Statistical Techniques for Business Problem Solving

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HA1011-APPLIED QUANTITATIVE
METHODS
ASSESSMENT 2
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Contents
1. Explain how statistical techniques can solve business problems..............................3
3. Explain and justify the results of statistical analysis in the context of critical
reasoning for business problem-solving...........................................................................4
4. Apply statistical knowledge to summarize data graphically and statistically, either
manually or via a computer package................................................................................4
Question 1 of 8.................................................................................................................6
Question 2 of 8.................................................................................................................8
Question 3 of 8...............................................................................................................11
References.....................................................................................................................13
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1. Explain how statistical techniques can solve business problems
The statistical techniques or the data analyzing tools and methods are very prominent
for handling any business with the best possible solutions. The business is not only
based on the sales and earning but also on the crunching of the numbers and predicting
the best through them. Considering a business which is looking for growth in the
business and for setting targets for the future, it is very important to understand that the
statistical analysis of the numbers plays an important role. The numbers are generated
from various aspects of the business like the capital invested for business, the daily
sales, market factors, revenue generation, targets, and growth.
For a business to be prepared for the future, it is important to predict future sales and
growth using those numbers. The statistical analysis provides the facility to forecast the
future sales and requirements which helps the business to be prepared for the future.
There are various methods in the statistical analysis that helps to find the dependencies
of business growth. The mean of the sales of some departments or products helps to
understand the average sales made for every product and what is the possibility for the
same. Methods like a collection of data and finding their correlation helps to understand
how well two different factors are co-related to each other and can be used to
manipulate the business terms to achieve utmost success for the company (Hickey,
2012).
2. Identify and evaluate valid statistical techniques in a given
scenario to solve business problems.
For considering a scenario, let us consider a company that has the operations of
manufacturing and selling products. For example, consider the company Nestle. The
company works in various lines of manufacturing but for instance, consider the Nestle
Chocolate bars manufacturing and selling sideline. The company knows that the sale of
the chocolate bars is high in the holiday seasons around the Christmas and therefore
the company decided to forecast and predict the number of chocolates that can be sold
this year to outreach last year sales (Dillard, 2016).
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There are various methods in statistics that can help in predicting the chocolate sales.
The company can calculate the various correlation factors to determine which factors of
manufacturing and sales more attention. Factors like quality, price, packaging, etc. can
be helpful in calculating sales. The other scenario can be the ice cream company that
produces various flavors of ice cream. For summers the company wants to know which
is the most preferred flavor so that the production of that flavor can be maximized and
for that, the company can use of Mode of the sales according to the flavor. The flavor
that occurs most in the sales list is the most preferred and needs to be manufactured in
the maximum amount.
3. Explain and justify the results of statistical analysis in the context
of critical reasoning for business problem-solving.
The process of critical thinking in business is the method using which the business
people conceptualize, analyze, apply and synthesize the data which is collected from a
various business process like sales, marketing, revenue, profit, loss, etc. and
observations. The critical reasoning is a way using which the important decisions of a
business are made and justified. As mentioned above, the statistical analysis is a
method of processing data based on the facts and visualizing the results to present a
clear picture. The statistical data analysis helps business companies to make valuable
decisions based on solid data. The main benefit of statistical analysis is that the process
makes it easy to read and study from various frames of reference (Critical Thinking,
2019).
Critical thinking is evidenced by the results of the statistical analysis. Suppose a
businessman finds his business going to complete loss and this can be proved to other
business partners by using the statistical analysis methods and the results will be used
to obtain a solution for the same.
4. Apply statistical knowledge to summarize data graphically and
statistically, either manually or via a computer package.
The statistical knowledge can be visualized using various graphs such as the
histograms, bar graphs, pie charts, line graph, scattered plots, and others. The graphs
4

help to represent the data in easily understandable forms. The visuals are more efficient
to explain and are widely used all over the world. The visualizations can be done by
using both manual and computer methods. As shown in the questions below, the
computerized methods use tools like the MS Excel, Tableau and other web-based
systems like IBM Watson. These are very simple to use and produce very accurate
results in a short time and less error. The tools need data to be uploaded on their
workspace and then the data can be analyzed. In the manual method of visualizing the
statistical data, the method of drawing and plotting graphs is used to present data. The
manual method is easy but it takes a lot of time and is prone to errors.
5.
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Question 1 of 8
The data of passengers:
456 1189 410 318 648 2300 382 248 379 1240 2048 272
267 1134 733 262 682 906 338 1750 530 1584 3045 323
1311 1536 1606 982 878 169 583 548 429 658 344 2450
538 494 1946 268 435 862 866 579 1348 1022 1618 1021
401 1181 1178 637 2745 1000 2900 962 697 401 1442 1115
a)The following table represents the class frequency, relative frequency, class midpoint,
and cumulative frequency:
Table 1: Answer 1
S.NO. CLASSES FREQUENCY CLASS MIDPOINT RELATIVE
FREQUNECY
COMMULATIVE
FREQUENCY
1 150-440 17 295 0.28 17
2 440-730 12 585 0.20 29
3 730-1020 8 875 0.13 37
4 1020-1310 8 1165 0.13 45
5 1310-1600 5 1455 0.08 50
6 1600-1890 3 1745 0.05 53
7 1890-2180 2 2035 0.03 55
8 2180-2470 2 2325 0.03 57
9 2470-2760 1 2615 0.02 58
10 2760-3050 2 2905 0.03 60
Smallest number 169
Largest number 3045 Range= largest no- smallest no= 2876
Class width= Range/No of class= 2876/10= 287.6 which will round of to 290 for easy
calculation.
Class midpoint= [(Beginning Class Endpoint + Ending Class Endpoint)]/2
Class midpoint= (Class Beginning Point + (1/2) Class Width)
Relative Frequency= Frequency/Total no of data
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b) The histogram is as follows:
150-440 440-730 730-
1020 1020-
1310 1310-
1600 1600-
1890 1890-
2180 2180-
2470 2470-
2760 2760-
3050
0
2
4
6
8
10
12
14
16
18
17
12
8 8
5
3 2 2 1 2
FREQUNECY OF PASSENGERS
Figure 1: Passenger frequency (class wise)
c) The mean, median and mode of the raw data are as following:
The data was sorted from acceding to descending and the formulae were used to
calculate mean median and mode
Figure 2: Mean
The mean= sum of all data/no of data
Mean= 976.5667
Median will be at n/2 position of the whole array list where (n: no of data entries)
So, the median will be at the 30th position of the array and therefore:
Median = 733
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The mode is the most occurring number and the mode is:
Mode= 401
Question 2 of 8
a) The data of the weekly attendance and chocolate sold is population and not the
sample. The reason behind the data being population is that the data is of the complete
population of the Holmes Institute student and respective chocolate sold. The data
would have been sample if it was of some particular number of students (Sharma,
2016). The major difference between sample and population are:
Figure 3: Sample VS Population
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b) Standard deviation is the square root of the variance
Weekly attendance = x x-μ (x-μ)2
472 -12.6 158.04
413 -71.6 5122.47
503 18.43 339.61
612 127.4 16238.04
399 -85.6 7322.47
538 53.43 2854.61
455 -29.6 874.47
Value of μ = Ʃ x/No of data entries
Value of μ= 484.5714286
Ʃ(x-μ)2 =23909.71
Variance= σ2= 4701.388
Standard Deviation (σ)= 68.56667
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c) The IQR is as following:
Weekly attendance Number of chocolate bars sold Quartile St Dev
472 6916 O3=6114 756.3098
413 5884 Q1=7216
503 7223 IQR=1102
612 8158
399 6014
538 7209
455 6214
d) Correlation coefficient:
Figure 4: Formulae for correlation coefficient
Using the formula, the correlation coefficient is= 0.967993
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Question 3 of 8
x (Attendance) y (sold bars) x2 xy
472 6916 222784 3264352
413 5884 170569 2430092
503 7223 253009 3633169
612 8158 374544 4992696
399 6014 159201 2399586
538 7209 289444 3878442
455 6214 207025 2827370
Ʃ 3392 47618 1676576 23425707
Figure 5: Formula for b1
Ʃx*Ʃy 161520256
Ʃxy 23425707
Ʃx2 184999795
(Ʃx*Ʃy)/n 23074322.29
Ʃx2 /n 26428542.14
Therefore, the value of b1= 0.002215942
Figure 6: Formula for b0
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Using the other formulae and considering x as weekly attendance and y as chocolate
bars, the regression equation is:
350 400 450 500 550 600 650
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
f(x) = 10.6772338171968 x + 1628.68898458119
Regression
y = 10.677x + 1628.7
Figure 7: Regression using Excel
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