DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 2
Descriptive Statistics, Ordinal Scale and Dichotomous Variable....................................................3
D3.4.1: (a) What is the mean visualization test score?...................................................................3
D3.4.1 (b) What is the skewness statistic for math achievement test? What does this tell us?......3
D3.4.1 (c) What is the minimum score for mosaic pattern test? How can that be?........................3
D3.4.2. (a) For which variables that we called scale, is the skewness statistic more than 1.00 or
less than –1.00?................................................................................................................................4
D3.4.2. (b) Why is the answer important?.......................................................................................4
D3.4.2. (c) Does this agree with the boxplot for Output 4.2? Explain............................................4
D3.4.3. (a) How many participants have missing data?..................................................................4
D3.4.3. (b) What percent of students have a valid (non-missing) motivation scale or competence
scale score?......................................................................................................................................4
D3.4.3. (c) Can you tell from Outputs 4.1 and 4.2b how many are missing both motivation scale
and competence scale scores? Explain............................................................................................5
D3.4.4. (a) Can you interpret the means? Explain...........................................................................5
D3.4.4. (b) How many participants are there altogether?................................................................5
D3.4.4. (c) How many have complete data (nothing missing)?.......................................................6
D3.4.4. (d) What percent are in the fast track?................................................................................6
D3.4.4. (e) What percent took algebra 1 in H.S.?............................................................................6
D3.4.5. (a) 9.6% of what group are Asian-Americans?...................................................................7
D3.4.5. (b) What percent of students have visualization 2 scores of 6?..........................................7
D3.4.5. (c) What percent had such scores of 6 or less?...................................................................7
References........................................................................................................................................8
Descriptive Statistics, Ordinal Scale and Dichotomous Variable
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 3
D3.4.1: (a) What is the mean visualization test score?
Preface 4.1b contains descriptive information for variables first categorized as Scale.
5.2433 is the mean score on the assessments of visualization.
D3.4.1 (b) What is the skewness statistic for math achievement test? What does this tell
us?
Output 4.1b provides descriptive information about the variables first designated as
Scale. The skewness of the arithmetic proficiency examination is 0.044. One tail of a frequency
distribution is skewed when it is much longer than the other. A skewed curve is easy to spot
because it is very different in size from the median and mean values (Morgan et al., 2020). Zero
is the skewed value of a curve characterized by perfect symmetry. When compared to the normal
distribution's skewness value of zero, the variable's skewness value of 0.044 indicates a slight
skewness. According to Morgan et al. (2020), the data set containing the value 0.044 adheres to a
distribution that is normal.
D3.4.1 (c) What is the minimum score for mosaic pattern test? How can that be?
Output 4.1b consists of descriptions of variables that have scale labels. -4.0 is the
minimal attainable result on the examination for mosaic patterns. When an error occurs, the most
efficient approach to detecting it is to consult the codebook or analyze the utilized data set. An
analysis of the codebook indicates that visualizations are assessed on a scale of -4.0 to 16. The
visualization score of -4.0 signifies that at least one participant attained the lowest possible score.
The reduced level of performance can be attributed to inaccurate speculation concerning the
inquiries (Morgan et al., 2020).
D3.4.2. (a) For which variables that we called scale, is the skewness statistic more than
1.00 or less than –1.00?
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 4
In consequence 4.1b, the variable denoted as the "competence scale" demonstrates
skewness values exceeding 1.00 and falling below -1.00, respectively. The skew of this data is
negative.
D3.4.2. (b) Why is the answer important?
The dataset exhibits a negative skewness in the "competence scale" variable, signifying a
lack of symmetry and inequality among the mode, mean, and median values. Skewness refers to
a circumstance wherein the curve's distribution fails to conform to the characteristics of
symmetry or normality (Morgan et al., 2020).
D3.4.2. (c) Does this agree with the boxplot for Output 4.2? Explain.
The boxplots in Output 4.2b depict the scales of competency and motivation. Attributing
an asymmetrical box plot to the median of the skewed data sets, the box is divided in half
equally. When the longer side of the box is situated beyond or to the right of the median, the data
are said to have a right skew. As is the case in our study (Morgan et al., 2020), the data are
deemed to have a negative or left skew if the longer segment is asymmetrical to the left or lies
below the median.
D3.4.3. (a) How many participants have missing data?
To represent the Competence and Motivation Scales, boxplots are constructed using
output 4.2b. The case processing report indicates that in four instances, the motivation and
competence scales are inadequate.
D3.4.3. (b) What percent of students have a valid (non-missing) motivation scale or
competence scale score?
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 5
Given the boxplots for these variables in output 4.2b, it is possible to infer that 94.7% of
students have valid scores on the motivation or competence scales. This indicates that no student
has an incomplete score on either of the two scales.
D3.4.3. (c) Can you tell from Outputs 4.1 and 4.2b how many are missing both
motivation scale and competence scale scores? Explain.
In output 4.1b, the population size is 75, the competency level is 73, and the motivation
level is also 73. In both outputs, two scores are absent. In output 4.2b, both the competence and
motivation scales are assigned a rating of 71. As a result, no individual is deficient in either
competence or desire scores. This is because four individuals are deficient in at least one of the
scores, while two are missing both (Morgan et al., 2020).
D3.4.4. (a) Can you interpret the means? Explain.
By applying descriptive statistics to dichotomous variables, the output, denoted as 4.4, is
analyzed. When analyzing dichotomous variables, the percentage of individuals belonging to
each of the two categories can be calculated using the mean. As an illustration, the academic
track exhibits an average score of 0.55, signifying that 55% of the participants were classified as
1 (regular track) and 45% as 0 (fast track). As the average number of students enrolled in the
conventional track exceeds that of the fast track (mean > 0.50), this difference between the two
tracks is evident. According to Morgan et al. (2020), dividing the data by the binary variable may
be impracticable when the mean value is close to 1 or 0. This is because of the significant
difference in participant numbers between the two groups, which contradicts the principles
taught in high school algebra and calculus.
D3.4.4. (b) How many participants are there altogether?
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 6
The determination that 75 participants comprise the population or N, is evident from the
results provided in the 4.4 output, Descriptives for Dichotomous Variables.
D3.4.4. (c) How many have complete data (nothing missing)?
The finding that each variable has a population size of 75, as shown in result 4.4, denotes
the absence of missing values and the availability of comprehensive information.
D3.4.4. (d) What percent are in the fast track?
Regarding academic courses, the average initial value of the variable is 0.55. The fast
track was rated as 0 by 45 percent of the participants, while 55 percent were rated as 1.
According to the calculated mean value of 0.79, 79% of high school algebra 1 pupils were
enrolled in the traditional track (categorized as 1). Conversely, 21% were on the fast track
(categorized as 0). 2.47 is the mean grade in Algebra 2 for secondary education. According to
these statistics, 53% of participants were on the fast track (0), while 47% were on the regular
track (1). A statistical measure of the average integer value is the definition of "mean" in high
school geometry. 48% of participants were on the regular track (track 1), while 52% were on the
fast track (track 0), according to the analytics. In high school trigonometry, the mean value was
0.27%; therefore, 27% of the population was classified as 1 (regular track), whereas 73% was
classified as 0. In calculus, secondary students acquire knowledge of mean concepts. 73% (fast
track) and 27% (regular track) of the participants were 0s, according to the data. Math in college.
41% of individuals were classified as 1 (regular track) and 59% as 0 (regular track) according to
the calculated mean value of 0.41.
D3.4.4. (e) What percent took algebra 1 in H.S.?
It is necessary to compute the mean and subsequently multiply it by the total number of
students to ascertain the proportion of students who were enrolled in algebra 1 throughout high
DESCRIPTIVE STATISTICS, ORDINAL SCALE AND DICHOTOMOUS VARIABLE 7
school. Divide 7 (representing the number of variables) by 75 (representing the population), then
multiply the result by 100% to obtain the percentage. Enrollment in algebra 1 comprises 11% of
the total high school student body.
D3.4.5. (a) 9.6% of what group are Asian-Americans?
The chart displays "valid" and "missing" when 4.5 is in use. The proportion of survey
participants who provided a valid response to this query and self-identified as Asian-Americans
is 9.6%.
D3.4.5. (b) What percent of students have visualization 2 scores of 6?
Given the absence of any missing values in this field, the valid percent and the percent
become synonymous when output 4.5 is utilized. A proportion of 5.3% is present.
D3.4.5. (c) What percent had such scores of 6 or less?
Using the cumulative percent column from output 4.5, which displays 70.7% of the total,
it is possible to determine this information.
