Data Analysis and Visualization

There are 32 ENSO conditions recorded, and out of these, 10 are neutral. The fraction of neutral conditions is therefore 0.3125. The data for the ENSO Cycle variable shows that 11 out of 32 conditions are El Nino, which represents a percentage of 34.375. The data for the Solar Irradiance variable displays a frequency distribution table with class intervals of equal width and a pie chart showing the main feature is the blue color shaded area representing 5 values. The box plot for the Solar Irradiance variable shows that the median is 1365.91, and there are no outliers found. For the CO2 variable, the population standard deviation of the 1979-1994 group is 6.810, while that of the 1995-2010 group is 8.740, showing a significant increase in dispersion between the two groups. If a glitch had reduced all data for the CO2 level by a factor of 10, the corrected standard deviations would be 87.43365 and 1171.937, respectively.

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Applying Mathematics Assessment Two Part One
ASSESSMENT TWO PART ONE: UNIVARIATE ANALYSIS
TOTAL OF UNIT MARK: 20%
DUE DATE: 11:59pm WST Sunday 15th April 2018 (Submit via Blackboard)
This assignment requires you to display and analyse the data in the table below by completing a
series of set tasks. The data is from a time series set over 32 years examining factors relating to
climate change.
The variables in the data are:
Year Year the data was collected
ENSO Cycle “El Nino-Southern Oscillation” Periodic variation in winds and sea surface
temperatures resulting in climatic cooling and warming phases
Sea Ice Recorded in 1,000,000’s of square kilometres, measured in September each
year, at the end of each melting season
Temperature The mean annual global surface temperature measured in degrees
centigrade
Solar Irradiance The power per unit area received by the Earth from the Sun, measured in
Watts per square metre
Atmospheric CO2 The volume of CO2 in the atmosphere, measured in Parts Per Million
The data table is on the next page.
*Hint: copy and paste this table into Excel if you plan to use Excel to assist with your calculations and
graphs, to help eliminate input error.

Applying Mathematics Assessment Two Part One
The data relating to climate change over a period of 32 years is as follows:
Year ENSO Cycle Sea Ice Temperature Solar Irradiance Atmospheric CO2
(×1,000,000 km2) (˚c) (W/m2) (ppm)
1979 El Nino 7.2 8 1366.06 336.67
1980 Neutral 7.85 19 1365.72 338.57
1981 Neutral 7.25 26 1366.51 339.92
1982 El Nino 7.45 4 1366.16 341.3
1983 La Nina 7.52 25 1366.18 342.71
1984 La Nina 7.17 9 1365.9 344.24
1985 Neutral 6.93 4 1365.77 345.81
1986 El Nino 7.54 12 1365.59 347.11
1987 El Nino 7.48 27 1365.67 348.72
1988 La Nina 7.49 31 1365.97 351.04
1989 Neutral 7.04 19 1366.46 352.68
1990 Neutral 6.24 36 1365.74 353.97
1991 El Nino 6.55 36 1366.34 355.37
1992 Neutral 7.55 13 1366.17 356.18
1993 Neutral 6.5 13 1365.86 356.69
1994 El Nino 7.18 23 1365.69 358.14
1995 La Nina 6.13 37 1366.02 360.02
1996 Neutral 7.88 29 1365.5 361.95
1997 El Nino 6.74 39 1365.65 363.18
1998 La Nina 6.56 56 1365.98 365.19
1999 La Nina 6.24 31 1366.18 367.86
2000 La Nina 6.32 33 1366.27 368.83
2001 Neutral 6.75 47 1366.33 370.43
2002 El Nino 5.96 56 1366.1 372.01
2003 Neutral 6.15 55 1365.92 374.45
2004 El Nino 6.05 48 1365.7 376.77
2005 La Nina 5.57 63 1365.51 378.3
2006 El Nino 5.92 55 1365.44 380.83
2007 La Nina 4.3 58 1365.32 382.56
2008 La Nina 4.68 44 1365.87 384.39
2009 El Nino 5.36 57 1366.03 386.34
2010 La Nina 4.9 63 1365.46 388.13

Applying Mathematics Assessment Two Part One
Use the information provided on the previous page to complete the following tasks. Remember to
carry as many decimal places (d.p.) in calculations to increase accuracy where appropriate to give
answers to decimal places (2 d.p.) unless otherwise stated and to include units (show working where
you can, as in some cases this may allow you to obtain partial marks for incorrect solutions):
1. For each of the following variables, state whether the data is best described as being binary,
nominal, ordinal, discrete or continuous and give brief supporting comment:
[2 marks]
a. ENSO Cycle
Is a nominal variable since this variable has 3 categories without having
any natural order.
b. Year
Year is a discrete variable as we can count the years 1,2,3…. Etc.
2. Display the data for the ENSO Cycle variable in a frequency distribution table and use it to
determine what fraction of the recorded ENSO conditions are neutral (in simplest form) .
[3 marks]
Refer excel sheet attached.
There are in total 32 and of those 32, neutral are 10
Hence fraction = 10/32 = 0.3125

Applying Mathematics Assessment Two Part One
3. Display the data for the ENSO Cycle variable in a column graph, and state what percentage of
conditions are El Nino. [3 marks]
Please refer excel sheet page 2.
El Nini La Nina Neutral
9.4
9.6
9.8
10
10.2
10.4
10.6
10.8
11
11.2
Series1
Percentage of El Nino = 11*100/32 = 34.375

Applying Mathematics Assessment Two Part One
4. Display the data for the Solar Irradiance variable in a frequency distribution table using class
intervals of equal width (the first one being 1365.2  w < 1365.4), then display this data in a pie
chart and give a brief comment detailing 1 main feature of the data that stands out on the pie
chart.
Refer excel
Mid
point Freq
I
1365.2-
<1365.4
1365.
3 1
2 1365.4-
<1365.6
1365.
5 5
3 1365.6-
<1365.8
1365.
7 7
4 1365.8-
<1366
1365.
9 6
5 1366-
<1366.2
1366.
1 8
6 1366.2-
<1366.4
1366.
3 3
7 1366.4-
<1366.6
1366.
5 2
Total 32
1
2
3
4
5
6
7
[6 marks]
Main data is the blue colour shaded more which pertains to 5 i.e.
1366.1366.2.

Applying Mathematics Assessment Two Part One
5. The following is a box plot for the Solar Irradiance variable, which you should use to answer the
questions below: [4 marks]
a. What is the median of the Solar Irradiance Variable?
Median = middle value = 1365.91

Applying Mathematics Assessment Two Part One
b. Using the upper and lower quartiles as labelled on the Box plot, determine the interquartile
range.
Inter quartile range = Upper quartile- Lower quartile
= 1366.1675 – 1365.675
= 0.4925
c. Which, if any, values are outliers for the Solar Irradiance variable?
If entry lies below Q1-1.5xiqr or above Q3+1.5 xiqr we call them
outliers.
Here Q1-1.5xIQr = 1365.675-1.5(0.4925)=1364.936
Q3+1.5xiqr = 1366.1675+1.5(0.4925)=1366.906
There are no values in the table which are not between these two values.
Hence no outliers found.
6. For the purposes of this question, split the data for the CO2 variable into two groups as indicated
by the dark line on the data table at the start of this assignment, the first reflecting the data
collected from 1979-1994 inclusive and the second reflecting data collected from 1995-2010
inclusive. [6 marks]
a. Determine the population standard deviation of the 1979-1994 group for the CO2 variable.
Refer excel sheet (sheet 1)
b. Determine the population standard deviation of the 1995-2010 group for the CO2 variable.
Refer excel sheet
c. Comment on how the dispersion of the 1979-1994 group for the CO2 variable compares to
the dispersion of the 1995-2010 group for the CO2 variable.
Std deviation of Co2 for 1979-1994 was 6.810 this increased to 8.740 in the
years 1995 – 2010.
There is a significant increase in std deviation of CO2 from the I group to II
group.

Applying Mathematics Assessment Two Part One
d. If it were discovered that a glitch in computer software had lead to all the given data for the
CO2 level being too low by a factor 10, (ie the CO2 level for 1979 should actually be 3366.70
ppm, not 336.67ppm and so on), state how each of the standard deviations calculated in
parts a and b would change, if at all and state what the new standard deviations should be
(rounded to 1 d.p.).
It is given that each entry is reduced by a scale factor of 10 inadvertently.
Hence std deviation corrected = 10 times the old standard deviation.
Std dev(population)
8.7433
65
6.8097
82
15.141
57
117.19
37
Corrected std dev
87.433
65
68.097
82
151.41
57
1171.9
37
7. Using two groups for the temperature variable, also split to reflect data from 1979-1994 and
1995-2010 and the two groups for the CO2 variable as outlined in question 6 above, complete
the following: [6 marks]
a. Determine the mean of each of the two groups for the CO2 variable.
Refer excel sheet for calculations(sheet 1 right side)
b. Determine the mean of each of the two groups for the temperature variable.
Refer excel sheet (sheet 1)
c. Comment on the difference between the means for the CO2 groups and then comment on
the difference between the means for the temperature groups. Comment on any similarity
or difference between the changes in means between the temperature and CO2 variables.
Mean CO2 25.75

Applying Mathematics Assessment Two Part One
differnce 75
Temperatu
re
29.12
5
Comments:
We find that in both the cases mean increases for the group from 1995-2010
than 1979-1994
But temperature increase is more higher than CO2.
TOTAL: 30 marks