Mike Kuschel
Math 110-17
The Problem: We want to determine whether or not there exists an association between
average heart rate and age, and between average heart rate and height for the students in
this class.
Building model: We can immediately conclude that there are 29 students in the class. But
since we are separating the samples by sex there are 13 males and 16 females. There are
many different parts to the problem we had to solve.
We had to find the mean, median, and mode for each aspect of the problems these
aspects are heart rates, age, and heights. We also had to find the range for all three. But
we also have to do one of each for each sex. The mean for male heart rates is
70.23076923 heartbeats. The median of male heartbeats is 72 heartbeats. The mode of
male heartbeats is 69 heartbeats. The heartbeat of male students range from 53 to 87
heartbeats (all work is shown on math spreadsheet1). The mean for male age is
19.46153846 years old. The median of male ages is 18 years old. The mode of male ages
is 18 years old. The age of male students range from 17 to 29 years old (all work is
shown on math spreadsheet 2). The mean of male height is 70.07692308 inches. The
median of male height is 70 inches. The mode of male height is 70 inches. The height of
male students range from 61 to 77 inches (all work shown in math spreadsheet 3). The
mean for female heartbeats is 68.5000 heartbeats. The median of female heartbeats is 66
heartbeats. The mode of female heartbeats is 61 heartbeats. The heartbeat of female
students range from 51 to 87 heartbeats (all work shown on math spreadsheet 4). The
mean of female ages is 20.0625 years old. The median is 18 years old the mode is 18
years old. The age of female students range from 17 to 33 years old (all work is shown on
math spreadsheet 5). The mean of female heights is 65.375 inches. The median of female
heights is 65 inches. The mode for female heights is 69 inches. The height of female
students range from 61 to 69 inches (all work shown in math spreadsheet 6).
I made some assumptions—everyone gave and accurate height and age, that everyone
gave an accurate heartbeat that nobody’s would have increased or decreased during the
45 seconds where we didn’t take our heart rate we just estimated it.
Generalized models:
For heart rate versus age using just male data points (Figure 1.1): y = 0.0857x + 13.431
For heart rate versus height using just male data points (Figure 1.2): y = -0.0963x +
76.852
For heart rate versus height for just female data points (Figure 1.3): y = -0.1116x +
27.709
For heart rate versus age using just female data points (Figure 1.4): y = -0.1387x +
74.878
Solving the problem:
For male heart rate and age the answers I came up with 20.85862 years old, 19.71538
years old, 18.68698 years old. The age that the male students actually are is 29 years old
for the first number, 17 years old for the second, and 21 years old for the third.
For male heart rate and height the answers I came up with 70.945921 inches, 71.716321
inches, 69.790321 inches. The actual height for the first male student is 66 inches, the
actual height for the second male student is 77 inches, and the actual height of the final
male student is 72 inches.
For female heart rate and height the I answers I came up with 65.816729 inches,
65.630871 inches, 66.371529 inches. The actual height for the first female student is 69
inches, the actual height for the second female student is 61 inches, and the actual
height for the last female student is 63 inches.
For female heart rate and age the answers I came up with 20.8646 years old, 22.0542
years old, 20.4182 years old. The actual age of the first female student is 33 years old,
the actual age for the second female student is 18 years old, and the actual age for the
final female student is 25.
Communicating the results:
For heart rate versus age using just male data points there a very weak association.
For heart rate versus age using just male data points the test value does not match up with
the expected age, because when the formula was made they used the average of heartbeat
and age, so this causes the actual and test ages to be off.
For heart rate versus height using just male data points there was an extremely weak
association.
For heart rate versus height using just male data points the test height did not match with
the actual height because when the formula was made they used the average of heartbeat
and height.
For heart rate versus height for just female data points there is a weak association.
For heart rate versus height for just female data points the test height did not match with
the actual height because when the formula was made they used the average of heartbeat
and height.
For heart rate versus age using just female data points there is a very weak association.
For heart rate versus age using just female data points the test value does not match up
with the expected age, because when the formula was made they used the average of
heartbeat and age, so this causes the actual and test ages to be off.
Evaluating the model: The assumption I made:
 Everyone gave and accurate height and age
 That everyone gave an accurate heartbeat

That nobody’s would have increased or decreased during the 45 seconds where
we didn’t take our heart rate we just estimated it.