Applied Quantitative Methods Solutions

University
Applied Quantitative Methods
by
Your Name
Date
 <Your Name> 2018 1 of

Solutions
Question 1: Summary of Statistics and Graph
Problem Statement
Dataset for the prices of parts at each shelf in auto parts showroom in Melbourne is
provided. It is required that the frequency distribution using 10 classes, the frequency,
relative frequency and class midpoint is constructed. Additionally, a histogram is to be
constructed and the mean, mode and median be determined in excel.
Solution
A. The frequency distribution for the prices of parts is as shown below
Table 1: Frequency Distribution
B. The histogram for the above is created in excel and is as shown below:
Fig 1: Histogram
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C. The mean is given by the sum of the prices divided by the total number of prices
taken as shown below:
∑ x
x = 12602
60 =210.03
The mode is the most commonly appearing price and is 140.
The median is the price that appears at the middle and is
170+180
2 =175
Question 2: Measures of Variability and Association
Problem Statement
Dataset is provided to the manager of a baggage’s show room in the airport to discern
whether there is a relationship between the number of flights at the airport each day and
the number of baggage’s sold so that they can be kept in stock when the airport is busy over
the upcoming holiday.
Solution
a. The data set is a sample indicating the number of flights in the airport and the
baggage’s sold for seven weeks.
b. The standard deviation for the sample is given by;
σ = √ ∑(x−μ)2
n−1
The values and computations need to be substituted above are as follows:
Table 2: Data for Standard Deviation
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Therefore, substituting the values to the equation, we find:
σ = √ ∑(x−μ)2
n−1 = √ 151.4286
6 =5.023
c. The interquartile range of the baggage’s sold is given by:
Q1= 33
Q2=35
Q3=40
IQR=Q 3−Q1
IQR=40−33=7
The interquartile range is more preferred to standard deviation when the data
distribution is highly skewed or contains outliers [1]. For example, in the case of
baggage’s sold 43 can be viewed as an outlier that makes the data to be highly
skewed to the right hence the interquartile range would be the suitable case to use
for analysis.
d. The correlation coefficient is denoted by r and is given by:
Table 3: Data for Calculating Correlation Coefficient
r =n ( ∑ xy ) −(∑ x )(∑ y )
√ ¿ ¿ ¿
r =7 ( 7324 ) −(201)(253)
√ ¿ ¿¿
The correlation coefficient indicates the degree of linear relationship between the
flights and the baggage’s sold [2]. In this case there is a weak positive relation,
meaning when the flights increase the baggage’s sold also increase. As the manager
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