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WWW.YORKVILLEU.CA
BUSI 1013: STATISTICS FOR BUSINESS
UNIT EXERCISES
Unit Exercise 1
BUSI 1013 S
TATISTICS
F
OR
B
USINESS
1
WWW.YORKVILLEU.CA
1.
As the Manager of Customer service at a Bank, you were assigned the job of revamping the Customer Service function at the branches. To get the project started, a research study at four branches was conducted to assess the effectiveness of a recent change in the customer account management process. Details of the study are as follows:
A group of customers from each of the four branches were selected randomly and invited to participate in the study.
Personal deposit and loan balances from these customers were extracted from the Bank’s databases before the change took place.
Personal deposit and loan balances from these customers were also extracted from the Bank two months after the change
A simple survey was conducted to ask the customers involved about their experiences with the change. A few variables from the survey were recorded and appended to the extracted deposit and loan file.
The attached Excel workbook, BUSI1013 Bank Dataset.xlsx
, contains the data collected from the research study. Answer the following questions using this data set. a.
What would the population of interest be for this study?
The population of interest in this study comprises the customers of the bank. Specifically, it includes individuals who have participated in the research study conducted by the bank. These customers are the focus of the investigation, and the findings from the study are likely intended to provide insights into the behavior, preferences,
and experiences of this particular group.
b.
Which method of sampling was used in this study?
Sampling is a technique used to gather representative data or observations from a larger group, known as the population. The method of sampling depends on how the data was collected. Here are the two primary types of sampling methods:
Probability sampling
: This method involves random selection, meaning every member
of the population has an equal chance of being selected. It allows you to make strong statistical inferences about the whole group. Types of probability sampling include simple random sampling, stratified sampling, and cluster sampling.
Non-probability sampling
: This method involves non-random selection based on convenience or other criteria. You won’t be able to make statistically valid inferences about the whole group, but it allows you to easily collect initial data. Types of non-probability sampling include convenience sampling, quota sampling, and purposive sampling.
From the given dataset simple random sampling method was used in the study.
BUSI 1013 S
TATISTICS
F
OR
B
USINESS
2
WWW.YORKVILLEU.CA
c.
How big is the sample size?
The sample size refers to the number of observations or replicates (the rows in your case) in your data. If you’re using Excel, you can determine the sample size by counting the number of rows of individual data entries in the Excel sheet. Each row usually represents a unique entry or individual participant’s information in the research study. So, there are 152 rows in the given data and the size of the sample data is very big.
d.
How many variables are in the data set?
The dataset includes several variables, each representing a different aspect of the participants and their interactions with the bank. The variables include:
1. Customer ID
2. Branch
3. Gender
4. Age
5. Income
6. Deposit Before
7. Deposit After
8. Increase in Deposits
9. Loans Before
10. Loans After
11. Increase in Loans
12. Rating
13. Recommend Before
14. Recommend After
These variables cover a range of demographic information, financial metrics, and customer feedback, providing a comprehensive dataset for analysis.
e.
Which of the variables are categorical?
Categorical variables are those that represent categories or labels. In this dataset, the following variables are categorical:
1. Customer ID (assuming it is a label and not a unique identifier)
2. Branch
3. Gender
4. Rating
5. Recommend Before
6. Recommend After
These variables involve discrete categories such as branch names, gender labels, and rating levels.
f.
Which of the variables are numerical?
BUSI 1013 S
TATISTICS
F
OR
B
USINESS
3
WWW.YORKVILLEU.CA
Numerical variables represent measurable quantities. In this dataset, the following variables are numerical:
1. Age
2. Income
3. Deposit Before
4. Deposit After
5. Increase in Deposits
6. Loans Before
7. Loans After
8. Increase in Loans
2.
Use a frequency distribution table to numerically summarize the variable Branch in the BUSI1013 Bank Dataset.xlsx
data set. Based on the table, use a pie chart to summarize this variable graphically. Branch
Frequency
A
65
B
40
C
27
D
20
152
65
40
27
20
Frequency
A
B
C
D
3.
Data from the Chase branch is extracted from the data set BUSI Bank Dataset.xlsx and is stored in BUSI1013 Chase Dataset.xlsx
. Use this file to answer the following.
a.
Construct a histogram for the variable income.
b.
What does the histogram tell us about the shape of the distribution of income?
c.
Construct a stem-and-leaf display for the variable age. Please be sure to include a leaf unit.
BUSI 1013 S
TATISTICS
F
OR
B
USINESS
4
WWW.YORKVILLEU.CA
a)
Income vs. Frequency
X Y
[5, ($43.70, $45.70)] [2, ($45.70, $47.70)] [6, ($47.70, $49.70)] [3, ($49.70, $51.70)] [8, ($51.70, $53.70)]
[3, ($53.70, $55.70)]
b)
Since there are more frequencies of values for smaller values of age, there is peak at left end and tail towards the right-end. The shape of the stem-and-leaf display shows that the skewness of the age is left-skewed. c)
A stem-and-leaf display for the variable age. Stem Leaf
3 0 0 1 2 2 4 6 6 9 9 9
4 1 1 2 2 7 9
5 5 7 8 8 8
6 0 1 1 1 1
------------------------------------------------------------------
4.
Use the data in BUSI1013 Chase Dataset.xlsx
to answer these questions:
a.
What is the sample mean of the variable income?
b.
What is the sample median of the variable income?
BUSI 1013 S
TATISTICS
F
OR
B
USINESS
5
WWW.YORKVILLEU.CA
c.
Find the range of the variable income.
d.
Find the sample standard deviation of the variable income.
e.
Compute the first and third quartile of the variable income.
f.
What is the IQR of the variable income?
g.
Give the five-number summary for the variable income.
h.
Use the IQR rule to determine whether there are outliers for the variable income.
Answer:
a)
X
52.1
49.2
50.1
51.1
48
45.5
49.3
50.6
48.1
54.9
54
51.9
48.9
53.2
52.7
44.4
43.7
49.5
54.2
53.6
52.8
53.5
46.9
44.5
44.2
52
47.2
Total
1346.1
n = Sample size = 27
BUSI 1013 S
TATISTICS
F
OR
B
USINESS
6
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