Week 3 - Assignment: Analyze Numerical Summaries of Data Using Excel and SPSS

6/17/22, 3:14 PM BUS-7105 v3: Statistics I (7103872203) - BUS-7105 v3: Statistics I (7103872203)

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Week 3

BUS-7105 v3: Statistics I (7103872203)

Central Tendency and Dispersion

After identifying a good project or investigation, and collecting the required data, the next

step is to summarize the data using both visualizations and numerical summaries. We call

these numerical summaries descriptive statistics. Descriptive statistics are used to help

understand where the center of the data is and how to spread out the data are. Measures

of the center typically include the mean, median, and mode. The spread of a dataset is

often measured using the range, variance, and standard deviation, most commonly the

latter.

The mode is the most frequently occurring value in a set of data. If we survey 10 people

and five drive Jeeps, three drive SUVs, and two drive luxury cars, the modal value is

represented by the Jeep because in this sample more people drive these than any other

brand of a vehicle reported.

The median is the value that falls in the center of an ordered array of data. If we have five

values -- 1, 2, 3, 4, 5 – the median is the center value. If we look at another five values –

1, 2, 3, 4, 3018 – the median value is still the center value of “3.” The value of the median

is that it is not swayed by extreme values as in this example.

If you think about how governments report their data, they usually use the median so as

to factor out the outliers. This helps researchers from misrepresenting results from a

sample of data. Say we are interested in the average income of a randomly selected group

of people. We ask 30 people what their annual income is and one of them happens to be

the Oracle of Omaha, Warren Buffett, his tens of millions of dollars in earnings each year

would throw off the average. But by using the median, we can factor out Mr. Buffett’s

earnings.

The most common and meaningful measure of central tendency is the mean. The mean is

the arithmetic average of a set of data. This is calculated simply by adding up the values

we are interested in and dividing by the number of values. The average of our previously

used five values – 1, 2, 3, 4, 5 – is 3.

(1+2+3+4+5)/5 = 3

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We can see by comparing our discussion of a median and mean that the mean can be

drastically swayed by extreme values or outliers. In our example of average income, the

median helps us to remove the effects of a non-representative outlier. However, the

mathematics behind the mean will allow it to be skewed. A good researcher will consider

both measures.

Dispersion is measured using the range, the variance, or more commonly the standard

deviation. The range is simply the largest value subtracted by the lowest value. Continuing

our example of 1, 2, 3, 4, 5, our highest value is 5 and our lowest is 1. Five less one equals

four. This is a range of four in this dataset.

A more complicated explanation of dispersion is the variance of an array of data. The

formula for calculating variance is noted below. This variance is not terribly useful at first

glance, but it is essential in some of the advanced tools we will explore toward the end of

this course. A more interpretable measure of dispersion is the standard deviation. The

standard deviation (SD) is an easy calculation if the variance is known. The standard

deviation is the square root of the variance value. We will revisit the standard deviation in

Week 5 when we discuss the normal distribution and the Central Limit Theorem.

Figure 2. Formulas for calculating variance and standard deviation n samples

To illustrate why these types of measures are so important, consider a production process

that manufacturers a certain car engine part such as a cylinder. Typically, a cylinder will

have engineering specifications called a lower specification limit (LSL) and an upper

specification limit (USL). Now, suppose that a batch of 10 cylinders has been produced

and the diameter is measured. By calculating the mean diameter, you can see if the

production process is properly centered between the specification limits (the LSL and the

USL). The standard deviation would also be calculated to determine if the variation of the

parts is small enough so that, say 99.7% of the parts are within the specification limits.

Another example illustrating the importance of the descriptive statistics is the SAT exam

that students take when they apply to colleges. These exams are scaled so that the

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Books and Resources for this Week

Knapp, H. (2017). Descriptive statistics,

categorical [Streaming video]. Retrieved

from SAGE Research Methods Link

Descriptive statistics. (n.d.-b). Week 3

Assignment Data (Excel) Excel Spreadsheet

Week 3 assignment data - Question 4

(SPSS) SAV File

average on each part (i.e., Mathematics and English) is 500 and the standard deviation is

100. By knowing the mean and the standard deviation, together with the fact that test

scores follow a normal distribution (to be discussed in detail in Week 4), test

administrators know that certain percentages of students will be within one or two

standard deviations of the mean. For example, 68% of the scores will be between 400 and

600. In this week’s assignment, you will look at some descriptive statistics calculations

that can be done with either Excel or SPSS. For additional information on Descriptive

Statistics and Exploratory Data Analysis, please refer to the NCU School of Business Best

Practice Guide for Quantitative Research Design and Methods in Dissertations.

Be sure to review this week's resources carefully. You are expected to apply the

information from these resources when you prepare your assignments.

87.5 % 7 of 8 topics complete

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Davis, S., & Davis, E. (2015). Data

analysis with SPSS software: Data

types, graphs, and measurement

tendencies. New York: Momentum

Press. Link

McCormick, K., Salcedo, J., & Poh, A.

(2015). SPSS statistics for dummies.

Hoboken, New Jersey: John Wiley &

Sons, Inc. Link

Introduction to Business Statistics (7th

ed.) External Learning Tool

NCU School of Business Best Practice

Guide for Quantitative Research Design

and Methods in Dissertations Link

Week 3 - Assignment: Analyze Numerical Summaries

of Data Using Excel and SPSS Assignment

Due June 19 at 11:59 PM

In this week’s assignment, you will answer the following questions using both Excel and

SPSS software. Results from these programs should be copied and pasted into a Word

document for submission.

For Questions 1 and 2 you will need to input the data provided below into both Excel and

SPSS. For Questions 3 and 4 you will use the dataset files provided in the resources for

this week (Descriptive statistics, n.d.-a, n.d.-b).

1. Suppose that a quality assurance manager took a random sample from a thread-cutting

machine. The sample consisted of 18 bolts and the manager tested their tensile strengths.

Results from the sample, in tons of force required for breakage, are given below:

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2.20 1.95 2.15 2.08 1.85 1.92

2.23 2.19 1.98 2.07 2.24 2.31

1.96 2.30 2.27 1.89 2.01 1.93

a. Use Excel to calculate the mean, median, and standard deviation for these data.

b. Use SPSS to calculate the mean, median, and standard deviation for these data.

c. Use SPSS to create a histogram of these data.

d. Interpret these results and explain any differences you find between the two

software tools (Hint. The results should be identical).

2. A manager of a food manufacturing company wants to estimate the percentage of fat in

one of its salad dressings. A sample of 20 bottles was taken and the results are given

below.

15.88 19.88 21.16 20.37 22.77 20.65

18.60 18.91 21.77 21.64 18.62 18.41

20.15 17.07 19.91 21.07 16.49 21.21

17.98 20.22

a. Use Excel to calculate the mean, median, and standard deviation for these data.

b. Use SPSS to calculate the mean, median, and standard deviation for these data.

c. Use SPSS to create a histogram of these data.

d. Interpret these results and explain whether or not it is honest for the manufacturer

to state that the fat content is 20%? Explain your answer.

3. A manager is worried that her employees are not engaged at work. She finds an

employee engagement survey and administers it to her workers. The individual scores are

provided in the dataset file.

a. Use Excel to calculate the mean, median, and standard deviation for the employee

engagement data.

b. Use SPSS to calculate the mean, median, and standard deviation for the employee

engagement data.

c. Use SPSS to create a histogram of these data.

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d. Next, conduct an analysis of the “age” and “gender” variables using the appropriate

measures of central tendency and dispersion. Use SPSS only. Also, create an

appropriate graphic for each variable.

d. Interpret the results for employee engagement, age, and gender. Identify what you

believe the next step should be in this analysis.

4. A shop supervisor wants to understand his workers better. He hires a consultant who

tells him that he should ask employees questions related to their lives if they feel

comfortable answering these questions. Please use SPSS to analyze the following

variables, create appropriate figures and charts, and explain the results of each variable.

Do not compare the variables in this assignment.

a. Age

b. Model of car

c. Rent or own their home

d. Hobbies

e. How happy they are (on a five-point scale)

Length: 4 to 6 pages

References: Include a minimum of 3 resources (two of these will be Excel and SPSS).

Your assignment should demonstrate thoughtful consideration of the ideas and concepts

presented in the course and provide new thoughts and insights relating directly to this

topic. Your response should reflect scholarly writing and current APA standards. Be sure

to adhere to Northcentral University's Academic Integrity Policy.

Upload your document and click the Submit to Dropbox button.