DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 1
Marcos Reis Campos, MBA
BUSI 820
Liberty University
June 2, 2024
Table of Contents
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 2
Descriptive Statistics, Ordinal Scale and Dichotomous Variable....................................................3
4.1. (a) Compute skewness for variables with five or more ordered levels.....................................4
4.1. (b) Describe the results…………………….............................................................................4
4.1. (c) Which variables in the dataset are approximately normally distributed/scale?..................5
4.1. (d) Which ones are ordered but not normal?............................................................................6
4.2. (a) Do a stem-and-leaf plot for the same-sex parent’s height split by sex at birth...................6
4.2. (b) Discuss the plots.................................................................................................................6
4.3. (a) Which variables are nominal?.............................................................................................7
4.3. (b) Run Frequencies for nominal variables and other variables with fewer than five
levels................................................................................................................................................7
4.3. (c) Comment on the results.......................................................................................................7
4.4. (a) Do boxplots for student height and for hours of study........................................................8
4.4. (b) Compare the two plots.........................................................................................................8
References........................................................................................................................................9
Figures............................................................................................................................................10
Figure 1: Skewness of variables with five or more ordered levels................................................10
Figure 2: Stem-and-Leaf Plot for the same-sex parent’s height split by sex at birth.....................11
Figure 3: Frequencies for variables with fewer than five levels....................................................14
Figure 4: Boxplots for student height and for hours of study........................................................16
Descriptive Statistics, Ordinal Scale and Dichotomous Variable
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 3
4.1. (a) Compute skewness for variables with five or more ordered levels.
See Figure1
4.1. (b) Describe the results.
The following variables consist of five or more levels arranged in a particular sequence:
● positive evaluation, institution
● positive evaluation, major
● positive evaluation, facilities
● positive evaluation, social life
The order of the levels of these four variables is as follows:
● “1” strongly disagree
● “2” disagree
● “3” neutral
● “4” agree and
● “5” strongly agree
At this moment, each of the remaining variables in the dataset possesses an ordered level
of less than three. On the contrary, the requested statistics are presented in the first row of the
outputs, whereas the variables are enumerated in the column on the left. The output is
supplemented with the subsequent descriptive statistics in order to finalize the analysis:
● the number of subjects (n)
● the range
● the minimum
1 Figure 1: Skewness of variables with five or more ordered levels
● the maximum scores
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 4
● the mean for each variable
● the standard deviation
● the variance
● the skewness statistic
● the standard error of the skewness
The Valid N value, denoted as 49 in the concluding paragraph of the findings, is
indicative of the number of participants included in the data file for the study. To determine
whether a distribution can be considered normal, it is essential to keep in mind that for the
skewness value of the distribution to be less than ±1.0, it must fall within the normality range.
This suggests that the distribution is considered to be normal. A distribution is considered non-
normal when its skewness values exceed ±1.0, a threshold that exceeds the normality range. As a
result, the distribution cannot be considered normal. In order to facilitate comprehension, permit
me to expound on the following: Right-skewed distributions are characterized by values that
surpass +1.0. The distribution will maintain its asymmetrical nature if the value falls below -1.0
(Morgan et al., 2020).
The favorable evaluation suggests that the statistical skewness of the institution is 0.059,
which is contained within the permissible range of ±1. In addition, it seems that the data adheres
to a normal distribution. The assessment is positive because the principal statistical skewness
value is -.115, the significance level is within the acceptable range of ±1, and the distribution
looks like it should be normal. Based on the dependable assessment, the statistical skewness of
the facilities is -0.136, which is within the permissible range of ±1. Furthermore, it seems to
correspond to a normal distribution. The statistical analysis reveals that the skewness value
pertaining to social life is 0.031, which is contained within the permissible range of ±1. As a
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 5
result, the distribution of social existence seems to be typical. Every single one of the four
variables provided is contained within the precisely ±1 envelope of the normal distribution
(Morgan et al., 2020).
4.1. (c) Which variables in the dataset are approximately normally distributed/scale?
Examining the skewness data and using a histogram to make sure that each of the four
variables exists leads to the conclusion that all four variables follow the characteristics of a
normal distribution at the same time. The prevailing characteristic that is most often noted is the
favorable evaluation of the establishment, despite the apparent discrepancies.
4.1. (d) Which ones are ordered but not normal?
Every single one of the four variables that have been introduced possesses an ordered or
ordinal quality. Moreover, in accordance with the previously determined result and using the
assumption of ±1, it appears that each variable follows a normal distribution. Despite having a
generally normal distribution in terms of overall distribution, the primary variable that is being
evaluated favorably demonstrates a small amount of negative left skewness. Although the
distribution as a whole is quite normal, this remains the case. The absence of a specific data item
from the analysis could potentially account for the slight left skewness (Morgan et al., 2020).
4.2. (a) Do a stem-and-leaf plot for the same-sex parent’s height split by sex at birth
See figure2
4.2. (b) Discuss the plots.
Morgan et al. (2020) found that the stems correspond to the initial digit of the height of
the progenitor plant of the same species, whereas the leaf is responsible for the final digit. All
measurements are presumed to be in inches, with one unit being equivalent to one inch. The
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 6
subsequent analyses are predicated on this presumption. Each participant has satisfactorily
completed their information, and there are no omitted entries.
● Men have a median height of 72 inches.
● Women have a median height of 62 inches.
● The most substantial assemblage of males measures approximately 74–75 inches in
length.
● The largest assembly of women comprises approximately 62 units.
To provide greater clarity, the parent of the individual who stood the tallest was a male
who measured 76 inches (6 feet 3 inches), whereas the parent of the individual who stood the
lowest was a female who measured 66 inches (5 feet 5 inches). It is apparent that both
distributions demonstrate attributes of normality upon examination of the normal distributions.
Additionally, a gender disparity is evident, as a male is measured at 69 inches in height, while no
female is present at 61 inches. With a height of 58 inches (4 feet 8 inches), one female individual
distinguishes herself as an anomaly in the group. The median height of men, as opposed to
women, is nearly ten inches greater. Given that men are typically taller than women, this is
foreseeable.
2 Figure 2: Stem-and-Leaf Plot for the same-sex parent’s height split by sex at birth
4.3. (a) Which variables are nominal?
With the exception of age, which has fewer than five levels, the nominal variables are sex
at birth, marital status, whether the subject has children, television shows, television news,
television blockbusters, and television sports.
4.3. (b) Run Frequencies for nominal variables and other variables with fewer than five
levels.
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 7
See Figure3
4.3. (c) Comment on the results.
Using valid percentages, the frequency charts show not only how many people chose
each group but also what proportion of the total fell into each. Furthermore, valid and cumulative
percentages have been incorporated into the charts. The following are several logical deductions
that can be made based on the supplied evidence:
● Birth sex: Males constitute 52% of the population, while females constitute 48%
● The marital status of 36.7% of the population is married, while 63.2% are not. The
absence of one item from the data should be acknowledged
● Only 48% of the population is without offspring, while 52% of the population has
children
● Population age distribution: 30% of the population is 30 years of age or greater, while
70% is under 30 years of age. More specifically, there are 17 individuals who are under the age
of 22
● According to the survey, 36% of the total population stated that they do not watch
sitcoms, while the remaining 64% indicated that they do
● Number of movie viewers: 36% of individuals watch movies, while 64% do not
● The percentage of individuals who do not watch sports is 48%, while 52% do
● In accordance with the news report, 54% of the respondents do not watch the news, while
the remaining 46% do
Furthermore, it would be beneficial to conduct an analysis of the numerous genres that
are present in each type of television program and to compare and contrast them. Movies and
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 8
news programs are the least popular among the numerous categories of television programming,
while sitcoms are the most popular.
3 Figure 3: Frequencies for variables with fewer than five levels
4.4. (a) Do boxplots for student height and for hours of study.
See Figures4
4.4. (b) Compare the two plot.
It was determined that each participant had responded to the inquiry after examining a
frequency table. There is a median height of 67.3 inches, a range of heights from 60 to 75 inches,
and the height that occurs the most frequently is 64 inches, indicating a typical distribution of
heights. The boxplot that illustrates the number of hours spent studying each week appears to
adhere to a normal distribution. Conversely, a histogram analysis indicates that the curve is right-
skewed and the highest-scoring points are not located in the center. Based on the results of a
frequency table study, the average number of hours spent studying per week is 15.62, with a
range of 2 to 38. According to 36% of students, the hours between 10 and 12 are the ones that are
most frequently studied. The second most frequently reported hours are 2 hours, as reported by
2% of students. In a nutshell, an individual who studied independently dedicated 38 hours per
week to their academic endeavors.
4 Figure 4: Boxplots for student height and for hours of study
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 9
References
Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2020). IBM SPSS for
Introductory Statistics Use and Interpretation (6th ed.). New York, NY, USA: Routledge.
Descriptive
Statistics
i
Aange.
Minimen
Maximum
dean
Std
Gewalioy
Variance
Skewnass
Staliahe
Ctalistic Stalistic
Syalistic
Slaballe
Sralistic
Salistc
Siatalit
Bid
Estar
Posiive
SamuanON,
50 a
iz
5
oJ
a4a4
Aa
058 aaT
Pomive
evauaton,
mapa
46 4
4
5
at
3
AO?
“114
40
poaiive
evanu
ater,
4 A
5
276
1.0m
1.124
=
138
3H
:
530
11024360
oan
3a
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 10
Figures: Figure 1: Skewness of variables with five or more ordered levels
- - - -
a
-
--
ye
-
-o
_
-y
-
Case
Processing
Summary
2565
Valid
Missing
Sec
at
birth
MN
Percent
hs
Parcant
Same
$6
parent's
heighl
malas
26
100.0% 0
im
farnales
24
100.0% o
0.0%
lotal
26
24
Percent
100.0%
100.0%
Sen
al
birth
Habs
Sid,
Error
SOME
S46
Parents
heign
maled
Waar
TO.5769
Telos
5%
Confidence
Intarvalfar
Lower
Bound
69.0056
ae
UpparBound
72.1482
5%
Thmmad
Maan
70.6538
Median
f2.0000
Variance
15.134
Si,
Dewiailion
a.e9022
Minimum
64.00
Maximum
76.00
Range
12.00
interquartile
Range
6.25
Skewness
-.369
456
rurtosis
-1
342
BGT
famales.
Mean
62.6667
46104
5%
Confidence
intarvalfor
Lower
Bound
61.7129
ean
Lipper
Bound
63.6204
5S
Temmed
Maan
62.7375
Wadian
62.5000
Variance
4101
Std
Deviailion
225864
Minimum
58.00
Mavairrvurri
66.00
Range
4.00
interquartie
Range
2.76
Skewness
149
ar
Hurtosis
-
475 a18
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 11
Figure 2: Stem-and-Leaf Plot for the same-sex parent’s height split by sex at birth
same
sex
parent's
height
Stem-and-Leaf
Plots
‘same
sex
parent"s
height
Stem-and-Leat
Plot
for
‘sbirth=
males
Frequency
Stem
«
Leaf
»00
¢.
‘
4.00
€.
4455
:
2.00
é.
€7
:
5.00
é
.
88866
1.00
7.
1
:
6.00
7.
#23333
7.00
7.
4444555
:
1.00
7.
6
:
Stem
width:
10.00
:
Each
leaf:
1
case(s)
ee
ee
ee
ee
ee
ee ee
ee
ee ee
ee ee
ee ee
a
eo
sam
s®x
parent's
height
Stem-and-Leaf
Plot
for
sbirth= females
Frequency
Stem
«
Leaf
1.00
Extremes
(=<52.0)
1.00
55.
O
3.00
60
.
000
.00
él.
7.00
62
.
0000000
5.00
63
.
o0000
1.00
cd.
O
2.00
65.
60
4.00
66.
6000
Stem
width:
1.00
Fach
leaf:
i
case(a)
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 12
Su
fernales
males
sex
at
birth
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 13
Statistics
telavision
television
does
subject
shows
jolayision
lelovision
shows-
news
seeatbinh
marital
status
hive
childran
sicoms
SnoWS-Movies
shows-Spons
shows
A
Valid
50 4g 50 40
50
50
5
Missing
0
1
0 0
o
a a
s@x
at
birth
Cumulative
Frequency
Percent
Valid
Parcend
Percent
Vaid
Ter
#8
2
S20
520°
Tarn
alieg
zt
48.0 46.0
100.0
Tolal
ao
100.0 100.0
marital
status
Cumulative
Freauiency
Percent
‘valid
Percent Parcant
Sa
ee
eee
ee
aoe
married
18
36.0 36.7
776
diverced
lk
22.0
224
100.0
Total
ag
99.0
100.0
_Mewaing
cla
2.0
Total
50
100.0
does
subject
have
children
Curlin
Frequency
Parant
Valid
Pantani
Percent
Valld
no
i
40
460
46.0
ee
260520
oe
100.0
Thlal
50
100.0 100.0
television
shows-sitcoms
Cumulative
Frequency
Parent
Valid
Percent Percent
Valid
nie
18
36.0 36.0 36.0
ves
a7
64.0 64.0
100.0
Total
50
100.0
100.0
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 14
Figure 3: Frequencies for variables with fewer than five levels
television
shows-movies
Cumulative
Frequency
Pereent
Valid
Percent Percent
Valid
ono
a2
640
64.0 64.0
yes
18
36.0
—
360
100.0
Total
40
100.0 100.0
television
shows-sports
Cumulative
Frequency
Percent
‘Valid
Percent
Percent
Walid
na
24
49.0 49.0 49.0
i
26
52.0
52.0
100.0.
Total
40
100-0 100.0
television
shows-news
shows
Cumulative
Frequency
Percent
‘Valid
Parceni
Percent
Valid
na
af
54.0
540
ao
yes
23a
46.0
100.0
Totial
40
100.0 100.0
age
group
Cumulatre
Frequency
Parcenl
‘valid
Percent
Percent
Valid
lipeg
Shan
22 17
44.0
340
a49
22-29
18
36.0 36.0
70.0
30
on
more:
145
30.0
300
100.0
Tota
so
190.0
100.0
-
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 15
Case
Processing
Summary
Canes
Valid
wissing
Tota
fl
Porcant
fl
Parmant
Fill
Patcant
shaders
hee
ight)
Ine
tees
Dd
a
0.0%
50
100.0%
hours
of
stucy
parwees
*0
100
0%
o
0.0%
So
100.0%
cA
a
"
-
a
a
a
—L—
student
height
in
inches
hours
of
stedy
per
week
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 16
Figure 4: Boxplots for student height and for hours of study
