Quantitative Analysis

Running Head: QUANTITATIVEANALYSIS
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Quantitative analysis
Student’s Name:
University Affiliation:

Running Head: QUANTITATIVEANALYSIS
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Problem 1
Temperatur
e
Frequenc
y
Cumulativ
e %
62 0 0.00%
64 0 0.00%
66 2 10.53%
68 2 21.05%
70 2 31.58%
72 3 47.37%
74 3 63.16%
76 1 68.42%
78 5 94.74%
80 1 100.00%
82 0 100.00%
More 0 100.00%
6264666870727476788082
More
0
1
2
3
4
5
6
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
Histogram
Frequency
Cumulative %
Tempereture
Frequency
Figure 1: A frequency distribution table for mean temperature in
Boston
The distribution has a long tail to the left, hence it is skewed to the left.
Year(n) Mean (x) x^2 p(x) x.p(x)
x^2.P(x
)
1998 72 5184
0.0495
5 3.56779
256.88
1
1999 69 4761
0.0474
9 3.27667
226.09
0
2000 78 6084
0.0536
8 4.18720
326.60
2

Running Head: QUANTITATIVEANALYSIS
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2001 70 4900
0.0481
8 3.37233
236.06
3
2002 67 4489 0.0461
1
3.08947 206.99
4
2003 74 5476 0.0509
3
3.76875 278.88
8
2004 73 5329 0.0502
4
3.66758 267.73
4
2005 65 4225 0.0447
4
2.90778 189.00
6
2006 77 5929 0.0529
9
4.08052 314.20
0
2007 71 5041 0.0488
6
3.46937 246.32
6
2008 75 5625 0.0516
2
3.87130 290.34
8
2009 68 4624 0.0468
0
3.18238 216.40
2
2010 72 5184 0.0495
5
3.56779 256.88
1
2011 77 5929 0.0529
9
4.08052 314.20
0
2012 65 4225
0.0447
4 2.90778
189.00
6
2013 79 6241
0.0543
7 4.29525
339.32
5
2014 77 5929
0.0529
9 4.08052
314.20
0
2015 78 6084
0.0536
8 4.18720
326.60
2
2016 72 5184
0.0495
5 3.56779
256.88
1
2017 74 5476
0.0509
3 3.76875
278.88
8
Sum of
Temp 1453
μ 72.8968
Std 4.2341
Max 79
Min 65
Range 14
∑p(x) 1
∑X^2.P(x)
5331.514
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Running Head: QUANTITATIVEANALYSIS
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The data above is normally distributed because the sum of individual
probabilities is 1.
b) An outlier can be defined as an observation point which is distant from the
rest of the observations.
c)
To identify outliers, we would plot a scatter plot of average temperature
against time(years).
1995 2000 2005 2010 2015 2020
0
10
20
30
40
50
60
70
80
90
A scatter plot of Temp Vs Time
Time (years)
Average Temperature ( ͦ F)
Figure 2: A scatter plot for mean temperature data in Boston.
From the above figure, it is evident that there are no outliers’ data.
d)
Given, μ=73.0 °F , σ =4.234088 , x=76
Now computing the test statistics using the formula