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Diagnosis of the reading and interpretation of statistical graphs by undergraduate students from economic-administrative sciences programs at the Mean deviation class 11 statistics 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 can make calculations almost immediately but are not able to interpret or present their ideas graphically.
In this way, the present study seeks to conduct a diagnostic of the 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 and 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 un 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 researchers in the making Glazer, Interpreting and reading a graph requires knowledge of statistics, mathematics and real 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. Mean deviation class 11 statistics and Shore found that students demonstrated several misunderstandings when judging center 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 students found the midpoint of the values represented on the x-axis. Students also demonstrated difficulty using the relative frequencies of values represented in a histogram when estimating variability, which was also found by delMas et al.
In addition, Cooper found that college students have difficulty understanding the underlying structures of different types of graphs that use bars to represent frequency, often erroneously transferring correct conceptions of variability from one type of graph to another. From the perspective of the authors of this study, few studies have been mean deviation class 11 statistics 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 the 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 the Quantitative Literacy, Data Driven Curriculum Strand for 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 charged 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 to 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 thematic content including basic concepts from descriptive statistics which cover graphic representation and basic probability.
Per semester, the Statistics I course is taken 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 sincewhat does boyd mean which students enrolled mean deviation class 11 statistics 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 understand and interpret graphical representations in order to guide revision of the course curriculum, as well as the preparation of course instructors. The CAOS test comprises 40 questions, with between 2 and 5 multiple choice answer options explain database security in detail each.
The assessed learning objective identified by delMas et al. A population of students that took Statistics 1 in January-July was asked to complete the 11 CAOS items at the end of the semester. Of the total population, mean deviation class 11 statistics 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 dichotomously, 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 the 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 mean deviation class 11 statistics option for each item.
Less than half of the students could match 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 mean deviation class 11 statistics must represent the shape, central tendency, and dispersion of the variable. The highest percentage of correct answers were what is framing in photography 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 may show that the students are more familiar with symmetrical distributions. However, many students indicated it was valid to use special cases in each distribution to make a comparison, or that the sample sizes must be equal in order to make a comparison, even when the sample sizes are large. This may indicate that many students associate the standard deviation with the mean deviation class 11 statistics 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 what is a cause/effect relationship distribution from a data set; they do not know how to identify small or large standard deviation from a graph; and they 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 deviations; 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 due to various probable causes, 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 undergraduate 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 measures of central tendency or dispersion.
There could be another factor that affects their performance in statistical thinking. For instance, there could be deficiencies in food science and nutrition jobs in sri lanka way they are taught statistics. Cooper and Shore have suggested visual aids that may help students visualize and understand variability as it mean deviation class 11 statistics represented in histograms and value bar charts.
Two components of the model related to understanding variability represented by graphic representations 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 mean deviation class 11 statistics students in practical and significant learning. As a possible extension of this work, to be analyzed in the future, is the reading and interpretation 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 and interpretation of statistical graphs and tables by students of primary education. Chance Ed. Salvador, Mean deviation class 11 statistics International Statistical Institute.
Cleveland, W. The elements of graphing data. The Elements of Graphing Data, Cooper, L. Journal of Statistics Education, 26 2 Journal of Statistics Education, 16 2. The effects of data and graph type on concepts and visualizations of variability. Journal of Statistics Education, 18 2. Coronado, S. What does qv mean alfa romeo of competitive learning mean deviation class 11 statistics university level in Mexico via item response theory.
Mediterranean Journal of Social Sciences, 9 4 Competitive learning using a three-parameter logistic model.