, and encompasses various characteristics such as shape, central tendency, and variability.
In the case of our heart rate data, organizing our data into a stem and leaf plot helps visualize its distribution clearly.
A stem and leaf plot arranges data so that we can see both individual values and how they cluster. For example, in this plot:

• The 'stem' represents the tens digit of each heart rate.
• The 'leaf' represents the ones digit.

This plot shows that most heart rate measurements fall between 90 and 98 beats per minute. Such visualization helps identify patterns or outliers easily.
Understanding these aspects aids in making more informed decisions based on the data.

Heart Rate Measurement

Heart rate measurement is an essential metric in evaluating cardiovascular fitness and health. It's typically expressed in beats per minute (bpm) and gives information about how your heart is functioning during different activities, such as rest or exercise.
Measuring heart rates, especially during exercise, helps determine how hard the heart is working. In the aqua running exercise study, where data were collected at 48 cycles per minute, the heart rates ranged from 78 to 112 bpm.
This range signifies varying levels of exertion experienced by the participants. Monitoring heart rate can reveal insights about personal fitness levels, and how efficiently the heart pumps blood during exertion.
Accurate measurement can be vital for athletes to optimize their training and recovery plans, ensuring they don't exceed safe limits.

Cardiovascular Conditioning

Cardiovascular conditioning involves exercises that improve the efficiency of the cardiovascular system in absorbing and transporting oxygen. Aqua running, as observed in the study, is a low-impact cardiovascular exercise.
It is particularly beneficial for injured athletes or individuals looking for aerobic workouts without the strain of high-impact activities. The heart rate data collected from the study offer a snapshot into how effective this form of exercise might be in strengthening cardiovascular fitness.
Regular cardiovascular conditioning brings numerous benefits such as a stronger heart, reduced risk of heart disease, and improved lung capacity. Programs like aqua running will build stamina and endurance over time, making heart rate monitoring crucial to track improvement and adjust difficulty progressively.

Exercise Statistics

Exercise statistics are crucial for gauging performance and health benefits derived from physical activities. The heart rate measurements obtained during aqua running can be seen as exercise statistics, offering concrete data to analyze the exercise's impact on cardiovascular fitness.
By looking at the heart rate data and distributing it in a stem and leaf plot, we gain insights into patterns and outliers which are critical for personalizing workout plans. Such statistics help quantify progress, identifying whether an exercise plan is effective and safe.
Understanding the variance and central tendency of data such as heart rates informs decisions both for physical trainers and individuals aiming to achieve specific health outcomes.
Thus, exercise statistics are integral to enhancing workout efficiency and ensuring safe progression for consistent improvement.