Quantitative Analysis

This document provides a detailed analysis of quantitative problems. It includes frequency distribution tables, scatter plots, and calculations for mean, median, mode, and probability. The data is analyzed using various statistical methods.

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Quantitative analysis
Student’s Name:
University Affiliation:

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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

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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
8

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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 ℉ , σ =4.234088 , x=76
Now computing the test statistics using the formula

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Z= x −μ
σ
Z= 76−73
4.234088
Z=0.708535
Now P(Z< 0.708535 ¿=0.7607
Then, P(Z>0.708535 ¿=1−0.7607=0.2393
Therefore, the what is the probability that the mean will be over 76 in any
given July is 0.2393.
e)
Given the following values.
μ=73.0 ℉ , σ =4.234088 , x=80
Using the formula Z= x −μ
σ to compute test statistics
Z= 80−73
4.244088 =1.64935
Now we can compute P(Z<1.64935 ¿=0.9505
Computing P(Z>1.64935 ¿=1−0.9505=0.0495
Therefore, the probability that the mean will be over 80 in any given July is
0.0495 .
Problem 2

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Temp
Range
Frequenc
y
Cumulative
%
82 0 0.00%
84 1 5.26%
86 4 26.32%
88 4 47.37%
90 5 73.68%
92 5 100.00%
94 0 100.00%
96 0 100.00%
More 0 100.00%
82
86
90
94
More
0
2
4
6
0.00%
40.00%
80.00%
120.00%
Histogram
Frequency
Cumulative %
Temperature
Frequency
Figure 3: A frequency graph for heatwave temperature.
From the given heat wave data, the following calculations are obtained.
Days(n) Temp (x) p(x) x.p(x)
1 93 0.05234 4.867192
2 88 0.04952 4.357907
3 91 0.05121 4.660101
4 86 0.04840 4.162071
5 92 0.05177 4.763084
6 91 0.05121 4.660101
7 90 0.05065 4.558244
8 88 0.04952 4.357907
9 85 0.04783 4.065841
10 91 0.05121 4.660101
11 84 0.04727 3.970737
12 86 0.04840 4.162071
13 85 0.04783 4.065841
14 90 0.05065 4.558244

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15 92 0.05177 4.763084
16 89 0.05008 4.457513
17 88 0.04952 4.357907
18 90 0.05065 4.558244
19 88 0.04952 4.357907
20 90 0.05065 4.558244
n=20 Sum 1777 1
88.92234
1
Mean 88.85
Median 89.5
Mode 88
n 20
Max 93
Min 84
Range 9
The data has a normal distribution because mean, median and mode are
fairly the same.
Heat wave ~three or more days with a high temperature over 90 degrees
Fare height.
P(n≥10)=P(n=12)*p(n=15)*p(n=18)
P(n≥10)= 0.04840 *0.05177 *0.05065=0.0001269
The probability that the heat wave will have a temperature more than 90 ℉ in three interval
days is 0.0001269
Problem 3
a) The situation of the customers’ behavior exactly fits the parameters
for a binomial distribution. This is because of exactly 2 possible outcomes of

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occurrences from the customers’ behavior to either buy online or from the
physical store. There is no any other possible alternative among customers
in the market, despite when the occurrence is repeated on multiple times.
b) P (customers purchase online) =40%
=40/100
=0.4
P (Customers purchase from the physical store )=60%
=60/100
=0.6
c) P (Exactly four sales bought online each day =4/12
=1/3
0.3333.
d) P (From 12 sales made each day, fewer than 6 are made online=1-
P(6 sales are made online)
=1-6/12
=1-0.5

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=0.5
e) From the 12 sales made each day more than 8 are made online
=1-P(8sales are made online)
=1-8/12
=1-2/3
=1/3
=0.3333.
Problem 4
a)
My company of choice is Apple Company. According to an article
written by Adrian Kinsley on December 29 2018, Apple company made it
clear that it would no longer report on iPhone, iPad and mac books unit sales
as their objective is to make great products for customer satisfaction.
However, this had sparked fears among Apple investors who are now

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believing that things are not going well for the company. This is because
both the iPhone and smartphone sales have been weakening as people no
longer buy the iPhone their new features but rather than but rather to
change the older used phones. Smartphones have also become dull and
Apple is keen on coming up with more exciting features. Together with trump
tariff of 10%, tariff increment on Chinese made phones and mac books.
Considering the above problems facing the company, Apple has a lot to do in
convincing the customer to buy their expensive iPhones so as to maintain a
constant revenue (Kinsley, 2018).
b)
I would carry out market analysis research.
The data to be collected Customer’s age, Customer’s Income, region
etc.
c)
The data would be a poison’s distribution.
This is because the collected data are both discrete and continuous.
d)
Customers’ buying trends and customer’s average age that use
iPhone.
e)

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The aim of every business is to make profits while providing quality
products to their esteem customers. Once, the customer is satisfied with the
product, their willingness to pay even for higher costing products increases.
The company, therefore, needs to provide funds for data collection and
analysis failure to which the company will incur losses.

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Refence
Livak, K. J., & Schmittgen, T. D. (2001). Analysis of relative gene
expression data using real-time quantitative PCR and the 2− ΔΔCT
method. methods, 25(4), 402-408.
Ramakers, C., Ruijter, J. M., Deprez, R. H. L., & Moorman, A. F. (2003).
Assumption-free analysis of quantitative real-time polymerase chain reaction
(PCR) data. Neuroscience letters, 339(1), 62-66.
A. K. (2018, December 29). Challenges fcing Apple in 2019. Hughes for
Hardware 2.0.

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