BUSI 820- Quantitative Analysis Assignment # 3
Darrell Smeltzer
BUSI 820- Quantitative Research Methods (B05)
09/09/2021
Assignment # 3
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BUSI 820- Quantitative Analysis Assignment # 3
Table of Content
Descriptive Statistics………………………………………………………. pg. 3-9
Research Questions…………………………………………………………pg. 9-
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Descriptive Statistics
4.1. Compute the skewness
Figure 1.1- Skewness for Variables
age group
Frequency Percent Valid Percent
Cumulative
Percent
Valid less than 22 17 34.0 34.0 34.0
22-29 18 36.0 36.0 70.0
30 or more 15 30.0 30.0 100.0
Total 50 100.0 100.0
Figure 1.2- Age Group
positive evaluation, institution
Frequency Percent Valid Percent
Cumulative
Percent
Valid disagree 10 20.0 20.0 20.0
neutral 17 34.0 34.0 54.0
agree 17 34.0 34.0 88.0
strongly agree 6 12.0 12.0 100.0
Total 50 100.0 100.0
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Figure 1.3- Positive Evaluation
positive evaluation, major
Frequency Percent Valid Percent
Cumulative
Percent
Valid strongly disagree 1 2.0 2.0 2.0
disagree 10 20.0 20.4 22.4
neutral 17 34.0 34.7 57.1
agree 17 34.0 34.7 91.8
strongly agree 4 8.0 8.2 100.0
Total 49 98.0 100.0
Missing System 1 2.0
Total 50 100.0
Figure 1.4- Positive Evaluation- Major
positive eval, social life
Frequency Percent Valid Percent
Cumulative
Percent
Valid strongly disagree 4 8.0 8.0 8.0
disagree 13 26.0 26.0 34.0
neutral 14 28.0 28.0 62.0
agree 12 24.0 24.0 86.0
strongly agree 7 14.0 14.0 100.0
Total 50 100.0 100.0
Figure 1.5- Positive Evaluation- Social Life
positive evaluation, facilities
Frequency Percent Valid Percent
Cumulative
Percent
Valid strongly disagree 8 16.0 16.0 16.0
disagree 9 18.0 18.0 34.0
neutral 22 44.0 44.0 78.0
agree 9 18.0 18.0 96.0
strongly agree 2 4.0 4.0 100.0
Total 50 100.0 100.0
Figure 1.6- Positive Evaluation- Facilities
Descriptive Statistics
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4.2. Steam and Leaf plot
Case Processing Summary
sex at birth
Cases
Valid Missing Total
N Percent N Percent N Percent
same sex parent's height males 26 100.0% 0 0.0% 26 100.0%
females 24 100.0% 0 0.0% 24 100.0%
Figure 1.7- Case Summary of Steam and Leaf Plot
Descriptive
sex at birth Statistic Std. Error
same sex parent's height males Mean 70.5769 .76294
95% Confidence Interval for
Mean
Lower Bound 69.0056
Upper Bound 72.1482
5% Trimmed Mean 70.6538
Median 72.0000
Variance 15.134
Std. Deviation 3.89022
Minimum 64.00
Maximum 76.00
Range 12.00
Interquartile Range 6.25
Skewness -.369 .456
Kurtosis -1.352 .887
females Mean 62.6667 .46104
95% Confidence Interval for
Mean
Lower Bound 61.7129
Upper Bound 63.6204
5% Trimmed Mean 62.7315
Median 62.5000
Variance 5.101
Std. Deviation 2.25864
Minimum 58.00
Maximum 66.00
Range 8.00
Interquartile Range 2.75
Skewness -.139 .472
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Kurtosis -.475 .918
Figure 1.8- All the descriptive from the variables
Figure 1.9- Steam-Leaf Plot Same sex parents’ height- Male
Figure 1.10- Same sex parent’s height- Females
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4.3. Frequencies for Nominal Variables
Figure 1.11- Frequencies for Nominal Variable
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4.4. Box Plots
Figure 1.12- Box plot of Student Height
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Figure 1.13- Box Plot Hours studied per week
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Research Questions
4.1. For the variables with five or more ordered levels, compute the skewness.
See figure 1.1 for the outputs of the skewness of the variables. The variables are listed in
the table on the columns.
4.1. (a). Describe the results.
In the figure 1.1, it shows the different variables and the skewness of each variable plus
the std error of the skewness. In the chart, under (age group) the skewness is .074 which is
extremely close to zero. The variable positive evaluation (institution) has skewness of .059
which is also close to zero which is the normally distributed amount on the scale. In looking
into the values, they are a positive shift from zero. In the chart also the variable positive
evaluation (social life), the skewness is .031 which is also close to zero and a positive shift from
the mean. The variable positive evaluation (major) has a negative value for the skewness which
is -.115 which means this is a skew below the mean value since it is negative. The variable
positive evaluation (facilities) also has a negative skew from the mean which is -.136. In the
data output we can tell from the data that if the mean is greater than the median there is a
positive skew and if the mean is less than the median the skew will be negative (Morgan, 2020).
A distribution is said to be symmetrical when the values of mean, median and mode are equal
(Zheng et al., 2017).
4.1. (b). Which variables in the dataset are approximately normally distributed/scale?
The variables that are going to be approximately normally distributed are the ones that
are closest to zero. (Age group) the skewness is .074, positive evaluation (institution) has
skewness of .059 and the other variable is positive evaluation (social life), the skewness is .031.
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These are the variables that are the closet to zero and are positively skewed. When a dataset is
“approximately normal” it means it roughly follows a “normal distribution” which has a bell-
curve shape, a median, mean, and top mode that are all equal and standard deviations that
follow the “68.25–95.–99.74” rule (68 percent of the population falls between 1 and -1, 95
between 2 & -2 and 99.74 between -3 & +3 standard deviations from the mean) (Morgan,
2020). Thus, when we say, “the distribution is approximately normal” we are saying “we can
probably run a t-test on this data without too much worry of a false positive.”
4.1. (c) Which ones are ordered but not normal?
The variable that is ordered but not normal in the data set is positive evaluation (major).
It has many ordered levels but as we see in the data set it is skewed. In the ordered levels it is
evident that the percent and valid percent are different, so this suggests that it has ordered
levels, but the data is not normal since it has been skewed by some numbers.
4.2. Do a stem-and-leaf plot for the same-sex parent’s height split by sex at birth. Discuss
the plots.
The stem-and-leaf plot for the same-sex parent’s height in figure 1.9, shows that the first
set of numbers that the leaf does not have a ending number which states that there is no last
digit in the same-sex parent’s plot. In looking at the frequency of 4 and the stem 6 and the
leaves of the plot are 4455. This states that 4 people had stems of 6 and leaves of 44 trough 55
states that there were scores between 44 and 55. The stem width shows 10 which states that
entries that have 0 for the stem and are less than 10, those with 1 as the stem range from 10 to
19.
The stem-and -leaf plot for the sex at birth in figure 1.10, shows that the first set of
numbers that the leaf is zero which means there were no ending numbers for the set of sex at
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birth. The other stems have extreme numbers and no leaves on the plot. The stem width shows 1
which states that entries that have 0 for the stem and less than 1.
4.3. (a) Which variables are nominal?
Nominal variables are categorical variables which has two or more categories but there is
no intrinsic ordering to the categories. A nominal variable is one that simply allows you to
assign categories, but you cannot clearly order the categories. In the data, the variables that are
nominal are sex at birth, marital status, children, tv sitcom, tv movies, tv sports, tv news.
4.3. (b) Run Frequencies for the nominal variables and other variables with fewer than
five levels. Comment on the results.
In figure 1.11, this shows the frequencies of all the nominal variables. The table gives the
mean, median, mode, std deviation, variance, and the skewness for each of the variables. The
mean ranges from .36 to 3.172. The mean is the arithmetic average, this average is done by how
many people are in the group plus how many categories there are in the mean. Take the mean of
3.172 which is the mean for student GPA we know the GPA ranges from 1-4 so the mean is
showing us that most students have scored a GPA of 3.172. The standard deviation is the
average amount of variability in your data set. It tells you, on average, how far each score lies
from the mean. We will look at the std deviation of the students GPA. The std deviation is .
3907. The standard deviation shows us how dispersed the data is in relation to the mean. The .
3907 is a small dispersion from the mean. This means most of the data is clustered around the
mean. The skewness of the frequency of students GPA .147 shows us that the data is skewed but
is a positive skew above the mean. If the skewness is between -0.5 and 0.5, the data are fairly
symmetrical. If the skewness is between -1 and – 0.5 or between 0.5 and 1, the data
are moderately skewed. If the skewness is less than -1 or greater than 1, the data are highly
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skewed (Morgan, 2020). This skewness of .147 is still fairly symmetrical.
4.4. Do boxplots for student height and for hours of study. Compare the two plots.
In figures 1.12 & 1.13 shows the boxplots of the student’s height and the hours of study.
In the boxplot of student height figure 1,12 shows that the median of the plot is 67 which is
verified by solid black line in the center of the boxplot. Below the blackline shows the blue
portion which shows the middle 50% and below that where there is no blue shows the expected
bottom 25% and above the blackline were there is no blue shows the expected top 25%. There
are no outliers present in the plot. In the plot of hours of study, figure 1.13 shows that the
median of this chart is 11. It shows the expected 25% below which is below the black line
which denotes the median and the expected 25% above the median line. In this boxplot it shows
a 11 with a circle which denotes the outliner. The outliner shows that the participant number 11
scored a 38 on the number of hours studied.
Conclusion
In the SPSS data which we ran in the SPSS software we found that certain variables are
nominal, scale, and ordinal. The data that was run was for the five or more ordered levels to
obtain the skewness of these variables. The data showed the difference of the skewness between
all the variables and how far from the mean they were. Some of the skewness was a positive
shift and some were are negative shift from the mean.
In SPSS, we ran a stem and leaf plot which shows to different variables and the different
outputs which happened between the variables. Some of the leaves had no data on variables and
the others had leaves. The leaves show the number of participants from low to high.
In SPSS, we found which variables were nominal and ran the frequencies for these
variables. These variables all had different frequencies, and some had similar skewness by one
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was negative and the other was a positive skew. The data showed the mean, median, mode, std
deviation and skewness and the data was commented on.
In SPSS, the boxplot shows the different variables hours of study and student height. The
box plots had different data sets and the boxplots were different one had an outlier and the other
did not. In this research, it was found that all variables are different, and the data shows the
differences in the outputs of the charts and plots.
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References
Zheng, S., Mogusu, E., Veeranki, S. P., Quinn, M., & Cao, Y. (2017). The relationship between
the mean, median, and mode with grouped data. Communications in Statistics - Theory
and Methods, 46(9), 4285-4295. https://doi.org/10.1080/03610926.2015.1081948
Morgan, G., Leech, N., Gloeckner, G., Barrett, K. (2020). IBM SPSS for Introductory Statistics:
Use and Interpretation. (6th Ed.). Routledge
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