nissan stocks - data analysis
TRANSCRIPT
Julie Boulos
Buzzelli
MPM4U1-02
December 2013
2
Nissan: Table of Contents
Part A: Business Description ………………………………………………….…..….Page 4
Part B: Mathematical Analysis of Collected Data
Line of Best Fit……………………………………………..………………………...…Page 6
Linear Regression…………………………………………………….………..…….Pages 7-9
Measures of Central Tendencies………………………………………...…………....Page 10
Standard Deviation……………………………………………………..……………...Page 10
Co-relation coefficient……………………………………………….…...…...…….….Page 11
Probability Distribution Formation………………………………………….……….Page 12
Box and Whisker Plot………………………………………………………...…...Pages 12-14
Part C: Written Paper on Mathematical Analysis with graphs
2008…………………………………………..…………………………………...Pages 16-19
2009………………………………………………………………………….……Pages 20-23
2010………………………………………………………………………...……..Pages 24-27
2011………………………………………………………………….…...……….Pages 28-31
2012………………………………………………………………….…............…Pages 32-35
2008-2012…………………………………………………………….…………...Pages 36-39
Part D: Written Report on Mathematical Understanding of material....................Page 41
Part E: Appendices, Rough Work, Miscellaneous and Bibliography…….……….Page 43
3
PART A: BUSINESS DESCRIPTION
4
“The power comes from inside.” This simple phrase familiar to every Nissan employee
conveys a powerful truth. Any company is only as strong as the people who bring it to life.
Companies do not create products, deliver services or solve problems; people do. The people
working at Nissan are facing major evolutions that are changing the global automotive industry
as we know it today.
The world's population is expanding at a rapid pace, from 6.7 billion today to more than
9 billion by 2050. More people will create the demand for more cars. Today, there are 600
million vehicles worldwide; by 2050, statistics show there may be up to 2.5 billion vehicles. A
car is an important symbol of freedom, status and personal achievement, and growing numbers
of new drivers will seek affordable transportation and the benefits that car ownership provides.
Another important trend is the growing demand for a cleaner environment. Automakers
are accelerating the development of products to offer greater fuel efficiency and fewer
CO2 emissions, from more efficient gasoline-fuelled engines to hybrids, clean diesel,
electric vehicles and fuel cell vehicles.
The world is changing, and Nissan is adapting with it. They are harnessing the power that's
inside Nissan to prepare solutions that our customers will want and value, now and in the years
to come. Solutions such as:
electric and fuel cell vehicles that are attractive, fun-to-drive cars with the appealing benefit
of zero emissions;
global entry cars that make mobility more accessible and affordable for all; and
innovative technological advances that are good for the environment, enhance safety,
improve dynamic performance or provide greater life-on-board satisfaction.
Nissan has a clear vision for the future, and - with their Alliance partner, Renault - they are
working with passion to achieve it. Their mission is to enrich people's lives, building trust with
their employees, customers, dealers, partners,
shareholders and the world at large.
5
PART B: MATHEMATICAL
ANALYSIS OF COLLECTED DATA
6
Line of Best Fit
Line of Best Fit (LOBF): the straight line that passes closest to the majority of the data points
on a scatter plot and best represents the relationship between two variables. The data is used to
form a curve of best fit. The stronger the correlation, the more closely the points cluster the
LOBF.
Formula used: y = ax + b, where the slope is represented by a, the y-intercept in represented by
b, and the individual point of the line is (x,y),
Slope = ∑ ∑ ∑
∑ ∑
Y-intercept = ̅ ̅
Let x represent the day # and y represent the open value.
In order to calculate the numerator, the total number of terms is multiplied by the sum of
Day*Open (∑ ), then yousubtract the product of the sum of Day (x)multiplied by the sum of
Open (y) from the first value (total number of terms by sum of day times open).
To calculate the denominator, the total number of terms is multiplied by the sum of Day^2
(∑ , followed by subtracting the sum of Day [∑ .
The numerator is then divided by the denominator, resulting in the slope.
Next, plug in your numbers and calculate the y-intercept, b = ̅ ̅.
To calculate the ̅ (mean of x) in the y-intercept equation, the sum of Day (∑ is divided by
the number of terms, the ̅ (mean of y) is similar except sum of Open (∑ rather than day.
After plugging in all the terms you can solve for the y-intercept
The LOBF is then determined by substituting the slope (a value), and y-intercept (b value) into
the equation
if using Microsoft Excel, calculate the numerator and denominator seperately so you can use
them to easily calculate the slope
A scatter plot is used to depict the line of best accurately
7
Linear Regression
Linear Regression: an analytical technique used to determine the relationship between a
dependent and independent variable.
When the two variables have a linear correlation, you can develop a model of a relationship
between the x and y variables by finding a line of best fit.
In order to extrapolate, the estimated day (x) is substituted in the equation y = ax+b for the
LOBF to solve for the open value (y).
For Example: in the Nissan stock, a year’s time period is 261 days and the five-year time period
is 1273 days. In order to extrapolate, it would be 1273 (the five years) and
as our independent
x value.
Estimating the stock one month into the future:
x = 1273 +
y = -0.005741814x + 19.87823496
y = -0.005741814(1273+21.75) + 19.87823496
y= -0.005741814(1294.75) + 19.87823496
y = -7.4342136765 + 19.87823496
y = 12.4440212835
Therefore, the estimated value of the stock one month into the future is $12.44. The
average stock value of the five years is $16.22. This means that investing in Nissan is not the
best idea because the stock value is expected to drop again meaning you would lose money.
8
6 months:
In order to extrapolate, it would be 1273 (the five years) and
as our independent x value.
Estimating the stock six months into the future:
x = 1273 +
y = -0.005741814x + 19.87823496
y = -0.005741814(1273+130.5) + 19.87823496
y= -0.005741814(1403.5) + 19.87823496
y = - 8.058635949 + 19.87823496
y = 11.819599011
The stock will only continue to decrease after six months still resulting in a poor
investment.
1 year:
In order to extrapolate, it would be 1273 (the five years) and
as our independent x value.
Estimating the stock one year into the future:
x = 1273 +
y = -0.005741814x + 19.87823496
y = -0.005741814(1273+261) + 19.87823496
y= -0.005741814(1534) + 19.87823496
y = - 8.807942676 + 19.87823496
y = 11.070292284
As the year concludes, the stock is estimated to continue decreasing in value.
9
10 years:
In order to extrapolate, it would be 1273 (the five years) and
as our independent x value.
Estimating the stock ten years into the future:
x = 1273 +
y = -0.005741814x + 19.87823496
y = -0.005741814(1273+2610) + 19.87823496
y= -0.005741814(3883) + 19.87823496
y = - 22.295463762 + 19.87823496
y = -2.417228802
After completing all the calculations, it is proven that by estimation, Nissan stocks are
estimated to continue to drop in value. By looking at the calulations, I have concluded that it is
possible that in 10 years the stock will lose its value and the company can become bankrupt.
10
Measures of Central Tendancy
When looking at a set of data, there are measures that can be taken in order to analyze the
data recorded
The three measures of central tendancy include the mean, median and mode
These are most frequently used to analyze the “middle”
Mean: the average of any set of data, takes the form of ∑
. (16.22069969)
Median: a method to calculate the middle number, but the data must be in ascending or
descending order. The number that sits in the middle is the median. (17.15)
Mode: the value that occurs most often, in most scenarios this is rarely used. It is not used as
much as the other measures because it does not accurately represent all the values in a set of
data, rather only the accounts for a certain set value that occurs most frequently. (16.45)
Calculations: y = ax + b, where a = ∑ ∑ ∑
∑ ∑ and b = ̅ ̅
Standard Deviations
Standard Deviation : the square root of the mean of the squares of the deviations of a set of
data. It is represented by the greek letter sigma and shows how much variation exists from the
average. The more spread out the data, the higher the deviation.
Formula : √∑
Start by calculating the numerator, the sum of each open value minus the mean of the data
square-rooted, then the overall difference is squared. Once you’ve calculated your numerator
you can divide it by your total number of terms.
The second method for standard deviation is the computer generated equation. It can be
calculated on Microsoft Excel using the equation =STDEV(C:C), C represents the column with
the open stock values.
11
Co-relation Coefficient
Correlation: a number between -1 and 1, calculated to represent the linear dependence of two
variables or sets of data.
The number shows the relation between two variables, it shows whether the increase/decrease of
one factor has an effect on the other and by how much.
If the correlation is positive, it is a positive relationship, vise versa for negative. The strength of
the correlation varies from weak to medium to perfect. As seen in the diagram below, each range
is categorized differently. If the number is very close to 0, however, it means that there is barely
or no relationship between the two variables.
The equation for the co-relation coefficient is as follows:
r = ∑ ∑ ∑
√[ ∑ ∑ [ ∑ ∑
where r represents the co-relation coefficient.
Positive Negative
-1 -0.67 -0.33 0 0.33 0.67 1
Perfect Strong Moderate Weak Weak Moderate Strong Perfect
12
Probability Distribution Formation
Probability Distribution Formation: taking the entire set of data and distributing it into various
possible occuring events, this can be represented using a histogram.
Histogram: similar to a bar graph, which helps group data into intervals. It can describe the
likeliness of the various events. I.e. which area will most sets of data occur.
To determine the probability distribution in excel, the maximum and minimum value of
each year is required. Then you must create intervals for which the sets of data are grouped in.
For example, if the minimum value is 3.6 and the maximum is 7.4, you need to choose and
interval that includes all the data points. 3 and 8 can be used in this example, with intervals of .5.
You can then proceed to code the document so that your first interval is calculated, you can do
this by creating a loop. Then, use your loop to calculate the next one and subtract your previous
intervals results to eliminate repetition.
Box and Whisker Plot
The box and whisker plot is a diagram that summarizes a set of data by representing the
first quartile, the median and third quartile. This is done with a box and the lowest and highest
data value with the ends of lines extending from the box.
0 10 20 30 40 50
Q1 Median Q3
13
Starbucks Open Value 2008: Box and Whisker Plot
Looking at the box and whisker plot, the median is closer to Q3 than Q1. This shows the
fluctuation in open stock values throughout the year. There was a larger overall decrease vs
increase of prices throughout the year.
Starbucks Open Value 2009: Box and Whisker Plot
Looking at the box and whisker plot, by a small value the median is closer to Q3 than Q1
again. This shows the fluctuation in open stock values throughout the year. There was a larger
overall decrease rather than increase of prices throughout the 2009 year.
Starbucks Open Value 2010: Box and Whisker Plot
Looking at the box and whisker plot, the median is much closer to Q1 than Q3. This
shows the fluctuation in open stock values throughout the year. There was a larger overall
increase than decrease of prices throughout the 2010 year. The company begins to improve their
stock profits.
Q1 Q3 Median
Q1 Q3
Median Q1 Q3
Median
Min. Max.
Min. Max.
Min. Max.
14
Starbucks Open Value 2011: Box and Whisker Plot
Looking at the box and whisker plot, the median is closer to Q1 than Q3. This shows the
fluctuation in open stock values throughout the year. There was a greater overall increase than
decrease of prices throughout the 2011 year. The company continues to improving their stock
profits.
Starbucks Open Value 2012: Box and Whisker Plot
Looking at the box and whisker plot, by a small value the median is still closer to Q1 than
Q3. This shows the fluctuation in open stock values throughout the year. The overall increase
was greater than the decrease of prices throughout the 2012 year.
Starbucks Open Value 2008-2012: Box and Whisker Plot
Looking at the box and whisker plot, by a small value the median is closer to Q3 than Q1
again. This shows the fluctuation in open stock values throughout the five years. Over the time
period, there was an overall decrease in stock prices since the open values kept fluctuating but
mostly declined. Even with some good years for Nissan, they still had an overall decline.
Q1 Q3 Median
Q1 Q3 Median
Q1 Q3 Median
Min. Max.
Min. Max.
Min. Max.
15
PART C: WRITTEN PAPER ON MATHEMATICAL
ANALYSIS WITH GRAPHS
16
2008
Line of Best Fit
m = ∑ ∑ ∑
∑ ∑ b = ̅ ̅
m =
b = 14.74411067 – (0.050099)(127)
m = 0.050099274 b = 8.381
Line of best fit: y = 0.050x + 8.381
The line of best fit indicates that the approximate initial stock value was $8.38. The initial
stock value was low, but the stock has a positive slope as the price is increasing at a good pace.
The lowest price for this year is $6.60 and the highest is $21.48.
y = 0.0501x + 8.3815 R² = 0.8106
0
5
10
15
20
25
0 50 100 150 200 250 300
Op
en (
$)
Day (x)
NISSAN OPEN STOCK VALUE 2008
Open
Linear (Open)
17
Standard Deviation
Calculations: = √∑
=
= 4.063989611
OR =STDEV(C3:C3000)
= 4.063989611
The standard deviation for the year 2008 indicates that Nissan’s open stock value
deviates a bit from the mean of the open stock values for the years, which was $7.16. The
deviation is also observed through the range ($), which indicates the overall fluctuation
throughout the year. Furthermore, the deviation of data in 2008 causes a larger gap to form
between the clusters of data which is represented by the fluctuation on the graph.
Co-relation Coefficient
Equation: r = ∑ ∑ ∑
√[ ∑ ∑ [ ∑ ∑
√[ [
= 0.900337514
The correlation coefficient of 2008 indicates that the data has a positive correlation,
which means as the stock progresses over the year, the open stock value will continue to
increase. The strength of this correlation is considered to be a strong positive linear
correlation.
18
Measures of Central Tendency
Equation: ∑
=
Mean: $14.74411067
Median: $16.08
Mode: $18.36
Therefore, the average Open Stock Value for the year 2008 is $14.74. The middle
number is $16.08 and the most frequently occuring value is $18.36. Considering the most
frequent value is higher than the average and the middle number, the 2008 year can be
considered to have positive values.
19
Probability Distribution Formation
In conclusion, looking at this histogram we are able to analyze the different ranges of
data for the open stock values. The stock prices range from $6-23.99 which gives a pretty wide
range for the year. Just at a quick glance it is easy to see that the most frequent stock values
range from $15-17.99. With such a wide range of stock values it shows that the open stock
values were inconsistent.
020406080
100120140
# o
f O
ccu
ren
ces
Range ($)
2008 Nissan Open Distribution
20
2009
Line of Best Fit
m = ∑ ∑ ∑
∑ ∑ b = ̅ ̅
m =
b = 11.63206349– (-0.043) (126.5)
m = -0.04295518 b = 17.06
Line of best fit: y = -0.043x + 17.06
The line of best fit indicates that the approximate initial stock value was $17.06. The
initial stock value was much higher then the year end. The 2009 stocks have a negative slope
since the price is gradually decreasing. The lowest price for this year is $5.65.
y = -0.043x + 17.066 R² = 0.8921
0
5
10
15
20
0 50 100 150 200 250 300
Op
en (
$)
Day
NISSAN OPEN STOCK VALUES 2009
Open Linear (Open)
21
Standard Deviations
Calculations: = √∑
=
= 3.308383127
OR =STDEV(C3:C3000)
= 3.308383127
The standard deviation for the year 2009 indicates that Nissan’s open stock value
deviates a bit from the mean of the open stock values for the years, which was $17.06.
The deviation is also observed through the range ($), which indicates the overall
fluctuation throughout the year. Furthermore, the deviation of data in 2009 causes a gap
to form between the clusters of data as seen above on the graph.
Co-relation Coefficient
Equation: r = ∑ ∑ ∑
√[ ∑ ∑ [ ∑ ∑
√[ [
= -0.94450933
The correlation coefficient of 2009 indicates that the data has a negative correlation,
which means as the stock progresses over the year, the open stock value will continue to
decrease. The strength of this correlation is considered to be a strong negative linear
correlation.
22
Measures of Central Tendency
Equation: ∑
=
Mean: $11.63206349
Median: $12.255
Mode: $14.35
Therefore, the average Open Stock Value for the year 2009 is $11.63. The middle number is
$12.26 and the most frequently occuring value is $14.35. Considering the most frequent value is
lower than the average and the middle number, the 2009 year is proving to be a declining year.
23
Probability Distribution Formation
In conclusion, looking at this histogram we are able to analyze the different ranges of
data for the open stock values. The stock prices range from $5-18.99 which doesn’t give as wide
a range as the previous year but still gives a wide range for the year. Just at a quick glance it is
easy to see that the most frequent stock values range from $13-14.99. With such range of stock
values, and more occurences in the lower values, it shows the gradual decrease in stock prices
throughout the year.
0
20
40
60
80
100
# o
f O
ccu
ren
ces
Intervals ($)
2009 Nissan Open Distributions
24
2010
Line of Best Fit
m = ∑ ∑ ∑
∑ ∑ b = ̅ ̅
m =
b = 16.74150794– (-0.00829)(126.5)
m = -0.00829696 b = 17.79
Line of best fit: y = -0.008x + 17.79
The line of best fit indicates that the approximate initial stock value was $17.79. The
initial stock value was not much higher then the year end. The 2010 stocks have a weak negative
slope since the price is decreasing. The lowest price for this year is $14.30.
y = -0.0083x + 17.791 R² = 0.1958
0
5
10
15
20
25
0 50 100 150 200 250 300
Op
en (
$)
Day (x)
NISSAN OPEN STOCK VALUES 2010
Open
Linear (Open)
25
Standard Deviations
Calculations: = √∑
=
= 1.36394361
OR =STDEV(C3:C3000)
= 1.36394361
The standard deviation for the year 2010 indicates that Nissan’s open stock value
deviates a bit from the mean of the open stock values for the years, which was $17.79.
The deviation is also observed through the range ($), which indicates the overall
fluctuation throughout the year. Furthermore, the deviation of data in 2010 causes a small
gap between the clusters of data which is represented by the line on the graph.
Co-relation Coefficient
Equation: r = ∑ ∑ ∑
√[ ∑ ∑ [ ∑ ∑
√[ [
= -0.44251615
The correlation coefficient of 2010 indicates that the data has a negative correlation,
which means as the stock progresses over the year, the open stock value will continue to
decrease. The strength of this correlation is considered to be a moderate negative linear
correlation.
26
Measures of Central Tendency
Equation: ∑
=
Mean: $16.74150794
Median: $16.45
Mode: $16.45
Therefore, the average Open Stock Value for the year 2010 is $16.74. The middle
number is $16.45 and the most frequently occuring value is $16.45. For this years the numbers
are generally in a small range, the average, most frequent, and middle numbers are all similar, if
not the same which shows very little change throughout the year. This year had a slight decrease
and then stayed in a very small range for the rest of the year.
27
Probability Distribution Formation
In conclusion, looking at this histogram we are able to analyze the different ranges of
data for the open stock values. The stock prices range from $13-20.99 which gives a pretty wide
range for the year. Just at a quick glance it is easy to see that the most frequent stock values
range from $16-16.99. Although there is a wide range of stock values the majority of open stock
values are within the $16-16.99 range, this shows how the correlation is moderate.
Mean: $14.74411067
Median: $16.08
Mode: $18.36
0
50
100
150
# o
f O
ccu
ren
ces
Intervals ($)
2010 Nissan Open Distributions
28
2011
Line of Best Fit
m = ∑ ∑ ∑
∑ ∑ b = ̅ ̅
m =
b = 18.92870079 – (0.009)(127.5)
m = 0.009695182 b = 17.79
Line of best fit: y = -0.009x + 17.69
The line of best fit indicates that the approximate initial stock value was $17.69. The
initial stock value was lower then the year end of $19.40. The 2011 stocks have a weak positive
slope since the price is slowly beginning to increase. The lowest price for this year is $16.20 and
the highest was $21.94. Although it had slow increases and a few drops, 2011 did much better
than 2009 and 2010.
y = 0.0097x + 17.693 R² = 0.2319
0
5
10
15
20
25
0 50 100 150 200 250 300
Op
en (
$)
Day (x)
NISSAN OPEN STOCK VALUES 2011
Open
Linear (Open)
29
Standard Deviations
Calculations: = √∑
=
= 1.476111981
OR =STDEV(C3:C3000)
= 1.476111981
The standard deviation for the year 2011 indicates that Nissan’s open stock value
deviates a bit from the mean of the open stock values for the years, which was $17.69. The
deviation is also observed through the range ($), which indicates the overall fluctuation
throughout the year. Furthermore, the deviation of data in 2011 does not have a large gap between
the clusters of data which is represented by the fluctuation on the graph.
Co-relation Coefficient
Equation: r = ∑ ∑ ∑
√[ ∑ ∑ [ ∑ ∑
√[ [
= 0.481588795
The correlation coefficient of 2011 indicates that the data has a positive correlation,
which means as the stock progresses over the year, the open stock value will continue to
increase. The strength of this correlation is considered to be a moderate positive linear
correlation.
30
Measures of Central Tendency
Equation: ∑
=
Mean: $18.92870079
Median: $18.725
Mode: $17.5
Therefore, the average Open Stock Value for the year 2011 is $18.93. The middle number is
$18.72 and the most frequently occuring value is $17.50. After looking at the past two years, all
the values have increased which shows that the company is gradually doing better.
31
Probability Distribution Formation
In conclusion, looking at this histogram we are able to analyze the different ranges of
data for the open stock values. The stock prices range from $16-21.99 which is not a wide range
for the year. Many different values occur frequently, but the most frequent open value is in the
$17-17.99 range. For the majority of the year there are not too many large increases or decreases,
this shows the company stablizing.
Mean: $14.74411067
Median: $16.08
Mode: $18.36
0
20
40
60
80
# o
f O
ccu
ren
ces
Intervals ($)
2011 Nissan Open Distribution
32
2012
Line of Best Fit
m = ∑ ∑ ∑
∑ ∑ b = ̅ ̅
m =
b = 18.94421456 – (0.007)(131)
m = 0.007533049 b = 17.79
Line of best fit: y = 0.007x + 17.95
The line of best fit indicates that the approximate initial stock value was $17.79. The
2012 stocks have a weak positive slope since the price is slowly continuing to increase. The
lowest price for this year is $16.60 and the highest was $21.77. The closing price for the 2008-
2012 five-year span was $17.70.
y = 0.0075x + 17.957 R² = 0.2397
0
5
10
15
20
25
0 50 100 150 200 250 300
Op
en (
$)
Day (x)
NISSAN OPEN STOCK VALUES 2012
Open
Linear (Open)
33
Standard Deviations
Calculations: = √∑
=
= 1.159305453
OR =STDEV(C3:C3000)
= 1.159305453
The standard deviation for the year 2012 indicates that Nissan’s open stock value
deviates a bit from the mean of the open stock values for the years, which was $17.79. The
deviation is also observed through the range ($), which indicates the overall fluctuation
throughout the year. Furthermore, the deviation of data in 2012 causes a gap to re-form between
the clusters of data which is represented by the fluctuation on the graph.
Co-relation Coefficient
Equation:r = ∑ ∑ ∑
√[ ∑ ∑ [ ∑ ∑
√[ [
= 0.489575394
The correlation coefficient of 2012 indicates that the data has a positive correlation,
which means as the stock progresses over the year, the open stock value will continue to
increase. The strength of this correlation is considered to be a moderate positive linear
correlation.
34
Measures of Central Tendency
Equation: ∑
=
Mean: $18.94421456
Median: $18.89
Mode: $18.71
Therefore, the average Open Stock Value for the year 2012 is $18.94. The middle number is
$18.89 and the most frequently occuring value is $18.71. Similarly to 2011, 2012 also has
similar measures of central tendancy. As seen on the line of best fit, the majority of the numbers
stay within the same range.
35
Probability Distribution Formation
In conclusion, looking at this histogram we are able to analyze the different ranges of
data for the open stock values. The stock prices range from $16-22.49 which gives a decent
variety for the range of the year. Just at a quick glance it is possible to see that the most frequent
stock values range from $18.50-19.49.
Mean: $14.74411067
Median: $16.08
Mode: $18.36
0
20
40
60
80
100
# o
f O
ccu
ren
ces
Intervals ($)
2012 Nissan Open Distribution
36
2008 – 2012
Line of Best Fit
m = ∑ ∑ ∑
∑ ∑ b = ̅ ̅
m =
b = 16.22069969 – (-0.0057)(637)
m = -0.005741814 b = 19.90
Line of best fit: y = -0.005x + 19.90
The line of best fit indicates that the approximate initial stock value was $19.90. The
initial stock value was lower then the year end of $21.48. Overall at the end of the five-year span
the stock value has an ending increased value. Even though the value has increased there is a
negative slope. The lowest price over the five years was $5.65 and the highest was $21.94.
Although it had many increases and drops, the Nissan stock managed to come back up to an
acceptable value. Using the data we can see that their worst year was 2009 since the data was
inconsistent and dropped significantally, and their best year was 2011 as the value finally
increased after a two-year decline.
y = -0.0058x + 19.908 R² = 0.3188
0
5
10
15
20
25
0 500 1000 1500
Op
en (
$)
Day (x)
NISSAN OPEN STOCK VALUES 2008 - 2012
Open x
Linear (Open x)
37
Standard Deviations
Calculations: = √∑
=
= 3.765369664
OR =STDEV(C3:C3000)
= 3.765369664
The standard deviation for the five years indicates that Nissan’s open stock value
deviates from the mean of the open stock values for the years, which was $7.16. The deviation is
also observed through the overall range of the five years ($), which indicates the overall
fluctuation throughout the time period. Furthermore, even with some slow years, the deviation of
data causes a large gap to form between the clusters of data which is represented by the
fluctuation on the graph.
Co-relation Coefficient
Equation: r = ∑ ∑ ∑
√[ ∑ ∑ [ ∑ ∑
√[ [
= -0.556553684
The correlation coefficient of the five years indicates that the data has a negative
correlation, which means as the stock progresses over the years, the open stock value will
continue to decrease. The strength of this correlation is considered to be a moderate negative
linear correlation. Even though the stock does have some positive years, the overall progress of
the stock is declining.
38
Measures of Central Tendency
Equation: ∑
=
Mean: $16.22069969
Median: $17.15
Mode: $16.45
Therefore, the average Open Stock Value for the five years is $16.22. The middle number is
$17.15 and the most frequently occuring value is $16.45. With a range going from $5 up to $23
these numbers are pretty high on the scale.
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Probability Distribution Formation
In conclusion, looking at this histogram we are able to analyze the different ranges of
data for the open stock values. The stock prices range from $6-22.99 which gives a pretty wide
range for the year. Just at a quick glance it is easy to see that the most frequent stock values
range from $17-19.99 (538 occurences), with $14-16.99 not too far behind (360 occurences).
The least occuring interval range $8-10.99 with only 59 occurences. With such a wide range of
stock values it shows that the open stock values had some inconsistency over the five years.
Mean: $14.74411067
Median: $16.08
Mode: $18.36
0100200300400500600
# o
f O
ccu
ren
ces
Intervals ($)
2008-2012 Nissan Open Distribution
40
PART D: WRITTEN REPORT ON
MATHEMATICAL UNDERSTANDING OF MATERIAL
41
By analyzing all of nissans stocks over the past five years, I’ve had the opportunity to
gain knowledge on the company and would not suggest investing into the NSANY stock. Before
doing this assignment I would have assumed Nissan was a good investment since their cars sell
well. Having done another stock project in the past, however, it is not a surprise to see the
fluxuation of stock prices with several declines and increases.
The line of best fit indicates that the approximate initial stock value was $19.90. The
initial stock value was lower then the year end of $21.48. Overall at the end of the five-year span
the stock value has an ending increased value. Even though the value has increased there is a
negative slope. The lowest price over the five years was $5.65 and the highest was $21.94.
Although it had many increases and drops, the Nissan stock managed to come back up to an
acceptable value. Using the data we can see that their worst year was 2009 since the data was
inconsistent and dropped significantally, and their best year was 2011 as the value finally
increased after a two-year decline.
Over the Five years the greatest range of stocks were approximately $17-$20 which is on
the higher end of their fluxuating prices. This is positive because although not completely
consistent, for some time throughout the past five years Nissan could have been considered a
good buy. Looking at the future prediction for a decline is what makes it more of a negative
stock.
By investing in the stock market, any investor should only be buying knowing about the
risk they are putting their money into. The market changes daily and if someone only invests in
one field of the economy they will either profit a lot quickly or lose everything all at once. In
order to keep balance it’s suggested that someone invest in multiple stocks not related to
eachother.
42
PART E: APPENDICES, ROUGH MATHEMATICAL WORK,
MISCELLANEOUS AND BIBLIOGRAPHY
43
Bibliography
“Historical Prices.” Yahoo Finance. n.a. n.d. Web. 3 Sept. 2013.
“Message/Vision.” Nissan-global. Carlos Ghosn, n.d. Web. 15 Sept. 2013.
“Nissan Work.” Coroflot. Nick Coughlan. 17 Jan. 2009. 25 Nov. 2013.
“Production Nissan Juke-R Sketches.” Auto Evolution. Mihnea Radu. 8 Aug. 2012. 25 Nov.
2013.