Name: Anushka Rahman
Grade: 9-B
Introduction…
I am going to investigate whether or not there is any correlation between
different features among mammals. Correlation is a complementary, parallel or
reciprocal relationship between two variables, which are different from each
other.
Task #1
a) Is there a correlation between body weight and brain weight in mammals?
This is the graph that I plotted from the given data, which shows that there is a
positive, but weak correlation between the chosen two variables. One can tell
that there is a positive correlation because the trend line suggests that when the
brain weight increases, so does the body weight. There are a few outliers, or
rogue quantities, like the gray seal. I say that because the gray seal is the only
mammal fish amongst the species being used for correlation. The rest are all four
legged animals. So there is a chance that the body weight and brain weight may
not be as correlated as it seems, as the correlation is weak with many outliers,
and the brain weight to body weight ratio may vary from mammal to mammal.
i) Is the mathematic tool that I am going to choose the most accurate?
I am going to choose the Ms Excel, as I think that it will be the most accurate in
chart making, which is its purpose. The chances of human error are therefore
eliminated. This is important, as extreme accuracy is vital for statistical analysis.
ii) What is the method that I am going to use, and how?
The method that I am going to use for this particular task, is to basically look at
different at the graphs, which will be plotted using Ms Excel, then look at the
correlation between them, the strength of which can be judged from R (the
correlation coefficient). Finally, equation on the chart will help me find
estimations. So far, these are the only methods that I have been able to discover,
but I intend to find more.
iii) What are the limitations of my method? How accurate are my results?
The method that I am using has its own limitations. For example, I cannot be any
more accurate than the equation given to me, which assumes that the
relationship is linear, which may not be the case. Estimations of brain weight
from body weight may not be accurate at all – the pig and gorilla, for example,
have very similar body weights, (192 kg and 207 kg respectively) but have very
different brain weights (180 g and 406 g respectively).
Name: Anushka Rahman
Grade: 9-B
Correlation Between Body Weight & Brain Weight
y = 0.0011x + 97.408
R 2 = 0.8623
800
Brain Weight (g)
700
600
500
400
300
200
100
0
0
100000
200000
300000
400000
500000
600000
Body Weight (g)
b) What is the brain weight of a Bengal Tiger?
To estimate the brain weight of a Bengal tiger, which has a body weight of about
200 kg, I could use the graph’s best-fit line to find the brain weight that matches
this body weight. Or, for a more accurate result, I could obtain the result from
the equation the regression line obtained from MS-Excel by substituting the
value of ‘x’ with 200000. The result is 317.408. This is the estimated weight, in
grams, of a tiger’s brain.
This result may not be very accurate, as it is based solely on the body weight of
the mammal, and the relation between brain weight and body weight, as
mentioned before, is not a strong one. Moreover, the tiger’s body weight lies in a
range, which does not support the equation of the regression line – at a body
weight of 207 kg, the gorilla’s brain weight is way off the best-fit line, as the
graph shows, and so is that of the pig, which has a body weight of 192. The
tiger’s weight lying in between these two extremes, may vary greatly from the
estimated weight as well.
Name: Anushka Rahman
Grade: 9-B
c) Does a human with body weight of 62 kg and a brain weight of 1320 fall into
the pattern?
The graph showing the correlation between brain weight and body weight for
mammals, suggests that at a body weight of 62 kg, the brain weight should be
about 166 g (0.0011 X 62000 + 97.408 = 165.608). But the actual weight is 1320 g,
which is literally off the chart. This shows that a human is definitely an outlier
that does not fit into the correlation pattern between brain weight and body
weight. This is yet another evidence showing that although humans are
mammals, they vary greatly from other species – the brain size of humans is
probably a result of the progress of the entire race, resulting in a larger use of the
brain than other animals. Humans don’t live in the same conditions that other
mammals do in nature, and therefore are exceptions. That is all that can be
concluded from this comparison, apart from the speculation that there is no
convincing relationship between brain weight and body weight.
d) Brain weight of a cow of Body weight 465 kg.
As the body weight of a cow is 465 kg, therefore 465,000 grams, then the estimate
of the brain weight, if the equation from the graph is used, would be (0.0011 X
465000 + 97.408 = 608.908) about 609 grams.
e) What is the brain weight of an elephant?
The body weight of an elephant is given to be 6650 kg. This value is not in the
range of the graph plotted, but an estimation can still be obtained from the
equation of regression line obtained from MS-Excel. By substituting the value of
x in the equation with 6650000 (body weight in grams) I obtained the
corresponding value of y, the brain weight of the elephant to be (0.0011 X
6650000 + 97.408 = 7412.408) about 7412 grams.
f) How accurate is my method?
Both the values vary greatly from the estimated ones. Yet both of them still
suggest a positive correlation. However, this correlation may not be the same as
that which I obtained from the given data. This could be because I assumed a
linear correlation, which may not be the case - perhaps there should be a curve
with diminishing gradient, instead of a line, to represent the pattern. The method
I used is limited to the equations of a straight line.
Another possibility is that there was not enough data – perhaps if more data was
taken into account, and the chosen independent variable was more restricted,
perhaps to herbivorous mammals only, or any other sub category, then perhaps
the estimations would be correct. As it is, the data given covered a large variety
of mammals, and the pattern is inconsistent within this selection, let alone others.
Name: Anushka Rahman
Grade: 9-B
All in all, this relationship is flawed and not to be depended upon – either there
is some other better correlation, or none at all which can best describe the trends.
Task #2
a) Is there correlation between gestation time and life span?
i) What method did I use, and why?
I am now going to investigate whether there is any correlation between
maximum lifespan and gestation period. I have used MS-Excel to plot the graph
of gestation period against maximum lifespan and set a best-fit straight line
through it. I have also obtained an equation and the value of R squared from the
graph using MS-Excel.
ii) What are the limitations of my method? How accurate are my results?
This method is highly accurate as the computer does all calculations and there
will hardly be any error in plotting and calculating. There maybe errors, though,
in estimation from this graph – it shows a positive, but quite weak correlation
between gestation period and maximum lifespan. The value of R squared is low,
and there are quite a few values far from the best-fit line and none of them are on
the line. The error in any estimation from this graph will be great.
Correlation between maximum lifespan and gestation
time
y = 0.0254x - 57.499
2
R = 0.6559
450
Gestation Time (in days)
400
350
300
250
200
150
100
50
0
0
2000
4000
6000
8000
10000
12000
Maximum Lifespan (in days)
14000
16000
18000
Name: Anushka Rahman
Grade: 9-B
b) What is the gestation time of a giant armadillo?
A giant armadillo has a maximum lifespan of 7 years. From the equation of
regression line of the graph, the gestation period of a giant armadillo comes to
about 7 days (.0254 X 2555 - 57.499 = 7.398).
This value is probably not very accurate. This is because the method is not
accurate and the line drawn to represent the correlation is not a fitting
description of the pattern between the two variables being discussed. Further
more, the line cuts the x-axis in at a positive value, suggesting that for very low
life spans, the gestation period is negative, which is impossible. Thus, maybe the
relationship fails at lower values of lifespan, and one cannot predict the gestation
period of a giant armadillo with more accuracy without the aid of other
information.
c) Is the human gestation period relatively long or short?
If a human’s maximum lifespan is assumed to be 100 years, its gestation period,
according to the graph should be around 866 years – over two years. (0.0254 X
36500 + 57.499 = 865.601) however, that is not the case. It is only around 270 days,
and so our maximum lifespan should have been much lower – according to the
graph, that is. This could be because human beings now live in much higher
security than other animals do. We have medical facilities, secure homes and
many other privileges that allow us to live longer than we would in the wild –
there was a time in before civilisation came when humans could live only up to
40 years – a lifespan that DOES match that from the data. But now that we have
better homes and don’t have to worry about food or health compared to other
animals, our lifespan has increased greatly.
A kangaroo also has a very short gestation period compared to its lifespan, as it
is way below the line of regression. The kangaroo is a marsupial, unlike the other
animals in the list. This may be a reason why it’s gestation period is not in par
with the pattern.
TASK #3
a) Is there correlation between predation index and sleep exposure index?
i) Predictions:
I think that there is a high chance that there will be a strong positive correlation
between predation index and sleep exposure index. Looking at the table, we can
immediately see that the numbers for predation index and sleep exposure index
are nearly always the same for each animal. If the animal is highly preyed upon,
then it is also the most exposed.
Name: Anushka Rahman
Grade: 9-B
Correlation Between Predation Index & Sleep
Exposure Index
y = 0.7325x + 1.379
2
R = 0.7005
Sleep Exposure Index
6
5
4
3
2
1
0
0
1
2
3
4
5
6
Predation Index
ii) What is my method, and the limitations of my results?
Again, just like in the case of body weight and brain weight, I have used Ms
Excel to draw my graphs. I have used the equation given to estimate other
results, and R squared to find out how strong the correlation is. My predictions
were right, but still some of the mammals are far away from the best-fit line,
which again suggests that all results and estimations will vary from mammal to
mammal.
TASK #4
i) Which chart would be the most suitable and why? What are the advantages
and disadvantages?
I have chosen a bar chart from MS-Excel to represent all the data given. This
chart seemed the most suitable choice as it is meant for representing a numerical
variable against a non-numerical or categorical one. It is also appropriate for
comparison – one can easily judge the height of bar compared to another. The
disadvantage is that small numbers are hard to read – one can say that India has
about 3500 tigers in it – but can one tell how many china has, without a ruler?
This is because of the enormous scale, and the differences between the extremes.
Yet, this graph is the most suitable – other graphs that maybe used instead, like
the pie chart, would be even more inconvenient. The India portion would take
up most of the space, leaving the other portions almost indistinguishable from
Name: Anushka Rahman
Grade: 9-B
each other, making them hard to compare with each other. The numerical value
is also hard to judge from a pie chart, or doughnut chart, since it involves
measuring angles and tedious calculations. The only thing that is easier to
understand from a pie chart is the percentage distribution – other than that, the
bar chart is a lot more convenient for this kind of data. A line chart is out of the
question as ‘country’ is a discreet, non-continuous variable and so the graph
cannot be continuous.
Tiger population in 1998
3500
Tiger population
3000
2500
2000
1500
1000
500
0
Bangladesh
Bhutan
China
India
Myanmar
Nepal
Countries
TASK #5
i) What type of chart am I going to use and why? Are there any alternatives?
For this purpose, I have used a line chart to represent the data, using MS-Excel.
The chart clearly shows the trends in the tiger populations over the years, and
allows a viewer to estimate the population in any year within the range of the
chart. A bar chart could be an alternative form of representation, but then one
cannot make estimations from, and the year becomes a discreet variable, instead
of a continuous one, and it would be harder to see a trend. The line chart does
make the assumption that there is no sudden change of population, some sharp
rise or fall in between the given years, so an estimation may be wrong – however,
for a general purpose, it serves well.
Name: Anushka Rahman
Grade: 9-B
Number of tigers
Tiger Population in India
5000
4000
3000
2000
1000
0
1970
1980
1990
2000
Years
ii) How effective has the Indian Government been?
The chart shows that the population has increased to a high of 4380 in 1989, from
1830 in 1972. Then it decreased to a little above 3500 where it appears to remain
constant. If this is to remain constant for a long period of time, then the Indian
government’s efforts have been fruitful – the population nearly doubled from
1972. It would definitely appear so from the upward trend up to 1989, and after
that, the population did fall, but not drastically – perhaps there was some other
reason behind it. It could be, however, that after the increase in the tiger
population, the Indian government slacked, either in maintenance or effort, and
the population declined. However, looking at the graph, there may be a chance
that the population might increase.
Task #6
i) What are the important facts that I have learnt through this investigation?
 Mammals vary in shape and size. So do their body weight and brain
weight, gestation time and maximum life span, their predation rate and
sleep exposure.
 Correlations between the above variables are strong, but estimations are
just as unreliable, as we cannot be accurate in any case.
 The various types of animals that are also mammals, and their lifestyles,
as well as some facts about them.
 The number of Bengal tigers in Asia.
Name: Anushka Rahman
Grade: 9-B
 I learnt some technical things, like how to make correlation charts, what R
squared is, and how I can use the equation given by Ms Excel to make
estimations.
ii) Three graphs to display some of the information given
A Comparison Between Lifespan & Gestation Time
18000
16000
Number of Days
14000
12000
10000
8000
6000
4000
2000
0
1 2
3
Maximum Lifespan
4
5
6
7
8
9
10 11 12 13 14 15
Animal No.
Gestation Time
Body Weight
Animal No.
15
13
11
9
7
5
Body Weight
3
15
13
11
9
7
5
3
Brain Weight
600000
500000
400000
300000
200000
100000
0
1
800
700
600
500
400
300
200
100
0
1
Weight in grams
Brain Weight
Weight in grams
i) Why did I chose these graphs?
I thought that another way that we often showed correlation with are multiple
bar graphs. I experimented with this idea by showing correlation through a bar
Name: Anushka Rahman
Grade: 9-B
graph that had both the gestation time and the maximum lifespan of the
mammals. Then I made two separate bar graphs of brain weight and body
weight, which showed two sets of data separately, side by side, so the difference
again could be seen. This way, we could clearly see the numbers, what they
stand for, and also use a method that we are familiar with, as we use bar graphs
the most.
Bibliography
http://en.wikipedia.org/wiki/Mammal
http://cda.mrs.umn.edu/~anderson/math1601/notes/ch2/node10.html
http://www.answers.com/correlation
Technology information about correlation
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WordNet information about correlation
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