Statistics Assignment: Analysis of Educational Data (Statistics)

This report analyzes a statistics assignment focused on educational data. It examines independent and dependent variables, measurement scales, and descriptive statistics such as measures of central tendency and dispersion. The report assesses the accuracy of boxplots, analyzes the distributional shape of histograms, and identifies the comprehension score with the most variability, discussing the implications of a large standard deviation. The report references key statistical concepts and provides a comprehensive analysis of the provided data, including the interpretation of the results, using the provided references. The assignment includes the analysis of the variables, standard deviation, and data representation.

Running head: STATISTICS FOR EDUCATIONAL DATA 1
Statistics for Educational Data
Student Name
Institution

STATISTICS FOR EDUCATIONAL DATA 2
Statistics for Educational Data
1. What are the independent and dependent variables and what is the measurement scale of
each?
 Independent variable is spatial aptitude-In this variable spatial comprehension and
ability were determined through a test known as PARC. Since these are scores,
the variable has a ratio scale.
 The dependent variable is Attitude towards instruction-Since variable measures
the degree of understanding, it has an ordinal scale.
2. Name three types of descriptive statistics that were reported in the manuscript?
 Measures of Central Tendency: The results in the manuscript reveals an average
score of 13.5 and a median of 13 achieved by Physics and chemistry students.
These are examples of measures of central tendency.
 Measures of Dispersion or Variation: The Physics and chemistry students had a
score with a standard deviation of 1.5 which is a measure of dispersion.
 Measures of Position: When measuring the spatial aptitude of students, three-
quarters of the data was over 19. Results on this variable were divided into
quartiles. This is a measure of position.
3. Review the boxplots in Figure 3. The legend to the right of the figure indicates that the
whiskers represent the standard deviation, the box represents the standard error, and the line
represents the median. Have the authors represented the elements of the boxplot correctly? If not,
what is incorrect?

STATISTICS FOR EDUCATIONAL DATA 3
NO: The center line represents the median score hence this part is correct (Holcomb,
2016). However, the whiskers represent the scores that lie outside the middle part (50%).
This part shows the scores that lie in the inter-quartile range. The upper whisker shows
the upper quartile that represents seventy-five percent of the scores. The lower part
represents the lower quartile that represents 25% of the score.
4. What is the general distributional shape (in terms of normality, Skewness, kurtosis) of the
histograms represented in Figure 6?
In general, the two curves form a fair bell shape which signifies normality. The
distributions are close to being symmetrical. However, both figures are slightly negatively
skewed (Ho & Yu, 2015). In terms of kurtosis, both figures are mesokurtic since they are close to
normality.
5. Based on the results in Table 3, which comprehension score reflected the most variability?
What are some reasons why variability differs between the different comprehension scores? Is a
large standard deviation reason to cause concern to the author? Why or why not?
In orbitals, the first option (without software) had the highest variability (s.d=1.25).
Large standard deviation should be a point of concern to the author since it is a measure of
variability. This signifies that the data points are spread far distances from the mean which is a
concern.

STATISTICS FOR EDUCATIONAL DATA 4
References
Holcomb, Z. C. (2016). Fundamentals of descriptive statistics. Routledge.
Ho, A. D., & Yu, C. C. (2015). Descriptive statistics for modern test score distributions:
Skewness, kurtosis, discreteness, and ceiling effects. Educational and Psychological
Measurement, 75(3), 365-388.