a.1 Line plot for eight of elk antler pairs at Mount St Helens NVM
The diagram is shown in figure 1.
a.2 Weight of elk antler pairs at Rocky Mountain NP
The diagram is shown in figure 2.
b. Calculate the following for each set of data:
We can found the
mean (µ) of a set of data points by adding them up and dividing by the number of data points.
b.1 Purple Mean:
Set:
[tex]\{34, 34, 30, 30, 30, 28, 28, 26\} \rightarrow \frac{34+34+30+30+30+28+28+26}{8} \rightarrow \boxed{\mu=30}[/tex]
b2. Red Mean:
Set:
[tex]\{40, 38, 36, 36, 36, 36, 34, 32\} \rightarrow \frac{40+38+36+36+36+36+34+32}{8} \rightarrow \boxed{\mu=36}[/tex]
b.3 Red Median
The Median is the middle of a sorted list of numbers.
The median of a finite list of numbers can be found by arranging all the numbers from smallest to greatest. So, arranging the red set we have:
[tex]\{32, 34, 36, 36, 36, 36, 38, 40\}[/tex]
Given that the number of elements is pair, the median can be solved as follows:
[tex]\overline{x}=\frac{x_{(n/2)}+ x_{((n/2)+1)}}{2}[/tex]
∴ [tex]n=8[/tex]
∴ [tex]x_{(n/2)}=x_{(4)}=36[/tex]
∴ [tex]x_{((n/2)+1)}=x_{(5)}=36[/tex]
Then:
[tex]\overline{x}=\frac{36+36}{2}=36[/tex]
b.4 Purple MAD
The
Mean Absolute Deviation (MAD) is when you find the distance of each data point from the mean and then find the mean
of those distances. So:
[tex]\{34, 34, 30, 30, 30, 28, 28, 26\}[/tex] has [tex]\mu=30[/tex]
[tex]distances=\{4, 4, 0, 0, 0, 2, 2, 4\} \rightarrow \frac{4+4+0+0+0+2+2+4}{8}= \boxed{MAD=2}[/tex]
b.5 Red MAD
[tex]\{40, 38, 36, 36, 36, 36, 34, 32\}[/tex] has [tex]\mu=36[/tex]
[tex]distances=\{4, 2, 0, 0, 0, 0, 2, 4\} \rightarrow \frac{4+2+0+0+0+0+2+4}{8}= \boxed{MAD=1.5}[/tex]
c. Calculate the means-to-MAD ratio for the two areas of collection
c.1 Purple set:
The ratio is the
relationship between the mean and the MAD indicating how many times the first number contains the second, so:
[tex]\frac{\mu}{MAD}= \frac{30}{2}=\boxed{15}[/tex]
c.2 Red set:[tex]\frac{\mu}{MAD}= \frac{36}{1.5}=\boxed{24}[/tex]
d. What inference can be made about the areas in regard to weight of dropped elk antlers?
MAD tells us how far, on average, all values are from the middle. So, in the example weight of elk antler pairs at Mount St Helens NVM are, on average, 2 away from the middle. On the other hand, weight of elk antler pairs at Rocky Mountain NP are, on average, 1.5 away from the middle. So, we can assure that elk antler pairs at Rocky Mountain NP weighs more than elk antler pairs at Mount St Helens NVM.
