Statistical analysis of Crude oil prices of historical data. Tried to analyze the data using statistical models and graphs and interpreted the meaning of results found. A thorough research on the industry is done. The report uses the following mathematical calculations: Mean & its types, Median, Mode, Variance, Standard Deviation, Range, Correlation & Regression, and Kurtosis Coefficient of Skewness. Tried to calculate it both manually and using MS Excel in built macros.

1. STATISTICAL ANALYSIS ON
CRUDE OIL PRICES

2. A REPORT ON:
Statistical Analysis on Crude Oil Prices
Submitted to: Dr. Rajni
In partial fulfilment of the requirement of the
Statistics for Management Course
By:
Mayank Agrawal
On:
November 06, 2018

3. Letter of Transmittal
November 06, 2018
Dr. Rajni
Assistant Professor
Statistics for Management
Department of Business Administration
Jindal Global Business School
Subject: Statistical Analysis Report on Crude Oil Prices
Dear Ma’am
As per the guidelines provided by you during the classroom discussion, we hereby submit a report on the
statistical analysis on Crude Oil prices. This report has been prepared after carefully scrutinizing the facts
and thus measuring and evaluating relevant statistical tendencies of measurement.
Kindly evaluate the same and provide your valuable inputs.
Best Regards,
Mayank Agrawal
Jindal Global Business School

4. Crude Oil Prices (Dollars per barrel)
Source: RWTC
0
20
40
60
80
100
120
140
160
Jan-1986
Jan-1987
Jan-1988
Jan-1989
Jan-1990
Jan-1991
Jan-1992
Jan-1993
Jan-1994
Jan-1995
Jan-1996
Jan-1997
Jan-1998
Jan-1999
Jan-2000
Jan-2001
Jan-2002
Jan-2003
Jan-2004
Jan-2005
Jan-2006
Jan-2007
Jan-2008
Jan-2009
Jan-2010
Jan-2011
Jan-2012
Jan-2013
Jan-2014
Jan-2015
Jan-2016
Jan-2017
Jan-2018
Cushing, OK WTI Spot Price FOB (Dollars per Barrel)
Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
1986 22.93 15.46 12.61 12.84 15.38 13.43 11.59 15.1 14.87 14.9 15.22 16.11
1987 18.65 17.75 18.3 18.68 19.44 20.07 21.34 20.31 19.53 19.86 18.85 17.28
1988 17.13 16.8 16.2 17.86 17.42 16.53 15.5 15.52 14.54 13.77 14.14 16.38
1989 18.02 17.94 19.48 21.07 20.12 20.05 19.78 18.58 19.59 20.1 19.86 21.1
1990 22.86 22.11 20.39 18.43 18.2 16.7 18.45 27.31 33.51 36.04 32.33 27.28
1991 25.23 20.48 19.9 20.83 21.23 20.19 21.4 21.69 21.89 23.23 22.46 19.5
1992 18.79 19.01 18.92 20.23 20.98 22.39 21.78 21.34 21.88 21.69 20.34 19.41
1993 19.03 20.09 20.32 20.25 19.95 19.09 17.89 18.01 17.5 18.15 16.61 14.52
1994 15.03 14.78 14.68 16.42 17.89 19.06 19.66 18.38 17.45 17.72 18.07 17.16
1995 18.04 18.57 18.54 19.9 19.74 18.45 17.33 18.02 18.23 17.43 17.99 19.03
1996 18.86 19.09 21.33 23.5 21.17 20.42 21.3 21.9 23.97 24.88 23.71 25.23
1997 25.13 22.18 20.97 19.7 20.82 19.26 19.66 19.95 19.8 21.33 20.19 18.33
1998 16.72 16.06 15.12 15.35 14.91 13.72 14.17 13.47 15.03 14.46 13 11.35
1999 12.52 12.01 14.68 17.31 17.72 17.92 20.1 21.28 23.8 22.69 25 26.1
2000 27.26 29.37 29.84 25.72 28.79 31.82 29.7 31.26 33.88 33.11 34.42 28.44
2001 29.59 29.61 27.25 27.49 28.63 27.6 26.43 27.37 26.2 22.17 19.64 19.39
2002 19.72 20.72 24.53 26.18 27.04 25.52 26.97 28.39 29.66 28.84 26.35 29.46
2003 32.95 35.83 33.51 28.17 28.11 30.66 30.76 31.57 28.31 30.34 31.11 32.13
2004 34.31 34.69 36.74 36.75 40.28 38.03 40.78 44.9 45.94 53.28 48.47 43.15
2005 46.84 48.15 54.19 52.98 49.83 56.35 59 64.99 65.59 62.26 58.32 59.41
2006 65.49 61.63 62.69 69.44 70.84 70.95 74.41 73.04 63.8 58.89 59.08 61.96
2007 54.51 59.28 60.44 63.98 63.46 67.49 74.12 72.36 79.92 85.8 94.77 91.69
2008 92.97 95.39 105.45 112.58 125.4 133.88 133.37 116.67 104.11 76.61 57.31 41.12
2009 41.71 39.09 47.94 49.65 59.03 69.64 64.15 71.05 69.41 75.72 77.99 74.47
2010 78.33 76.39 81.2 84.29 73.74 75.34 76.32 76.6 75.24 81.89 84.25 89.15
2011 89.17 88.58 102.86 109.53 100.9 96.26 97.3 86.33 85.52 86.32 97.16 98.56
2012 100.27 102.2 106.16 103.32 94.66 82.3 87.9 94.13 94.51 89.49 86.53 87.86
2013 94.76 95.31 92.94 92.02 94.51 95.77 104.67 106.57 106.29 100.54 93.86 97.63
2014 94.62 100.82 100.8 102.07 102.18 105.79 103.59 96.54 93.21 84.4 75.79 59.29
2015 47.22 50.58 47.82 54.45 59.27 59.82 50.9 42.87 45.48 46.22 42.44 37.19
2016 31.68 30.32 37.55 40.75 46.71 48.76 44.65 44.72 45.18 49.78 45.66 51.97
2017 52.5 53.47 49.33 51.06 48.48 45.18 46.63 48.04 49.82 51.58 56.64 57.88
2018 63.7 62.23 62.73 66.25 69.98 67.87 70.98 68.06 70.23

5. Arithmetic Mean:
It is defined as the average of a set of numerical values, as calculated by adding them together and dividing
by the number of terms in the set.
𝑥̅ =
∑ 𝑥𝑖
𝑛
𝑖=1
𝑛
𝑥̅ =
17163.48
393
𝑥̅ = 43.67
Value of 𝑥̅ represents the average mean price of crude oil for 33 years.
Arithmetic Mean for Grouped Data:
Here data are grouped into categories or intervals and presented as diagrams or tables, the definition of the
mean is unchanged, but the method of obtaining it differs from that used for ungrouped data. The mean is
then obtained by dividing this sum by the number of cases.
Prices Frequency
21-30 199
30-40 27
40-50 33
50-60 26
60-70 23
70-80 22
80-90 17
90-100 22
100-110 19
110-120 2
120-130 1
130-140 2
𝑥̅ =
∑𝑓𝑋
𝛴𝑓
𝑥̅ =
18135
393
𝑥̅ = 46.15

6. Arithmetic Mean by Step Deviation Method:
Prices
Mid Value
(Xi) Frequency(fi) di = xi - a ui = di/h fiui
20-30 25 199 -55 -5 -995
30-40 35 27 -45 -4.1 -110.5
40-50 45 33 -35 -3.2 -105.0
50-60 55 26 -25 -2.3 -59.1
60-70 65 23 -15 -1.4 -31.4
70-80 75 22 -5 -0.5 -10.0
80-90 85 17 5 0.5 7.7
90-100 95 22 15 1.4 30.0
100-110 105 19 25 2.3 43.2
110-120 115 2 35 3.2 6.4
120-130 125 1 45 4.1 4.1
130-140 135 2 55 5 10
Total ( ∑ ) 393 -1209.55
𝑥̅ = 𝑎 +
∑𝒇𝒊𝒖𝒊
∑𝒇𝒊
∗ ℎ
where
• x̄ is the mean which we're trying to find.
• a is the assumed mean.
• h is the class interval which we looked at in the section on data.
• fi is the frequency of each class, we find the total frequency of all the classes in the
data set (∑fi) by adding up all the fi 's
• Each ui is found from the following formula:
Prices Frequency(Fi) Mid Value (Xi) FiXi
20-30 199 25 4975
30-40 27 35 945
40-50 33 45 1485
50-60 26 55 1430
60-70 23 65 1495
70-80 22 75 1650
80-90 17 85 1445
90-100 22 95 2090
100-110 19 105 1995
110-120 2 115 230
120-130 1 125 125
130-140 2 135 270
Total ( ∑ ) 393 18135

7. • where h is the class interval and each di is the difference between the mid element in a
class and the assumed mean.
• d is calculated from the following formula:
• where x is the midpoint of a given class.
• x is obtained from the following:
• xi is the number in the middle of a given class.
𝑥̅ = 𝑎 +
∑𝒇𝒊𝒖𝒊
∑𝒇𝒊
∗ ℎ
Here,
a = 80
h = 30-20+1 = 11
𝑥̅ = 80 +
−1209.55
393
∗ 11
𝑥̅ = 80 +
−1209.55
393
∗ 11
𝑥̅ = 46.145
Grouped data mean = Step deviation method mean

8. Arithmetic Mean by Assumed Mean Method:
Prices
Mid Value
(Xi) Frequency(fi) di = xi - a fidi
20-30 25 199 -55 -10945
30-40 35 27 -45 -1215
40-50 45 33 -35 -1155
50-60 55 26 -25 -650
60-70 65 23 -15 -345
70-80 75 22 -5 -110
80-90 85 17 5 85
90-100 95 22 15 330
100-110 105 19 25 475
110-120 115 2 35 70
120-130 125 1 45 45
130-140 135 2 55 110
Total ( ∑ ) 393 -13305
𝑥̅ = 𝑎 +
∑𝒇𝒊𝒅𝒊
∑𝒇𝒊
where
• fi is the frequency of each class
• d is calculated from the following formula:
• a is the assumed mean.
Here,
a = 80
𝑥̅ = 80 +
−13305
393
𝑥̅ = 46.145
Grouped data mean = Step deviation method mean = Assumed mean method

9. Geometric Mean:
It is defined as the central number in a geometric progression (e.g. 9 in 3, 9, 27), also calculable as the nth
root of a product of n numbers.
Prices Mid Value (Xi) Frequency(fi) Log Xi
Fi*Log
Xi
20-30 25 199 1.4 278.2
30-40 35 27 1.5 41.7
40-50 45 33 1.7 54.6
50-60 55 26 1.7 45.2
60-70 65 23 1.8 41.7
70-80 75 22 1.9 41.3
80-90 85 17 1.9 32.8
90-100 95 22 2.0 43.5
100-110 105 19 2.0 38.4
110-120 115 2 2.1 4.1
120-130 125 1 2.1 2.1
130-140 135 2 2.1 4.3
Total ( ∑ ) 393 22.2 627.8
𝐺. 𝑀. = 𝐴𝑛𝑡𝑖𝑙𝑜𝑔 𝑜𝑓
∑𝒇 𝒍𝒐𝒈𝒙
∑𝒇𝒊
𝐺. 𝑀. = 𝐴𝑛𝑡𝑖𝑙𝑜𝑔 𝑜𝑓
627.8
393
𝐺. 𝑀. = 𝐴𝑛𝑡𝑖𝑙𝑜𝑔 𝑜𝑓 1.59
𝐺. 𝑀. = 𝐴𝑛𝑡𝑖𝑙𝑜𝑔 𝑜𝑓 1.59
𝐺. 𝑀. = 4.9037
G.M value indicates the central tendency or typical value of a set of numbers by using the product of their
values.
Harmonic Mean:
The harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average, and in
particular one of the Pythagorean means. Typically, it is appropriate for situations when the average
of rates is desired.
The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals of the given
set of observations.

10. Prices Frequency(fi) Mid Value (Xi) 1/x f/x
20-30 199 25 0.040 7.96
30-40 27 35 0.029 0.77
40-50 33 45 0.022 0.73
50-60 26 55 0.018 0.47
60-70 23 65 0.015 0.35
70-80 22 75 0.013 0.29
80-90 17 85 0.012 0.20
90-100 22 95 0.011 0.23
100-110 19 105 0.010 0.18
110-120 2 115 0.009 0.02
120-130 1 125 0.008 0.01
130-140 2 135 0.007 0.01
Total ( ∑ ) 393 11.24
𝐻. 𝑀. =
∑𝑓𝑖
∑
𝒇𝒊
𝒙𝒊
𝐻. 𝑀. =
393
11.24
𝐻. 𝑀. = 34.96
Median:
It is defined as denoting or relating to a value or quantity lying at the midpoint of a frequency distribution of
observed values or quantities, such that there is an equal probability of falling above or below it.
Prices Frequency (Fi)
Mid Value
(Xi)
FiXi
Cumulative
frequency (Cf)
20-30 199 25 4975 199
30-40 27 35 945 226
40-50 33 45 1485 259
50-60 26 55 1430 285
60-70 23 65 1495 308
70-80 22 75 1650 330
80-90 17 85 1445 347
90-100 22 95 2090 369
100-110 19 105 1995 388
110-120 2 115 230 390
120-130 1 125 125 391
130-140 2 135 270 393
Total ( ∑ ) 393 18135 3885

11. 𝑋 = 𝐿 +
𝑁
2
−𝐶𝑓
𝑓
* h
where
L = Lower limit of the median class
f = frequency of the median class
h = class interval of the median class
𝑋 = 70 +
196.5 −308
22
* 10
X = 29.45
It's the middle value of all the observation.
Mode:
The mode is a statistical term that refers to the most frequently occurring number found in a set of numbers.
The mode is found by collecting and organizing data in order to count the frequency of each result. The
result with the highest number of occurrences is the mode of the set.
Prices Frequency(Fi)
Mid Value
(Xi)
FiXi
Cumulative
frequency
20-30 199 25 4975 199
30-40 27 35 945 226
40-50 33 45 1485 259
50-60 26 55 1430 285
60-70 23 65 1495 308
70-80 22 75 1650 330
80-90 17 85 1445 347
90-100 22 95 2090 369
100-110 19 105 1995 388
110-120 2 115 230 390
120-130 1 125 125 391
130-140 2 135 270 393
Total ( ∑ ) 393 18135 3885
𝑀𝑜𝑑𝑒 = 𝐿 +
𝑓1−𝑓0
[( 𝑓1−𝑓0)+(𝑓1−𝑓2)]
* h
Here,
L = Lower limit of the median class
h = class length of the median class
f1 = frequency of the modal class
f0 = frequency of the pre-modal class
f2 = frequency of the post-modal class

12. 𝑀𝑜𝑑𝑒 = 20 +
199−0
[(199−0)+(199−27)]
* 10
𝑀𝑜𝑑𝑒 = 25.36
So 25.36 is the most frequently occurring observation.
Variance:
Variance is the expectation of the squared deviation of a random variable from its mean. Informally, it
measures how far a set of (random) numbers are spread out from their average value.
𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 =
∑𝑥2
𝑁
- µ^2
Where
µ =
∑𝑥
𝑁
µ = Mean
x = Crude oil prices
N = No of observations
𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 =
∑𝑥2
𝑁
- µ^2
𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 =
1092281
393
– 1907.32
𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 872.280
It tells how far a set of (random) numbers are spread out from their arithmetic mean.

13. Date
Crude
Oil Price
x
2
Jan-1986 22.93 525.7849
Feb-1986 15.46 239.0116
Mar-1986 12.61 159.0121
Apr-1986 12.84 164.8656
May-1986 15.38 236.5444
Jun-1986 13.43 180.3649
Jul-1986 11.59 134.3281
Aug-1986 15.1 228.01
Sep-1986 14.87 221.1169
Oct-1986 14.9 222.01
Nov-1986 15.22 231.6484
Dec-1986 16.11 259.5321
Jan-1987 18.65 347.8225
Feb-1987 17.75 315.0625
Mar-1987 18.3 334.89
Apr-1987 18.68 348.9424
May-1987 19.44 377.9136
Jun-1987 20.07 402.8049
Jul-1987 21.34 455.3956
Aug-1987 20.31 412.4961
Sep-1987 19.53 381.4209
Oct-1987 19.86 394.4196
Nov-1987 18.85 355.3225
Dec-1987 17.28 298.5984
Jan-1988 17.13 293.4369
Feb-1988 16.8 282.24
Mar-1988 16.2 262.44
Apr-1988 17.86 318.9796
May-1988 17.42 303.4564
Jun-1988 16.53 273.2409
Jul-1988 15.5 240.25
Aug-1988 15.52 240.8704
Sep-1988 14.54 211.4116
Oct-1988 13.77 189.6129
Nov-1988 14.14 199.9396
Dec-1988 16.38 268.3044
Jan-1989 18.02 324.7204
Feb-1989 17.94 321.8436
Mar-1989 19.48 379.4704
Apr-1989 21.07 443.9449
May-1989 20.12 404.8144
Jun-1989 20.05 402.0025
Jul-1989 19.78 391.2484
Aug-1989 18.58 345.2164
Sep-1989 19.59 383.7681
Oct-1989 20.1 404.01
Nov-1989 19.86 394.4196
Dec-1989 21.1 445.21
Jan-1990 22.86 522.5796
Feb-1990 22.11 488.8521
Mar-1990 20.39 415.7521
Apr-1990 18.43 339.6649
May-1990 18.2 331.24
Jun-1990 16.7 278.89
Jul-1990 18.45 340.4025
Aug-1990 27.31 745.8361
Sep-1990 33.51 1122.92
Oct-1990 36.04 1298.882
Nov-1990 32.33 1045.229
Dec-1990 27.28 744.1984
Jan-1991 25.23 636.5529
Feb-1991 20.48 419.4304
Mar-1991 19.9 396.01
Apr-1991 20.83 433.8889
May-1991 21.23 450.7129
Jun-1991 20.19 407.6361
Jul-1991 21.4 457.96
Aug-1991 21.69 470.4561
Sep-1991 21.89 479.1721
Oct-1991 23.23 539.6329
Nov-1991 22.46 504.4516
Dec-1991 19.5 380.25
Jan-1992 18.79 353.0641
Feb-1992 19.01 361.3801
Mar-1992 18.92 357.9664
Apr-1992 20.23 409.2529
May-1992 20.98 440.1604
Jun-1992 22.39 501.3121
Jul-1992 21.78 474.3684
Aug-1992 21.34 455.3956
Sep-1992 21.88 478.7344
Oct-1992 21.69 470.4561
Nov-1992 20.34 413.7156
Dec-1992 19.41 376.7481
Jan-1993 19.03 362.1409
Feb-1993 20.09 403.6081
Mar-1993 20.32 412.9024
Apr-1993 20.25 410.0625
May-1993 19.95 398.0025
Jun-1993 19.09 364.4281
Jul-1993 17.89 320.0521
Aug-1993 18.01 324.3601
Sep-1993 17.5 306.25
Oct-1993 18.15 329.4225
Nov-1993 16.61 275.8921
Dec-1993 14.52 210.8304
Jan-1994 15.03 225.9009
Feb-1994 14.78 218.4484
Mar-1994 14.68 215.5024
Apr-1994 16.42 269.6164
May-1994 17.89 320.0521
Jun-1994 19.06 363.2836
Jul-1994 19.66 386.5156
Aug-1994 18.38 337.8244
Sep-1994 17.45 304.5025
Oct-1994 17.72 313.9984
Nov-1994 18.07 326.5249
Dec-1994 17.16 294.4656
Jan-1995 18.04 325.4416
Feb-1995 18.57 344.8449
Mar-1995 18.54 343.7316
Apr-1995 19.9 396.01
May-1995 19.74 389.6676
Jun-1995 18.45 340.4025
Jul-1995 17.33 300.3289
Aug-1995 18.02 324.7204
Sep-1995 18.23 332.3329
Oct-1995 17.43 303.8049
Nov-1995 17.99 323.6401
Dec-1995 19.03 362.1409
Jan-1996 18.86 355.6996
Feb-1996 19.09 364.4281
Mar-1996 21.33 454.9689
Apr-1996 23.5 552.25
May-1996 21.17 448.1689
Jun-1996 20.42 416.9764
Jul-1996 21.3 453.69
Aug-1996 21.9 479.61
Sep-1996 23.97 574.5609
Oct-1996 24.88 619.0144
Nov-1996 23.71 562.1641
Dec-1996 25.23 636.5529
Jan-1997 25.13 631.5169
Feb-1997 22.18 491.9524
Mar-1997 20.97 439.7409
Apr-1997 19.7 388.09
May-1997 20.82 433.4724
Jun-1997 19.26 370.9476
Jul-1997 19.66 386.5156
Aug-1997 19.95 398.0025
Sep-1997 19.8 392.04
Oct-1997 21.33 454.9689
Nov-1997 20.19 407.6361
Dec-1997 18.33 335.9889
Jan-1998 16.72 279.5584
Feb-1998 16.06 257.9236
Mar-1998 15.12 228.6144
Apr-1998 15.35 235.6225
May-1998 14.91 222.3081
Jun-1998 13.72 188.2384
Jul-1998 14.17 200.7889
Aug-1998 13.47 181.4409
Sep-1998 15.03 225.9009
Oct-1998 14.46 209.0916
Nov-1998 13 169
Dec-1998 11.35 128.8225
Jan-1999 12.52 156.7504
Feb-1999 12.01 144.2401
Mar-1999 14.68 215.5024
Apr-1999 17.31 299.6361
May-1999 17.72 313.9984
Jun-1999 17.92 321.1264
Jul-1999 20.1 404.01
Aug-1999 21.28 452.8384
Sep-1999 23.8 566.44
Oct-1999 22.69 514.8361
Nov-1999 25 625
Dec-1999 26.1 681.21
Jan-2000 27.26 743.1076
Feb-2000 29.37 862.5969
Mar-2000 29.84 890.4256
Apr-2000 25.72 661.5184
May-2000 28.79 828.8641
Jun-2000 31.82 1012.512
Jul-2000 29.7 882.09
Aug-2000 31.26 977.1876
Sep-2000 33.88 1147.854
Oct-2000 33.11 1096.272
Nov-2000 34.42 1184.736
Dec-2000 28.44 808.8336
Jan-2001 29.59 875.5681
Feb-2001 29.61 876.7521
Mar-2001 27.25 742.5625
Apr-2001 27.49 755.7001
May-2001 28.63 819.6769
Jun-2001 27.6 761.76
Jul-2001 26.43 698.5449
Aug-2001 27.37 749.1169
Sep-2001 26.2 686.44
Oct-2001 22.17 491.5089
Nov-2001 19.64 385.7296
Dec-2001 19.39 375.9721
Jan-2002 19.72 388.8784
Feb-2002 20.72 429.3184
Mar-2002 24.53 601.7209
Apr-2002 26.18 685.3924
May-2002 27.04 731.1616
Jun-2002 25.52 651.2704
Jul-2002 26.97 727.3809
Aug-2002 28.39 805.9921
Sep-2002 29.66 879.7156
Oct-2002 28.84 831.7456
Nov-2002 26.35 694.3225
Dec-2002 29.46 867.8916
Jan-2003 32.95 1085.703
Feb-2003 35.83 1283.789
Mar-2003 33.51 1122.92
Apr-2003 28.17 793.5489
May-2003 28.11 790.1721
Jun-2003 30.66 940.0356
Jul-2003 30.76 946.1776
Aug-2003 31.57 996.6649
Sep-2003 28.31 801.4561
Oct-2003 30.34 920.5156
Nov-2003 31.11 967.8321
Dec-2003 32.13 1032.337
Jan-2004 34.31 1177.176
Feb-2004 34.69 1203.396
Mar-2004 36.74 1349.828
Apr-2004 36.75 1350.563
May-2004 40.28 1622.478
Jun-2004 38.03 1446.281
Jul-2004 40.78 1663.008
Aug-2004 44.9 2016.01
Sep-2004 45.94 2110.484
Oct-2004 53.28 2838.758
Nov-2004 48.47 2349.341
Dec-2004 43.15 1861.923
Jan-2005 46.84 2193.986
Feb-2005 48.15 2318.423
Mar-2005 54.19 2936.556
Apr-2005 52.98 2806.88
May-2005 49.83 2483.029
Jun-2005 56.35 3175.323
Jul-2005 59 3481
Aug-2005 64.99 4223.7
Sep-2005 65.59 4302.048
Oct-2005 62.26 3876.308
Nov-2005 58.32 3401.222
Dec-2005 59.41 3529.548
Jan-2006 65.49 4288.94
Feb-2006 61.63 3798.257
Mar-2006 62.69 3930.036
Apr-2006 69.44 4821.914
May-2006 70.84 5018.306
Jun-2006 70.95 5033.903
Jul-2006 74.41 5536.848
Aug-2006 73.04 5334.842
Sep-2006 63.8 4070.44
Oct-2006 58.89 3468.032
Nov-2006 59.08 3490.446
Dec-2006 61.96 3839.042
Jan-2007 54.51 2971.34
Feb-2007 59.28 3514.118
Mar-2007 60.44 3652.994
Apr-2007 63.98 4093.44
May-2007 63.46 4027.172
Jun-2007 67.49 4554.9
Jul-2007 74.12 5493.774
Aug-2007 72.36 5235.97
Sep-2007 79.92 6387.206
Oct-2007 85.8 7361.64
Nov-2007 94.77 8981.353
Dec-2007 91.69 8407.056
Jan-2008 92.97 8643.421
Feb-2008 95.39 9099.252
Mar-2008 105.45 11119.7
Apr-2008 112.58 12674.26
May-2008 125.4 15725.16
Jun-2008 133.88 17923.85
Jul-2008 133.37 17787.56
Aug-2008 116.67 13611.89
Sep-2008 104.11 10838.89
Oct-2008 76.61 5869.092
Nov-2008 57.31 3284.436
Dec-2008 41.12 1690.854
Jan-2009 41.71 1739.724
Feb-2009 39.09 1528.028
Mar-2009 47.94 2298.244
Apr-2009 49.65 2465.123
May-2009 59.03 3484.541
Jun-2009 69.64 4849.73
Jul-2009 64.15 4115.223
Aug-2009 71.05 5048.103
Sep-2009 69.41 4817.748
Oct-2009 75.72 5733.518
Nov-2009 77.99 6082.44
Dec-2009 74.47 5545.781
Jan-2010 78.33 6135.589
Feb-2010 76.39 5835.432
Mar-2010 81.2 6593.44
Apr-2010 84.29 7104.804
May-2010 73.74 5437.588
Jun-2010 75.34 5676.116
Jul-2010 76.32 5824.742
Aug-2010 76.6 5867.56
Sep-2010 75.24 5661.058
Oct-2010 81.89 6705.972
Nov-2010 84.25 7098.063
Dec-2010 89.15 7947.723
Jan-2011 89.17 7951.289
Feb-2011 88.58 7846.416
Mar-2011 102.86 10580.18
Apr-2011 109.53 11996.82
May-2011 100.9 10180.81
Jun-2011 96.26 9265.988
Jul-2011 97.3 9467.29
Aug-2011 86.33 7452.869
Sep-2011 85.52 7313.67
Oct-2011 86.32 7451.142
Nov-2011 97.16 9440.066
Dec-2011 98.56 9714.074
Jan-2012 100.27 10054.07
Feb-2012 102.2 10444.84
Mar-2012 106.16 11269.95
Apr-2012 103.32 10675.02
May-2012 94.66 8960.516
Jun-2012 82.3 6773.29
Jul-2012 87.9 7726.41
Aug-2012 94.13 8860.457
Sep-2012 94.51 8932.14
Oct-2012 89.49 8008.46
Nov-2012 86.53 7487.441
Dec-2012 87.86 7719.38
Jan-2013 94.76 8979.458
Feb-2013 95.31 9083.996
Mar-2013 92.94 8637.844
Apr-2013 92.02 8467.68
May-2013 94.51 8932.14
Jun-2013 95.77 9171.893
Jul-2013 104.67 10955.81
Aug-2013 106.57 11357.16
Sep-2013 106.29 11297.56
Oct-2013 100.54 10108.29
Nov-2013 93.86 8809.7
Dec-2013 97.63 9531.617
Jan-2014 94.62 8952.944
Feb-2014 100.82 10164.67
Mar-2014 100.8 10160.64
Apr-2014 102.07 10418.28
May-2014 102.18 10440.75
Jun-2014 105.79 11191.52
Jul-2014 103.59 10730.89
Aug-2014 96.54 9319.972
Sep-2014 93.21 8688.104
Oct-2014 84.4 7123.36
Nov-2014 75.79 5744.124
Dec-2014 59.29 3515.304
Jan-2015 47.22 2229.728
Feb-2015 50.58 2558.336
Mar-2015 47.82 2286.752
Apr-2015 54.45 2964.803
May-2015 59.27 3512.933
Jun-2015 59.82 3578.432
Jul-2015 50.9 2590.81
Aug-2015 42.87 1837.837
Sep-2015 45.48 2068.43
Oct-2015 46.22 2136.288
Nov-2015 42.44 1801.154
Dec-2015 37.19 1383.096
Jan-2016 31.68 1003.622
Feb-2016 30.32 919.3024
Mar-2016 37.55 1410.003
Apr-2016 40.75 1660.563
May-2016 46.71 2181.824
Jun-2016 48.76 2377.538
Jul-2016 44.65 1993.623
Aug-2016 44.72 1999.878
Sep-2016 45.18 2041.232
Oct-2016 49.78 2478.048
Nov-2016 45.66 2084.836
Dec-2016 51.97 2700.881
Jan-2017 52.5 2756.25
Feb-2017 53.47 2859.041
Mar-2017 49.33 2433.449
Apr-2017 51.06 2607.124
May-2017 48.48 2350.31
Jun-2017 45.18 2041.232
Jul-2017 46.63 2174.357
Aug-2017 48.04 2307.842
Sep-2017 49.82 2482.032
Oct-2017 51.58 2660.496
Nov-2017 56.64 3208.09
Dec-2017 57.88 3350.094
Jan-2018 63.7 4057.69
Feb-2018 62.23 3872.573
Mar-2018 62.73 3935.053
Apr-2018 66.25 4389.063
May-2018 69.98 4897.2
Jun-2018 67.87 4606.337
Jul-2018 70.98 5038.16
Aug-2018 68.06 4632.164
Sep-2018 70.23 4932.253
Total = 17163.48 1092281

14. Standard Deviation:
A quantity expressing by how much the members of a group differ from the mean value for the group.
S.D. = √Variance
S.D. = √872.280
S.D. = 29.53
S.D value shows that other observations are largely spread out from mean.
Range:
Range = Upper limit(max) – Lower limit(min)
Range = 133.88 – 11.35
Range = 122.53

15. Correlation:
Cushing, OK
WTI Spot
Price FOB
(Dollars per
Barrel)
Europe Brent Spot
Price FOB (Dollars
per Barrel)
X Y XY X2
Y2
22.93 20.78 476.4854 525.7849 431.8084
15.46 20.58 318.1668 239.0116 423.5364
12.61 20.38 256.9918 159.0121 415.3444
12.84 20.05 257.442 164.8656 402.0025
15.38 19.88 305.7544 236.5444 395.2144
13.43 19.78 265.6454 180.3649 391.2484
11.59 19.61 227.2799 134.3281 384.5521
15.1 19.39 292.789 228.01 375.9721
14.87 19.12 284.3144 221.1169 365.5744
14.9 18.95 282.355 222.01 359.1025
15.22 18.82 286.4404 231.6484 354.1924
16.11 18.71 301.4181 259.5321 350.0641
18.65 18.66 348.009 347.8225 348.1956
17.75 18.61 330.3275 315.0625 346.3321
18.3 18.6 340.38 334.89 345.96
18.68 18.59 347.2612 348.9424 345.5881
19.44 18.58 361.1952 377.9136 345.2164
20.07 18.86 378.5202 402.8049 355.6996
21.34 19.86 423.8124 455.3956 394.4196
20.31 18.98 385.4838 412.4961 360.2404
19.53 18.31 357.5943 381.4209 335.2561
19.86 18.76 372.5736 394.4196 351.9376
18.85 17.78 335.153 355.3225 316.1284
17.28 17.05 294.624 298.5984 290.7025
17.13 16.75 286.9275 293.4369 280.5625
16.8 15.73 264.264 282.24 247.4329
16.2 14.73 238.626 262.44 216.9729
17.86 16.6 296.476 318.9796 275.56
17.42 16.31 284.1202 303.4564 266.0161
16.53 15.54 256.8762 273.2409 241.4916
15.5 14.91 231.105 240.25 222.3081
15.52 14.89 231.0928 240.8704 221.7121
14.54 13.18 191.6372 211.4116 173.7124
13.77 12.41 170.8857 189.6129 154.0081
14.14 13.02 184.1028 199.9396 169.5204
16.38 15.31 250.7778 268.3044 234.3961
18.02 17.17 309.4034 324.7204 294.8089
17.94 16.89 303.0066 321.8436 285.2721
19.48 18.7 364.276 379.4704 349.69
21.07 20.32 428.1424 443.9449 412.9024
20.12 18.63 374.8356 404.8144 347.0769
20.05 17.67 354.2835 402.0025 312.2289
19.78 17.62 348.5236 391.2484 310.4644
18.58 16.77 311.5866 345.2164 281.2329
19.59 17.77 348.1143 383.7681 315.7729
20.1 18.91 380.091 404.01 357.5881
19.86 18.73 371.9778 394.4196 350.8129
21.1 19.84 418.624 445.21 393.6256
22.86 21.25 485.775 522.5796 451.5625
22.11 19.81 437.9991 488.8521 392.4361
20.39 18.39 374.9721 415.7521 338.1921
18.43 16.61 306.1223 339.6649 275.8921
18.2 16.35 297.57 331.24 267.3225
16.7 15.1 252.17 278.89 228.01
18.45 17.17 316.7865 340.4025 294.8089
27.31 27.17 742.0127 745.8361 738.2089
33.51 34.9 1169.499 1122.92 1218.01
36.04 36.02 1298.161 1298.882 1297.44
32.33 33.07 1069.153 1045.229 1093.625
27.28 28.27 771.2056 744.1984 799.1929
25.23 23.57 594.6711 636.5529 555.5449
20.48 19.54 400.1792 419.4304 381.8116
19.9 19.08 379.692 396.01 364.0464
20.83 19.18 399.5194 433.8889 367.8724
21.23 19.19 407.4037 450.7129 368.2561
20.19 18.17 366.8523 407.6361 330.1489
21.4 19.4 415.16 457.96 376.36
21.69 19.77 428.8113 470.4561 390.8529
21.89 20.5 448.745 479.1721 420.25
23.23 22.21 515.9383 539.6329 493.2841
22.46 21.11 474.1306 504.4516 445.6321
19.5 18.41 358.995 380.25 338.9281
18.79 18.16 341.2264 353.0641 329.7856
19.01 18.05 343.1305 361.3801 325.8025
18.92 17.63 333.5596 357.9664 310.8169
20.23 18.92 382.7516 409.2529 357.9664
20.98 19.89 417.2922 440.1604 395.6121
22.39 21.16 473.7724 501.3121 447.7456
21.78 20.24 440.8272 474.3684 409.6576
21.34 19.74 421.2516 455.3956 389.6676
21.88 20.27 443.5076 478.7344 410.8729
21.69 20.26 439.4394 470.4561 410.4676
20.34 19.21 390.7314 413.7156 369.0241
19.41 18.14 352.0974 376.7481 329.0596
19.03 17.39 330.9317 362.1409 302.4121
20.09 18.47 371.0623 403.6081 341.1409
20.32 18.79 381.8128 412.9024 353.0641
20.25 18.67 378.0675 410.0625 348.5689
19.95 18.51 369.2745 398.0025 342.6201
19.09 17.65 336.9385 364.4281 311.5225
17.89 16.78 300.1942 320.0521 281.5684
18.01 16.7 300.767 324.3601 278.89
17.5 16.01 280.175 306.25 256.3201
18.15 16.61 301.4715 329.4225 275.8921
16.61 15.2 252.472 275.8921 231.04
14.52 13.73 199.3596 210.8304 188.5129
15.03 14.29 214.7787 225.9009 204.2041
14.78 13.8 203.964 218.4484 190.44
14.68 13.82 202.8776 215.5024 190.9924
16.42 15.23 250.0766 269.6164 231.9529
17.89 16.19 289.6391 320.0521 262.1161
19.06 16.76 319.4456 363.2836 280.8976
19.66 17.6 346.016 386.5156 309.76
18.38 16.89 310.4382 337.8244 285.2721
17.45 15.9 277.455 304.5025 252.81
17.72 16.49 292.2028 313.9984 271.9201
18.07 17.19 310.6233 326.5249 295.4961
17.16 15.93 273.3588 294.4656 253.7649
18.04 16.55 298.562 325.4416 273.9025
18.57 17.11 317.7327 344.8449 292.7521
18.54 17.01 315.3654 343.7316 289.3401
19.9 18.65 371.135 396.01 347.8225
19.74 18.35 362.229 389.6676 336.7225
18.45 17.31 319.3695 340.4025 299.6361
17.33 15.85 274.6805 300.3289 251.2225
18.02 16.1 290.122 324.7204 259.21
18.23 16.7 304.441 332.3329 278.89
17.43 16.11 280.7973 303.8049 259.5321
17.99 16.86 303.3114 323.6401 284.2596
19.03 17.93 341.2079 362.1409 321.4849
18.86 17.85 336.651 355.6996 318.6225
19.09 18 343.62 364.4281 324
21.33 19.85 423.4005 454.9689 394.0225
23.5 20.9 491.15 552.25 436.81
21.17 19.15 405.4055 448.1689 366.7225
20.42 18.46 376.9532 416.9764 340.7716
21.3 19.57 416.841 453.69 382.9849
21.9 20.51 449.169 479.61 420.6601
23.97 22.63 542.4411 574.5609 512.1169
24.88 24.16 601.1008 619.0144 583.7056
23.71 22.76 539.6396 562.1641 518.0176
25.23 23.78 599.9694 636.5529 565.4884
25.13 23.54 591.5602 631.5169 554.1316
22.18 20.85 462.453 491.9524 434.7225
20.97 19.13 401.1561 439.7409 365.9569
19.7 17.56 345.932 388.09 308.3536
20.82 19.02 395.9964 433.4724 361.7604
19.26 17.58 338.5908 370.9476 309.0564
19.66 18.46 362.9236 386.5156 340.7716
19.95 18.6 371.07 398.0025 345.96
19.8 18.46 365.508 392.04 340.7716
21.33 19.87 423.8271 454.9689 394.8169
20.19 19.17 387.0423 407.6361 367.4889
18.33 17.18 314.9094 335.9889 295.1524
16.72 15.19 253.9768 279.5584 230.7361
16.06 14.07 225.9642 257.9236 197.9649
15.12 13.1 198.072 228.6144 171.61
15.35 13.53 207.6855 235.6225 183.0609
14.91 14.36 214.1076 222.3081 206.2096
13.72 12.21 167.5212 188.2384 149.0841
14.17 12.08 171.1736 200.7889 145.9264
13.47 11.91 160.4277 181.4409 141.8481
15.03 13.34 200.5002 225.9009 177.9556
14.46 12.7 183.642 209.0916 161.29
13 11.04 143.52 169 121.8816
11.35 9.82 111.457 128.8225 96.4324
12.52 11.11 139.0972 156.7504 123.4321
12.01 10.27 123.3427 144.2401 105.4729
14.68 12.51 183.6468 215.5024 156.5001
17.31 15.29 264.6699 299.6361 233.7841
17.72 15.23 269.8756 313.9984 231.9529
17.92 15.86 284.2112 321.1264 251.5396
20.1 19.08 383.508 404.01 364.0464
21.28 20.22 430.2816 452.8384 408.8484
23.8 22.54 536.452 566.44 508.0516
22.69 22 499.18 514.8361 484
25 24.58 614.5 625 604.1764
26.1 25.47 664.767 681.21 648.7209
27.26 25.51 695.4026 743.1076 650.7601
29.37 27.78 815.8986 862.5969 771.7284
29.84 27.49 820.3016 890.4256 755.7001
25.72 22.76 585.3872 661.5184 518.0176
28.79 27.74 798.6346 828.8641 769.5076
31.82 29.8 948.236 1012.512 888.04
29.7 28.68 851.796 882.09 822.5424
31.26 30.2 944.052 977.1876 912.04
33.88 33.14 1122.783 1147.854 1098.26
33.11 30.96 1025.086 1096.272 958.5216
34.42 32.55 1120.371 1184.736 1059.503
28.44 25.66 729.7704 808.8336 658.4356
29.59 25.62 758.0958 875.5681 656.3844
29.61 27.5 814.275 876.7521 756.25
27.25 24.5 667.625 742.5625 600.25
27.49 25.66 705.3934 755.7001 658.4356
28.63 28.31 810.5153 819.6769 801.4561
27.6 27.85 768.66 761.76 775.6225
26.43 24.61 650.4423 698.5449 605.6521
27.37 25.68 702.8616 749.1169 659.4624
26.2 25.62 671.244 686.44 656.3844
22.17 20.54 455.3718 491.5089 421.8916
19.64 18.8 369.232 385.7296 353.44
19.39 18.71 362.7869 375.9721 350.0641
19.72 19.42 382.9624 388.8784 377.1364
20.72 20.28 420.2016 429.3184 411.2784
24.53 23.7 581.361 601.7209 561.69
26.18 25.73 673.6114 685.3924 662.0329
27.04 25.35 685.464 731.1616 642.6225
25.52 24.08 614.5216 651.2704 579.8464
26.97 25.74 694.2078 727.3809 662.5476
28.39 26.65 756.5935 805.9921 710.2225
29.66 28.4 842.344 879.7156 806.56
28.84 27.54 794.2536 831.7456 758.4516
26.35 24.34 641.359 694.3225 592.4356
29.46 28.33 834.6018 867.8916 802.5889
32.95 31.18 1027.381 1085.703 972.1924
35.83 32.77 1174.149 1283.789 1073.873
33.51 30.61 1025.741 1122.92 936.9721
28.17 25 704.25 793.5489 625
28.11 25.86 726.9246 790.1721 668.7396
30.66 27.65 847.749 940.0356 764.5225
30.76 28.35 872.046 946.1776 803.7225
31.57 29.89 943.6273 996.6649 893.4121
28.31 27.11 767.4841 801.4561 734.9521
30.34 29.61 898.3674 920.5156 876.7521
31.11 28.75 894.4125 967.8321 826.5625
32.13 29.81 957.7953 1032.337 888.6361
34.31 31.28 1073.217 1177.176 978.4384
34.69 30.86 1070.533 1203.396 952.3396
36.74 33.63 1235.566 1349.828 1130.977
36.75 33.59 1234.433 1350.563 1128.288
40.28 37.57 1513.32 1622.478 1411.505
38.03 35.18 1337.895 1446.281 1237.632
40.78 38.22 1558.612 1663.008 1460.768
44.9 42.74 1919.026 2016.01 1826.708
45.94 43.2 1984.608 2110.484 1866.24
53.28 49.78 2652.278 2838.758 2478.048
48.47 43.11 2089.542 2349.341 1858.472
43.15 39.6 1708.74 1861.923 1568.16
46.84 44.51 2084.848 2193.986 1981.14
48.15 45.48 2189.862 2318.423 2068.43
54.19 53.1 2877.489 2936.556 2819.61
52.98 51.88 2748.602 2806.88 2691.534
49.83 48.65 2424.23 2483.029 2366.823
56.35 54.35 3062.623 3175.323 2953.923
59 57.52 3393.68 3481 3308.55
64.99 63.98 4158.06 4223.7 4093.44
65.59 62.91 4126.267 4302.048 3957.668
62.26 58.54 3644.7 3876.308 3426.932
58.32 55.24 3221.597 3401.222 3051.458
59.41 56.86 3378.053 3529.548 3233.06
65.49 62.99 4125.215 4288.94 3967.74
61.63 60.21 3710.742 3798.257 3625.244
62.69 62.06 3890.541 3930.036 3851.444
69.44 70.26 4878.854 4821.914 4936.468
70.84 69.78 4943.215 5018.306 4869.248
70.95 68.56 4864.332 5033.903 4700.474
74.41 73.67 5481.785 5536.848 5427.269
73.04 73.23 5348.719 5334.842 5362.633
63.8 61.96 3953.048 4070.44 3839.042
58.89 57.81 3404.431 3468.032 3341.996
59.08 58.76 3471.541 3490.446 3452.738
61.96 62.47 3870.641 3839.042 3902.501
54.51 53.68 2926.097 2971.34 2881.542
59.28 57.56 3412.157 3514.118 3313.154
60.44 62.05 3750.302 3652.994 3850.203
63.98 67.49 4318.01 4093.44 4554.9
63.46 67.21 4265.147 4027.172 4517.184
67.49 71.05 4795.165 4554.9 5048.103
74.12 76.93 5702.052 5493.774 5918.225
72.36 70.76 5120.194 5235.97 5006.978
79.92 77.17 6167.426 6387.206 5955.209
85.8 82.34 7064.772 7361.64 6779.876
94.77 92.41 8757.696 8981.353 8539.608
91.69 90.93 8337.372 8407.056 8268.265
92.97 92.18 8569.975 8643.421 8497.152
95.39 94.99 9061.096 9099.252 9023.1
105.45 103.64 10928.84 11119.7 10741.25
112.58 109.07 12279.1 12674.26 11896.26
125.4 122.8 15399.12 15725.16 15079.84
133.88 132.32 17715 17923.85 17508.58
133.37 132.72 17700.87 17787.56 17614.6
116.67 113.24 13211.71 13611.89 12823.3
104.11 97.23 10122.62 10838.89 9453.673
76.61 71.58 5483.744 5869.092 5123.696
57.31 52.45 3005.91 3284.436 2751.003
41.12 39.95 1642.744 1690.854 1596.003
41.71 43.44 1811.882 1739.724 1887.034
39.09 43.32 1693.379 1528.028 1876.622
47.94 46.54 2231.128 2298.244 2165.972
49.65 50.18 2491.437 2465.123 2518.032
59.03 57.3 3382.419 3484.541 3283.29
69.64 68.61 4778 4849.73 4707.332
64.15 64.44 4133.826 4115.223 4152.514
71.05 72.51 5151.836 5048.103 5257.7
69.41 67.65 4695.587 4817.748 4576.523
75.72 72.77 5510.144 5733.518 5295.473
77.99 76.66 5978.713 6082.44 5876.756
74.47 74.46 5545.036 5545.781 5544.292
78.33 76.17 5966.396 6135.589 5801.869
76.39 73.75 5633.763 5835.432 5439.063
81.2 78.83 6400.996 6593.44 6214.169
84.29 84.82 7149.478 7104.804 7194.432
73.74 75.95 5600.553 5437.588 5768.403
75.34 74.76 5632.418 5676.116 5589.058
76.32 75.58 5768.266 5824.742 5712.336
76.6 77.04 5901.264 5867.56 5935.162
75.24 77.84 5856.682 5661.058 6059.066
81.89 82.67 6769.846 6705.972 6834.329

16. Correlation is a statistical measure that indicates the extent
to which two or more variables fluctuate together. A
positive correlation indicates the extent to which those
variables increase or decrease in parallel; a negative
correlation indicates the extent to which one variable
increases as the other decreases.
If r = Zero, this means no association or correlation between
the two variables.
If 0 < r< 0.25 = weak correlation.
If 0.25 ≤ r< 0.75 = intermediate correlation.
If 0.75 ≤ r< 1 = strong correlation.
If r = l = perfect correlation.
Pearson’s coefficient of skewness
=
𝟑(𝑴𝒆𝒂𝒏−𝑴𝒆𝒅𝒊𝒂𝒏)
𝑺𝒕𝒂𝒏𝒅𝒂𝒓𝒅 𝑫𝒆𝒗𝒊𝒂𝒕𝒊𝒐𝒏
=
𝟑(𝟒𝟔. 𝟏𝟒𝟓 − 𝟐𝟗. 𝟒𝟓)
𝟐𝟗. 𝟓𝟑
= 1.696
From this value it can be interpreted that the standard
distribution is positively skewed.
84.25 85.28 7184.84 7098.063 7272.678
89.15 91.45 8152.768 7947.723 8363.103
89.17 96.52 8606.688 7951.289 9316.11
88.58 103.72 9187.518 7846.416 10757.84
102.86 114.64 11791.87 10580.18 13142.33
109.53 123.26 13500.67 11996.82 15193.03
100.9 114.99 11602.49 10180.81 13222.7
96.26 113.83 10957.28 9265.988 12957.27
97.3 116.97 11381.18 9467.29 13681.98
86.33 110.22 9515.293 7452.869 12148.45
85.52 112.83 9649.222 7313.67 12730.61
86.32 109.55 9456.356 7451.142 12001.2
97.16 110.77 10762.41 9440.066 12269.99
98.56 107.87 10631.67 9714.074 11635.94
100.27 110.69 11098.89 10054.07 12252.28
102.2 119.33 12195.53 10444.84 14239.65
106.16 125.45 13317.77 11269.95 15737.7
103.32 119.75 12372.57 10675.02 14340.06
94.66 110.34 10444.78 8960.516 12174.92
82.3 95.16 7831.668 6773.29 9055.426
87.9 102.62 9020.298 7726.41 10530.86
94.13 113.36 10670.58 8860.457 12850.49
94.51 112.86 10666.4 8932.14 12737.38
89.49 111.71 9996.928 8008.46 12479.12
86.53 109.06 9436.962 7487.441 11894.08
87.86 109.49 9619.791 7719.38 11988.06
94.76 112.96 10704.09 8979.458 12759.96
95.31 116.05 11060.73 9083.996 13467.6
92.94 108.47 10081.2 8637.844 11765.74
92.02 102.25 9409.045 8467.68 10455.06
94.51 102.56 9692.946 8932.14 10518.55
95.77 102.92 9856.648 9171.893 10592.53
104.67 107.93 11297.03 10955.81 11648.88
106.57 111.28 11859.11 11357.16 12383.24
106.29 111.6 11861.96 11297.56 12454.56
100.54 109.08 10966.9 10108.29 11898.45
93.86 107.79 10117.17 8809.7 11618.68
97.63 110.76 10813.5 9531.617 12267.78
94.62 108.12 10230.31 8952.944 11689.93
100.82 108.9 10979.3 10164.67 11859.21
100.8 107.48 10833.98 10160.64 11551.95
102.07 107.76 10999.06 10418.28 11612.22
102.18 109.54 11192.8 10440.75 11999.01
105.79 111.8 11827.32 11191.52 12499.24
103.59 106.77 11060.3 10730.89 11399.83
96.54 101.61 9809.429 9319.972 10324.59
93.21 97.09 9049.759 8688.104 9426.468
84.4 87.43 7379.092 7123.36 7644.005
75.79 79.44 6020.758 5744.124 6310.714
59.29 62.34 3696.139 3515.304 3886.276
47.22 47.76 2255.227 2229.728 2281.018
50.58 58.1 2938.698 2558.336 3375.61
47.82 55.89 2672.66 2286.752 3123.692
54.45 59.52 3240.864 2964.803 3542.63
59.27 64.08 3798.022 3512.933 4106.246
59.82 61.48 3677.734 3578.432 3779.79
50.9 56.56 2878.904 2590.81 3199.034
42.87 46.52 1994.312 1837.837 2164.11
45.48 47.62 2165.758 2068.43 2267.664
46.22 48.43 2238.435 2136.288 2345.465
42.44 44.27 1878.819 1801.154 1959.833
37.19 38.01 1413.592 1383.096 1444.76
31.68 30.7 972.576 1003.622 942.49
30.32 32.18 975.6976 919.3024 1035.552
37.55 38.21 1434.786 1410.003 1460.004
40.75 41.58 1694.385 1660.563 1728.896
46.71 46.74 2183.225 2181.824 2184.628
48.76 48.25 2352.67 2377.538 2328.063
44.65 44.95 2007.018 1993.623 2020.503
44.72 45.84 2049.965 1999.878 2101.306
45.18 46.57 2104.033 2041.232 2168.765
49.78 49.52 2465.106 2478.048 2452.23
45.66 44.73 2042.372 2084.836 2000.773
51.97 53.31 2770.521 2700.881 2841.956
52.5 54.58 2865.45 2756.25 2978.976
53.47 54.87 2933.899 2859.041 3010.717
49.33 51.59 2544.935 2433.449 2661.528
51.06 52.31 2670.949 2607.124 2736.336
48.48 50.33 2439.998 2350.31 2533.109
45.18 46.37 2094.997 2041.232 2150.177
46.63 48.48 2260.622 2174.357 2350.31
48.04 51.7 2483.668 2307.842 2672.89
49.82 56.15 2797.393 2482.032 3152.823
51.58 57.51 2966.366 2660.496 3307.4
56.64 62.71 3551.894 3208.09 3932.544
57.88 64.37 3725.736 3350.094 4143.497
63.7 69.08 4400.396 4057.69 4772.046
62.23 65.32 4064.864 3872.573 4266.702
62.73 66.02 4141.435 3935.053 4358.64
66.25 72.11 4777.288 4389.063 5199.852
69.98 76.98 5387.06 4897.2 5925.92
67.87 74.41 5050.207 4606.337 5536.848
70.98 74.25 5270.265 5038.16 5513.063
68.06 72.53 4936.392 4632.164 5260.601
70.23 78.89 5540.445 4932.253 6223.632
Total (∑) 17163.48 17574.11 1144679 1092281 1208837

17. Pearson’s Correlation coefficient
=
𝒏 ∑ 𝒙𝒚 − (∑ 𝒙 ∑ 𝒚)
√𝒏 ∑ 𝒙 𝟐 − (∑ 𝒙) 𝟐 ∗ 𝒏 ∑ 𝒚 𝟐 − (∑ 𝒚) 𝟐
=
𝟑𝟕𝟔(𝟏𝟏𝟑𝟗𝟕𝟓𝟖.𝟑𝟒)−(𝟏𝟔𝟗𝟎𝟗.𝟔𝟔∗𝟏𝟕𝟐𝟔𝟑.𝟔𝟎)
√((𝟑𝟕𝟔∗𝟏𝟎𝟖𝟖𝟏𝟑𝟐.𝟏𝟐)−𝟏𝟔𝟗𝟎𝟗.𝟔𝟔 𝟐)∗√((𝟑𝟕𝟔∗𝟏𝟐𝟎𝟐𝟖𝟎𝟏.𝟖𝟑)−(𝟏𝟕𝟐𝟔𝟑.𝟔𝟎) 𝟐)
= 0.99
From the Pearson’s Correlation Coefficient, it can be interpreted that it is a strong correlation.
Bowley’s Coefficient of Skewness
Q1=
𝑪𝑭+𝟏
𝟒
= 971. 5
Q2=
𝑪𝑭+𝟏
𝟐
= 1943
Q3= (
𝑪𝑭+𝟏
𝟐
) ∗ 𝟑 = 3886
Thus, Bowley’s Coefficient of Skewness is equal to
=
𝑸𝟏 + 𝑸𝟑 − (𝟐 ∗ 𝑸𝟐)
𝑸𝟑 − 𝑸𝟏
= 0.33

18. Kurtosis Coefficient of Skewness
m2 =
330207.39
377
m2 = 875.881
m4 =
772412272.00
377
m4 = 2048838.918
k =
2048838.918
875.881^2
k = 2.67
Since the value of Kurtosis = 2.67 , it is greater than zero. this imples that the kurtosis
curve is said to be LEPTOPKUTIC.
Leptopkutic represents a frequency distribution having a greater kurtosis than the
normal distribution, more concentrated about the mean.

19. Date
Cushing, OK
WTI Spot Price
FOB (Dollars
per Barrel)
m2 m4
May-1987 19.44 587.09 344678.07
Jun-1987 20.07 556.96 310204.44
Jul-1987 21.34 498.63 248630.78
Aug-1987 20.31 545.69 297777.14
Sep-1987 19.53 582.74 339585.44
Oct-1987 19.86 566.92 321393.86
Nov-1987 18.85 616.03 379495.92
Dec-1987 17.28 696.43 485017.67
Jan-1988 17.13 704.37 496139.35
Feb-1988 16.80 722.00 521279.52
Mar-1988 16.20 754.60 569422.52
Apr-1988 17.86 666.16 443763.95
May-1988 17.42 689.06 474807.13
Jun-1988 16.53 736.58 542549.51
Jul-1988 15.50 793.55 629719.86
Aug-1988 15.52 792.42 627933.42
Sep-1988 14.54 848.56 720048.81
Oct-1988 13.77 894.01 799253.88
Nov-1988 14.14 872.02 760420.45
Dec-1988 16.38 744.74 554643.77
Jan-1989 18.02 657.92 432862.02
Feb-1989 17.94 662.03 438287.56
Mar-1989 19.48 585.16 342407.66
Apr-1989 21.07 510.76 260875.78
May-1989 20.12 554.60 307583.93
Jun-1989 20.05 557.90 311257.32
Jul-1989 19.78 570.73 325735.13
Aug-1989 18.58 629.51 396280.45
Sep-1989 19.59 579.85 336221.85
Oct-1989 20.10 555.54 308630.14
Nov-1989 19.86 566.92 321393.86
Dec-1989 21.10 509.40 259493.35
Jan-1990 22.86 433.06 187537.59
Feb-1990 22.11 464.83 216070.28
Mar-1990 20.39 541.96 293718.91
Apr-1990 18.43 637.06 405842.39
May-1990 18.20 648.72 420838.81
Jun-1990 16.70 727.38 529082.97
Jul-1990 18.45 636.05 404557.57
Aug-1990 27.31 267.65 71636.31
Sep-1990 33.51 103.23 10655.52
Oct-1990 36.04 58.22 3389.21
Nov-1990 32.33 128.60 16536.83
Dec-1990 27.28 268.63 72163.21
Jan-1991 25.23 340.03 115622.85
Feb-1991 20.48 537.78 289203.13
Mar-1991 19.90 565.01 319239.58
Apr-1991 20.83 521.67 272135.00
May-1991 21.23 503.55 253566.23
Jun-1991 20.19 551.31 303943.16
Jul-1991 21.40 495.95 245969.28
Aug-1991 21.69 483.12 233405.32
Sep-1991 21.89 474.37 225025.38
Oct-1991 23.23 417.79 174551.49
Nov-1991 22.46 449.86 202377.71
Dec-1991 19.50 584.19 341276.67
Jan-1992 18.79 619.01 383178.83
Feb-1992 19.01 608.12 369804.58
Mar-1992 18.92 612.56 375232.82
Apr-1992 20.23 549.43 301877.28
May-1992 20.98 514.84 265056.21
Jun-1992 22.39 452.84 205062.62
Jul-1992 21.78 479.17 229605.90
Aug-1992 21.34 498.63 248630.78
Sep-1992 21.88 474.80 225438.93
Oct-1992 21.69 483.12 233405.32
Nov-1992 20.34 544.29 296250.41
Dec-1992 19.41 588.55 346388.28
Jan-1993 19.03 607.13 368606.35
Feb-1993 20.09 556.02 309154.24
Mar-1993 20.32 545.22 297267.57
Apr-1993 20.25 548.50 300848.30
May-1993 19.95 562.64 316561.97
Jun-1993 19.09 604.18 365029.12
Jul-1993 17.89 664.61 441704.33
Aug-1993 18.01 658.44 433537.44
Sep-1993 17.50 684.87 469045.41
Oct-1993 18.15 651.27 424153.13
Nov-1993 16.61 732.24 536180.69
Dec-1993 14.52 849.72 722028.33
Jan-1994 15.03 820.25 672809.41
Feb-1994 14.78 834.63 696610.74
Mar-1994 14.68 840.42 706305.94
Apr-1994 16.42 742.56 551399.07
May-1994 17.89 664.61 441704.33
Jun-1994 19.06 605.65 366814.47
Jul-1994 19.66 576.48 332329.31
Aug-1994 18.38 639.58 409067.82
Sep-1994 17.45 687.49 472640.30
Oct-1994 17.72 673.40 453470.93
Nov-1994 18.07 655.36 429496.73
Dec-1994 17.16 702.78 493899.87
Jan-1995 18.04 656.90 431513.54
Feb-1995 18.57 630.01 396912.60
Mar-1995 18.54 631.52 398813.59
Apr-1995 19.90 565.01 319239.58
May-1995 19.74 572.64 327922.18
Jun-1995 18.45 636.05 404557.57
Jul-1995 17.33 693.80 481352.33
Aug-1995 18.02 657.92 432862.02
Sep-1995 18.23 647.19 418859.56
Oct-1995 17.43 688.54 474084.03
Nov-1995 17.99 659.46 434890.66
Dec-1995 19.03 607.13 368606.35
Jan-1996 18.86 615.54 378884.69
Feb-1996 19.09 604.18 365029.12
Mar-1996 21.33 499.08 249076.45
Apr-1996 23.50 406.83 165509.75
May-1996 21.17 506.25 256289.06
Jun-1996 20.42 540.56 292207.82
Jul-1996 21.30 500.42 250417.07
Aug-1996 21.90 473.93 224612.39
Sep-1996 23.97 388.09 150613.85
Oct-1996 24.88 353.06 124654.26
Nov-1996 23.71 398.40 158723.83
Dec-1996 25.23 340.03 115622.85
Jan-1997 25.13 343.73 118151.41
Feb-1997 22.18 461.82 213277.80
Mar-1997 20.97 515.29 265523.78
Apr-1997 19.70 574.56 330120.23
May-1997 20.82 522.12 272611.91
Jun-1997 19.26 595.85 355034.96
Jul-1997 19.66 576.48 332329.31
Aug-1997 19.95 562.64 316561.97
Sep-1997 19.80 569.78 324645.72
Oct-1997 21.33 499.08 249076.45
Nov-1997 20.19 551.31 303943.16
Dec-1997 18.33 642.12 412312.44
Jan-1998 16.72 726.30 527515.32
Feb-1998 16.06 762.31 581119.74
Mar-1998 15.12 815.10 664392.09
Apr-1998 15.35 802.02 643239.93
May-1998 14.91 827.14 684156.61
Jun-1998 13.72 897.00 804613.49
Jul-1998 14.17 870.25 757335.06
Aug-1998 13.47 912.04 831816.96
Sep-1998 15.03 820.25 672809.41
Oct-1998 14.46 853.22 727991.36
Nov-1998 13.00 940.65 884820.35
Dec-1998 11.35 1044.58 1091152.39
Jan-1999 12.52 970.32 941525.75
Feb-1999 12.01 1002.36 1004716.75
Mar-1999 14.68 840.42 706305.94
Apr-1999 17.31 694.85 482815.97
May-1999 17.72 673.40 453470.93
Jun-1999 17.92 663.06 439651.88
Jul-1999 20.10 555.54 308630.14
Aug-1999 21.28 501.31 251313.82
Sep-1999 23.80 394.82 155880.38
Oct-1999 22.69 440.16 193741.18
Nov-1999 25.00 348.57 121500.28
Dec-1999 26.10 308.70 95298.72
Jan-2000 27.26 269.29 72516.08
Feb-2000 29.37 204.49 41816.16
Mar-2000 29.84 191.27 36583.79
Apr-2000 25.72 322.20 103814.45
May-2000 28.79 221.41 49024.34
Jun-2000 31.82 140.42 19718.48
Jul-2000 29.70 195.16 38087.78
Aug-2000 31.26 154.01 23718.49
Sep-2000 33.88 95.84 9186.09
Oct-2000 33.11 111.51 12435.28
Nov-2000 34.42 85.56 7320.94
Dec-2000 28.44 231.95 53802.15
Jan-2001 29.59 198.25 39301.64
Feb-2001 29.61 197.68 39078.81
Mar-2001 27.25 269.62 72693.00
Apr-2001 27.49 261.79 68535.26
May-2001 28.63 226.20 51167.16
Jun-2001 27.60 258.24 66690.43
Jul-2001 26.43 297.22 88338.30
Aug-2001 27.37 265.69 70591.18
Sep-2001 26.20 305.20 93147.59
Oct-2001 22.17 462.25 213675.06
Nov-2001 19.64 577.44 333437.99
Dec-2001 19.39 589.52 347531.94
Jan-2002 19.72 573.60 329019.83
Feb-2002 20.72 526.70 277415.52
Mar-2002 24.53 366.34 134204.70
Apr-2002 26.18 305.90 93574.87
May-2002 27.04 276.56 76483.72
Jun-2002 25.52 329.42 108519.18
Jul-2002 26.97 278.89 77779.63
Aug-2002 28.39 233.48 54512.16
Sep-2002 29.66 196.28 38525.88
Oct-2002 28.84 219.93 48368.72
Nov-2002 26.35 299.98 89989.44
Dec-2002 29.46 201.92 40773.34
Jan-2003 32.95 114.92 13206.24
Feb-2003 35.83 61.47 3778.02
Mar-2003 33.51 103.23 10655.52
Apr-2003 28.17 240.25 57720.06
May-2003 28.11 242.11 58619.00
Jun-2003 30.66 169.26 28648.98
Jul-2003 30.76 166.67 27778.26
Aug-2003 31.57 146.41 21435.89
Sep-2003 28.31 235.93 55662.78
Oct-2003 30.34 177.69 31573.35
Nov-2003 31.11 157.75 24886.20
Dec-2003 32.13 133.17 17734.68
Jan-2004 34.31 87.61 7675.44
Feb-2004 34.69 80.64 6502.87
Mar-2004 36.74 48.02 2306.39
Apr-2004 36.75 47.89 2293.11
May-2004 40.28 11.49 132.07
Jun-2004 38.03 31.81 1011.85
Jul-2004 40.78 8.35 69.76
Aug-2004 44.90 1.51 2.29
Sep-2004 45.94 5.15 26.55
Oct-2004 53.28 92.35 8528.91
Nov-2004 48.47 23.04 530.84
Dec-2004 43.15 0.27 0.07
Jan-2005 46.84 10.05 100.98
Feb-2005 48.15 20.07 402.82
Mar-2005 54.19 110.67 12247.94
Apr-2005 52.98 86.68 7512.75
May-2005 49.83 37.95 1439.87
Jun-2005 56.35 160.78 25850.98
Jul-2005 59.00 235.01 55229.18
Aug-2005 64.99 454.54 206608.79
Sep-2005 65.59 480.49 230867.18
Oct-2005 62.26 345.59 119431.13
Nov-2005 58.32 214.62 46062.82
Dec-2005 59.41 247.75 61378.87
Jan-2006 65.49 476.11 226683.02
Feb-2006 61.63 322.56 104045.99
Mar-2006 62.69 361.76 130870.59
Apr-2006 69.44 664.09 441019.38
May-2006 70.84 738.21 544952.38
Jun-2006 70.95 744.20 553831.26
Jul-2006 74.41 944.95 892925.97
Aug-2006 73.04 862.60 744073.41
Sep-2006 63.80 405.22 164200.74
Oct-2006 58.89 231.65 53660.98
Nov-2006 59.08 237.47 56391.10
Dec-2006 61.96 334.52 111906.37
Jan-2007 54.51 117.51 13807.57
Feb-2007 59.28 243.67 59376.09
Mar-2007 60.44 281.23 79091.94
Apr-2007 63.98 412.50 170153.03
May-2007 63.46 391.64 153385.10
Jun-2007 67.49 567.39 321934.14
Jul-2007 74.12 927.20 859704.48
Aug-2007 72.36 823.12 677520.11
Sep-2007 79.92 1314.06 1726760.25
Oct-2007 85.80 1774.94 3150401.00
Nov-2007 94.77 2611.21 6818417.66
Dec-2007 91.69 2305.92 5317268.89
Jan-2008 92.97 2430.49 5907281.64
Feb-2008 95.39 2674.96 7155402.44
Mar-2008 105.45 3816.77 14567721.02
Apr-2008 112.58 4748.59 22549088.94
May-2008 125.40 6679.79 44619633.19
Jun-2008 133.88 8137.84 66224506.60
Jul-2008 133.37 8046.09 64739564.29
Aug-2008 116.67 5329.00 28398241.00
Sep-2008 104.11 3652.99 13344362.24
Oct-2008 76.61 1085.04 1177319.61
Nov-2008 57.31 186.05 34614.45
Dec-2008 41.12 6.50 42.28
Jan-2009 41.71 3.84 14.76
Feb-2009 39.09 20.98 440.01
Mar-2009 47.94 18.23 332.44
Apr-2009 49.65 35.76 1278.81
May-2009 59.03 235.93 55662.78
Jun-2009 69.64 674.44 454870.53
Jul-2009 64.15 419.43 175921.86
Aug-2009 71.05 749.66 561996.71
Sep-2009 69.41 662.55 438969.32
Oct-2009 75.72 1027.20 1055144.98
Nov-2009 77.99 1177.86 1387359.83
Dec-2009 74.47 948.64 899917.85
Jan-2010 78.33 1201.32 1443159.17
Feb-2010 76.39 1070.60 1146180.93
Mar-2010 81.20 1408.50 1983874.79
Apr-2010 84.29 1649.98 2722448.52
May-2010 73.74 904.20 817586.50
Jun-2010 75.34 1002.99 1005986.73
Jul-2010 76.32 1066.02 1136403.97
Aug-2010 76.60 1084.38 1175890.61
Sep-2010 75.24 996.66 993340.92
Oct-2010 81.89 1460.77 2133844.32
Nov-2010 84.25 1646.74 2711740.77
Dec-2010 89.15 2068.43 4278404.32
Jan-2011 89.17 2070.25 4285935.06
Feb-2011 88.58 2016.91 4067918.28
Mar-2011 102.86 3503.46 12274204.64
Apr-2011 109.53 4337.54 18814249.78
May-2011 100.90 3275.27 10727412.57
Jun-2011 96.26 2765.71 7649141.29
Jul-2011 97.30 2876.18 8272393.56
Aug-2011 86.33 1819.88 3311947.20
Sep-2011 85.52 1751.42 3067480.77
Oct-2011 86.32 1819.02 3308842.86
Nov-2011 97.16 2861.18 8186351.56
Dec-2011 98.56 3012.91 9077639.32
Jan-2012 100.27 3203.56 10262796.67
Feb-2012 102.20 3425.76 11735837.74
Mar-2012 106.16 3905.00 15249025.78
Apr-2012 103.32 3558.12 12660235.73
May-2012 94.66 2599.98 6759896.52
Jun-2012 82.30 1492.28 2226890.35
Jul-2012 87.90 1956.29 3827081.91
Aug-2012 94.13 2546.21 6483193.51
Sep-2012 94.51 2584.71 6680703.04
Oct-2012 89.49 2099.47 4407784.36
Nov-2012 86.53 1836.98 3374494.05
Dec-2012 87.86 1952.76 3813256.39
Jan-2013 94.76 2610.19 6813081.92
Feb-2013 95.31 2666.69 7111233.42
Mar-2013 92.94 2427.53 5892915.98
Apr-2013 92.02 2337.72 5464946.49
May-2013 94.51 2584.71 6680703.04
Jun-2013 95.77 2714.41 7368021.65
Jul-2013 104.67 3721.00 13845841.00
Aug-2013 106.57 3956.41 15653180.09
Sep-2013 106.29 3921.26 15376314.49
Oct-2013 100.54 3234.20 10460029.59
Nov-2013 93.86 2519.04 6345542.87
Dec-2013 97.63 2911.68 8477889.74
Jan-2014 94.62 2595.90 6738709.79
Feb-2014 100.82 3266.12 10667556.19
Mar-2014 100.80 3263.84 10652631.31
Apr-2014 102.07 3410.56 11631919.51
May-2014 102.18 3423.42 11719805.18
Jun-2014 105.79 3858.89 14891065.99
Jul-2014 103.59 3590.41 12891018.12
Aug-2014 96.54 2795.24 7813349.33
Sep-2014 93.21 2454.21 6023154.58
Oct-2014 84.40 1658.93 2752058.37
Nov-2014 75.79 1031.69 1064393.33
Dec-2014 59.29 243.98 59528.39
Jan-2015 47.22 12.60 158.82
Feb-2015 50.58 47.75 2279.88
Mar-2015 47.82 17.22 296.61
Apr-2015 54.45 116.21 13504.39
May-2015 59.27 243.36 59224.09
Jun-2015 59.82 260.82 68028.38
Jul-2015 50.90 52.27 2732.46
Aug-2015 42.87 0.64 0.41
Sep-2015 45.48 3.28 10.73
Oct-2015 46.22 6.50 42.28
Nov-2015 42.44 1.51 2.29
Dec-2015 37.19 41.99 1763.19
Jan-2016 31.68 143.76 20666.97
Feb-2016 30.32 178.22 31763.26
Mar-2016 37.55 37.45 1402.83
Apr-2016 40.75 8.53 72.70
May-2016 46.71 9.24 85.41
Jun-2016 48.76 25.91 671.23
Jul-2016 44.65 0.96 0.92
Aug-2016 44.72 1.10 1.22
Sep-2016 45.18 2.28 5.20
Oct-2016 49.78 37.33 1393.69
Nov-2016 45.66 3.96 15.68
Dec-2016 51.97 68.89 4745.83
Jan-2017 52.50 77.97 6079.15
Feb-2017 53.47 96.04 9223.68
Mar-2017 49.33 32.04 1026.28
Apr-2017 51.06 54.61 2982.48
May-2017 48.48 23.14 535.28
Jun-2017 45.18 2.28 5.20
Jul-2017 46.63 8.76 76.77
Aug-2017 48.04 19.10 364.69
Sep-2017 49.82 37.82 1430.54
Oct-2017 51.58 62.57 3914.77
Nov-2017 56.64 168.22 28298.27
Dec-2017 57.88 201.92 40773.34
Jan-2018 63.70 401.20 160962.16
Feb-2018 62.23 344.47 118662.06
Mar-2018 62.73 363.28 131974.97
Apr-2018 66.25 509.86 259953.55
May-2018 69.98 692.22 479163.13
Jun-2018 67.87 585.64 342974.21
Jul-2018 70.98 745.84 556271.49
Aug-2018 68.06 594.87 353872.82
Sep-2018 70.23 705.43 497636.56
Sum 16909.66 330207.39 772412272.00

20. Regression:
Regression analysis is a set of statistical processes for estimating the relationships among variables.
𝑏 =
2779.340
1907.408
𝑏 = 1.1005
-10
10
30
50
70
90
110
130
150
0 20 40 60 80 100 120 140
X
Y
Regression

21. Comparison:
EXCEL FORMULAES VERIFICATION
MEAN 43.6729771 43.67
MEDIAN 29.66 29.45
MODE 21.34 25.36
STANDARD DEVIATION 29.56749459 29.53
VARIANCE 872.0122153 872.2
RANGE 122.53 122.53