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Aqua running has been suggested as a method of
Chapter 1, Problem 24SE(choose chapter or problem)
Aqua running has been suggested as a method of cardiovascular conditioning for injured
athletes and others who desire a low-impact aerobics program. In a study to investigate the
relationship between exercise cadence and heart rate,1 the heart rates of 20 healthy volunteers
were measured at a cadence of 48 cycles per minute (a cycle consisted of two steps). The data
are as follows:
87 |
109 |
79 |
80 |
96 |
95 |
90 |
92 |
96 |
98 |
101 |
91 |
78 |
112 |
94 |
98 |
94 |
107 |
81 |
96 |
a Use the range of the measurements to obtain an estimate of the standard deviation.
b Construct a frequency histogram for the data. Use the histogram to obtain a visual approximation to \(\bar{y}\) and .
c Calculate \(\bar{y}\) and . Compare these results with the calculation checks provided by parts (a) and (b).
d Construct the intervals \(\bar{y} \pm k s\), \(k=1\), 2, and 3, and count the number of measurements falling in each interval. Compare the fractions falling in the intervals with the fractions that you would expect according to the empirical rule.
Equation Transcription:
Text Transcription:
^1
y bar
y bar
y bar +/- ks
k=1
Questions & Answers
QUESTION:
Aqua running has been suggested as a method of cardiovascular conditioning for injured
athletes and others who desire a low-impact aerobics program. In a study to investigate the
relationship between exercise cadence and heart rate,1 the heart rates of 20 healthy volunteers
were measured at a cadence of 48 cycles per minute (a cycle consisted of two steps). The data
are as follows:
87 |
109 |
79 |
80 |
96 |
95 |
90 |
92 |
96 |
98 |
101 |
91 |
78 |
112 |
94 |
98 |
94 |
107 |
81 |
96 |
a Use the range of the measurements to obtain an estimate of the standard deviation.
b Construct a frequency histogram for the data. Use the histogram to obtain a visual approximation to \(\bar{y}\) and .
c Calculate \(\bar{y}\) and . Compare these results with the calculation checks provided by parts (a) and (b).
d Construct the intervals \(\bar{y} \pm k s\), \(k=1\), 2, and 3, and count the number of measurements falling in each interval. Compare the fractions falling in the intervals with the fractions that you would expect according to the empirical rule.
Equation Transcription:
Text Transcription:
^1
y bar
y bar
y bar +/- ks
k=1
ANSWER:
Solution
Step 1 of 4
a) We have to find the standard deviation by using the range
From the given values
Minimum value =80
Maximum value =112
Standard deviation=(Maximum value - Minimum value)/4
=(112-78)/4
=8.5
Hence the standard deviation is 8.5