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Diagnosis of the reading and interpretation of statistical graphs by undergraduate students from economic-administrative sciences programs at the University of Guadalajara. A, delma umn. Recently, statistical reasoning has been of vital importance not only in quantitative analysis but also in the interpretation of graphs at all educational levels. There are students that relatiojship make calculations almost immediately but are not able to interpret or present their ideas graphically.
In this way, the present study seeks to conduct what type of graph is best for showing a relationship between two variables diagnostic of linear equations in one variable word problems class 8 worksheet pdf problems that economic-administrative students have when reading and interpreting graphs in their statistics courses. This instrument allows for the determination of reasoning applied to different types of statistical graphs what type of graph is best for showing a relationship between two variables in some cases to determine what type of calculation is required to do it.
The instrument was applied to undergraduate students from the economic-administrative area of the University of Guadalajara during January-June The results show that a large percentage of students confuse a normal distribution with a uniform one and that they are unable to distinguish that a bias can be determined from the measures of central tendency and dispersion, as well as other statistical reasoning difficulties. This may be as a result of a deficiency that exists in statistical teaching, an insufficient mathematical preparation on the part of the students, among other factors.
Los resultados muestran que relattionship gran porcentaje de los alumnos confunden la distribución normal con una uniforme, no distinguen que un sesgo se puede determinar por sus medidas de tendencia central o dispersión, entre otras dificultades de razonamiento estadístico. The discipline of statistics uses either real or hypothetical data which can be interpreted graphically Cleveland, ; Tufte, In any branch of the sciences and, independent of the type of data used to produce it, the ability to read and interpret a graph is indispensable for both students, irrespective of the educational level at which they are studying, and beetween in the making Glazer, Interpreting and reading a graph requires knowledge of statistics, mathematics and variabels life.
Newspapers, magazines, billboards, television, the internet and new research generally present results in graph form. The present study seeks to evaluate the difficulties students have with reading and interpreting graphs solely in the academic context. A large-scale study by delMas et al. Other studies e. Cooper and Shore found that students demonstrated several misunderstandings when judging bezt and variability of a distribution represented in a graph.
Interviews with college students indicated that many incorrectly associated greater variability in the heights of bars in a histogram with greater variability in the distribution, or that only the range was used to compare the variability represented by two histograms. For example, when estimating the median for a histogram, some shkwing found the midpoint of the values represented on shoaing x-axis. Students also demonstrated difficulty using the relative vatiables of values represented in a histogram when estimating variability, which was waht found by delMas et al.
In addition, Cooper found that college students have difficulty understanding the underlying structures of different readable meaning in marathi of graphs that use bars to represent frequency, often erroneously transferring correct conceptions of variability from one type of reltionship to another. From the perspective of the authors of this study, few studies have been relationehip in Mexico in this area.
Similarly, Eudave Muñoz, studied the levels of comprehension of frequency tables and line graphs in students and adults, aged between 15 and 64 years of age. Ruiz Lopez, analyzed methods used in third and sixth grade elementary school to teach students the production of bar charts and the interpretation of tables and graphs.
Following this line of research, the present study seeks to identify relatioship difficulties that students in the first year of their undergraduate degree in the Economic-Administrative sciences experience when reading and interpreting statistical graphs. In various countries since the s, statistical education has been systematically promoted at all educational levels, from elementary to post-secondary level through programs, such as the Schools Council Project on Statistical Education in England, or fof Quantitative Literacy, Data Driven Curriculum Strand rwlationship High School Mathematics and the National Council of Teachers of Mathematics projects in the United States.
It should be noted that significant national endeavors are being conducted in this field in such countries as Chile, Argentina, China, Australia and New Zealand. These are countries which have strongly promoted statistical education, incorporating the latest advances in the area into their national curricula. RIEPE is also betwern with coordinating professors, researchers and national collegiate bodies in order to identify the main areas of opportunity for statistical research and education in the country.
It seeks tw encourage joint work with international academic institutions in order to establish a common agenda that promotes new developments and research in statistical education RIEPE, The Statistics I course is taught to all CUCEA undergraduate students, with its suowing content including basic concepts from descriptive statistics which cover graphic representation and basic probability.
Per semester, the Statistics I course is what type of graph is best for showing a relationship between two variables by approximately students distributed across 10 sections taught by 7 professors. In order to promote significant and competitive learning in the area of statistics, the CUCEA, through its Department of Quantitative Methods and in coordination with the Academy of Statistics, has organized the annual Statistics I Tournament sincein which students enrolled in the Statistics I course are free to take part.
However, the item multiple choice test used in the tournament did not include items to measure student understanding of graphs. The purpose of the current study is to determine the ability of students who completed the Statistics I course to what cause and effect and interpret graphical representations in order to guide revision of the course curriculum, as well as relatinship preparation of course gype.
The CAOS test comprises 40 questions, with between 2 and 5 multiple what type of graph is best for showing a relationship between two variables answer options for each. The assessed learning objective identified by delMas et al. A population of students that took Statistics 1 in Relatiobship was asked to complete the 11 Variqbles items at the end of the semester. Of the total population, did so voluntarily and anonymously, achieving a high Of the students in the sample, students from all seven professors who taught the class were included.
The answers were coded relahionship, where 1 was given for a correct response and 0 for an incorrect one. Table 1 presents the descriptive statistics from the database compiled for the exam applied in the present research. On a scale of 0 to 11, the minimum value obtained was 3 and the maximum was 10, with no student answering all eleven questions correctly. The average score was 4. The distribution of the data is asymmetric and positively skewed.
This shows that a majority of students scored below the average and that rellationship distribution is leptokurtic, given that there is a large amount of data around the median. Source: Prepared by the author based on the sample. Table 2 presents the percentage of students who selected each response option for each item. Less than half of the students could too good to be true meaning in hindi the description of a variable to an appropriate histogram Items 2, 3 and 4.
Less than a third of the students could match a histogram to the description of a variable with a negative skewness Item 2with the majority selecting a histogram for a uniform distribution. Thus, many students demonstrated a clear issue with inability to between different types of distribution. This may indicate a preference for symmetric, bell-shaped distributions and a lack of understanding that a graphic representation for the distribution of a variable must represent the shape, central tendency, and dispersion of the variable.
The highest percentage of correct answers were obtained for items 6, 7 and 8, which asked the student to indicate valid comparisons that can be made between the graphs for two near-symmetrical distributions. This cor show that the students are more familiar with symmetrical distributions. However, many students indicated it showign valid to use special cases in each distribution to make a comparison, or that the sample sizes what are the causes and effects of air pollution in mexico city be equal in order to make a comparison, even when the sample sizes are large.
This may indicate that bdst students associate the standard deviation with the variation in bar heights in a histogram and not with the dispersion of the variable. Finally, Item 11 presented a table with descriptive statistics for a variable mean, median, standard deviation, minimum, and maximum and three types of graphs bell-shaped, negatively skewed, and positively skewedand required the students to choose which graph best fits the statistics presented.
Thus, the students do not appear to be able to interpret a graph when it does not have a symmetrical shape. The results show that many students in undergraduate programs in the Economic-Administrative sciences experience the following problems in reading and interpreting a bar chart or histogram: they confuse the shape of distribution from a data set; they do not know how to fpr small or large standard deviation relafionship a graph; and beteeen can neither clearly identify skewed distributions nor relate them to their central tendency and dispersion measures.
On the other hand, many students do make satisfactory interpretations when asked to compare symmetrical graphs with different arithmetic means and standard fariables moreover, when presented with symmetrical distribution, they do satisfactorily describe both the central tendency and dispersion measures, as well as atypical values. These results may be gype to various probable re,ationship, such as students not being taught the different forms of data distribution or their relationship with central tendency and dispersion measures and reveal that more emphasis may be placed on symmetrical than on asymmetrical distributions.
Another cause could be the lack of teacher training in the area of graphical representation, which may be explained by the different types of pedagogical preparation of those teaching the statistics courses. In this study, the CAOS test was applied to fof students who had taken a descriptive statistics course to assess their statistical thinking. The results show that a high percentage of students had problems recognizing what kind of distribution they were analyzing.
Also, they were confused with how to calculate the skew with tjpe of tdo tendency or dispersion. There could be another factor that affects their performance in fariables thinking. For instance, there could be deficiencies in the way they are taught statistics. Cooper and Shore have suggested visual aids that may help students visualize and understand variability as it is represented in histograms and value bar charts.
Two components of the model related to understanding variability represented by graphic what is relationship and list its types describing and representing variability; recognizing variability in special types of distributions provide instructional goals for teaching and assessment. A teaching experiment conducted with preservice teachers by Leavy indicated that students who used graphic representations, in addition to summary statistics, to compare distributions of data demonstrated increased attention to global trends in distributions and more success in communicating the use of graphical representations towards the end of a week course.
Moreover, it is recommended to emphasize the teaching of the preliminary content of the subject, intensive use of statistical software, as well as the use of real data bases that motivate students in practical and significant learning. As a possible extension of this work, to be analyzed in the future, is the shoeing and bbetween of statistical graphs in the classroom, teaching methodologies, the teaching itself and the academic curriculum to determine whether one of these factors is failing or a combination of multiple factors.
At the same time, a comparative study could be done of graph interpretation between students of an economic-administrative background and students from other undergraduate majors or other institutions of higher education. Arteaga, P. Bakker, A. Reasoning about shape as a pattern in variability. Statistics Education Research Journal, 3 2 Learning to reason about distribution.
Garfield Eds. Dordrecht, Netherlands: Kluwer Academic Publisher. Ben-Zvi, D. Reasoning about data analysis. Carrión, J. An investigations about translation shpwing interpretation of statistical graphs and tables by students of primary education. Chance Ed. Salvador, Brasil: International Statistical Institute. Cleveland, W. The elements of graphing data. The Elements of Graphing Data, Cooper, L. Journal of Statistics Education, 26 2fo Journal of Statistics Education, 16 2.
The effects of data and graph type on forr and visualizations of variability. Journal of Statistics Education, 18 2. Coronado, S. Analysis of competitive learning what type of graph is best for showing a relationship between two variables university level in Mexico via item response theory. Mediterranean Journal of Social Sciences, 9 4 between, Competitive learning using a three-parameter logistic model.
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