Browsing by Author "Rashid, Mamunur"

Now showing 1 - 10 of 15
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    Depicting Bivariate Relationship with a Gaussian Ellipse
    (2021) Sarkar, Jyotirmoy; Rashid, Mamunur; Mathematical Sciences, School of Science
    For data on two continuous variables, how should one depict the summary statistics (means, SDs, correlation coefficient, coefficient of determination, regression lines) so that their values can be read off easily from the depiction and potential outliers can be flagged also? We propose the Gaussian covariance ellipse as an answer that will benefit all users of statistics.
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    Estimating the Parameters of a Simple Linear Regression Model Without Using Differential Calculus
    (Susan Rivers' Cultural Institute, 2022-10-03) Sarkar, Jyotirmoy; Rashid, Mamunur; Mathematical Sciences, School of Science
    To estimate the parameters of a simple linear regression model, students who already know calculus can minimize the total squared deviations by setting its first-order partial derivatives to zero and solving simultaneously. For students who do not know calculus, most teachers/textbooks simply state the formulas without justifying them. Students accept the formulas on faith; and for given data, they evaluate the estimates using a calculator or a statistical software. In this paper, we justify the formulas without invoking calculus. We hope the users of statistics will benefit from our proposed justifications.
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    Guess the Mean: Which Method is Better?
    (Depauw, 2020-08) Rashid, Mamunur; Sarkar, Jyotirmoy; Mathematical Sciences, School of Science
    The mean of a set of numbers may be guessed in one of two ways: (1) as a fulcrum placed under the dot plot; or (2) as a vertical line that equalizes areas of two regions bounded by the step plot (also known as the empirical cumulative distribution function). Which of these two methods is better? We design, conduct and analyze a statistical experiment to address this question. While our findings support better performance by the latter method at the aggregate level, each individual user may respond differently to the question. We hope all users will learn both methods and determine for themselves which method they are better at. We also hope educators will empower their students by including both methods in their syllabi.
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    Have You Seen the Standard Deviation?
    (NepJOL, 2019) Sarkar, Jyotirmoy; Rashid, Mamunur; Mathematical Sciences, School of Science
    Background: Sarkar and Rashid (2016a) introduced a geometric way to visualize the mean based on either the empirical cumulative distribution function of raw data, or the cumulative histogram of tabular data. Objective: Here, we extend the geometric method to visualize measures of spread such as the mean deviation, the root mean squared deviation and the standard deviation of similar data. Materials and Methods: We utilized elementary high school geometric method and the graph of a quadratic transformation. Results: We obtain concrete depictions of various measures of spread. Conclusion: We anticipate such visualizations will help readers understand, distinguish and remember these concepts.
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    IVY plots and Gaussian interval plots
    (Wiley, 2021) Sarkar, Jyotirmoy; Rashid, Mamunur; Mathematical Sciences, School of Science
    While a dot plot depicts data on a quantitative variable without distortion, a boxplot shows only the five-number summary. For large data, to aid in counting, we propose an IVY plot as a companion to a dot plot. Also, for large data, if the variable is approximately normally distributed, as a companion to a boxplot, we propose a Gaussian interval plot that depicts the five-number summary, the mean, the SD, the sample size, and the counts of outliers. We hope these enhanced visualizations will add value to the commonly used methods.
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    Mathematical Musings on the External Anatomy of the Novel Corona Virus Part 1: The Overall Shape of the n-CoV
    (Springer, 2022) Sarkar, Jyotirmoy; Rashid, Mamunur; Mathematical Sciences, School of Science
    What is the shape of the novel coronavirus which has turned our world upside down? Even though under a microscope it looks dull, unattractive, and even disgusting, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathematician contribute to this effort? We take a purist’s point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from reality but still obeying the rules of mathematics, anyone can enjoy this ethereal beauty of the mind’s creation, beckoning others to join in the pleasure. Our musings are split into four parts. We fondly hope that while readers await the future parts to appear, they will indulge in their own musings, tell others about them, and propagate the good virus of mathematical thinking.
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    Mathematical Musings on the External Anatomy of the Novel Corona Virus Part 4: Models of n-Cov
    (Springer, 2022) Sarkar, Jyotirmoy; Rashid, Mamunur; Mathematical Sciences, School of Science
    What is the shape of the novel coronavirus (n-CoV) which has turned our world upside down? Even though under a microscope, it looks dull, unattractive, and even disgusting, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathematician contribute to this effort? We take a purist’s point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from reality but still constrained by the rules of mathematics, anyone can enjoy this ethereal beauty of the mind’s creation, beckoning others to join in the pleasure. Our musings end with this Part 4. We fondly hope readers have benefited from our suggestion that they indulge in their own musings, tell others about them, and propagate the good virus of mathematical thinking.
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    Mathematical Musings on the External Anatomy of the Novel Corona Virus, Part 3: Spherical Triangles
    (Springer Nature, 2022) Sarkar, Jyotirmoy; Rashid, Mamunur; Mathematical Sciences, School of Science
    What is the shape of the novel coronavirus (n-CoV) which has turned our world upside down? Even though under a microscope, it looks dull, unattractive, and even disgusting, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathematician contribute to this effort? We take a purist’s point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from reality but still constrained by the rules of mathematics, anyone can enjoy this ethereal beauty of the mind’s creation, beckoning others to join in the pleasure. Our musings are split into four parts. We fondly hope while readers wait for the future parts to appear, they will indulge in their own musings, tell others about them, and propagate the good virus of mathematical thinking.
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    Mathematical Musings on the External Anatomy of the Novel Coronavirus Part 2: Chasing After Quasi-Symmetry
    (Springer, 2022) Sarkar, Jyotirmoy; Rashid, Mamunur; Mathematical Sciences, School of Science
    What is the shape of the novel Coronavirus which has turned our world upside down? Even though it looks dull, unattractive, and even disgusting under a microscope, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathematician contribute to this effort? We take a purist’s point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from reality but still constrained by the rules of mathematics, anyone can enjoy this ethereal beauty of the mind’s creation, beckoning others to join in the pleasure. Our musings are split into four parts. We fondly hope while readers wait for the future parts to appear, they will indulge in their own musings, tell others about them, and propagate the good virus of mathematical thinking.
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    Shutter Plot: A Visual Display of Summary Statistics over a Scatter Plot
    (Univ. of Rajshahi, 2020-10) Sarkar, Jyotirmoy; Rashid, Mamunur; Mathematical Sciences, School of Science
    While a dot plot of one variable is naturally extended to a scatter plot of two variables, how should a box plot of one variable be extended to two variables? We propose a shutter plot that depicts the means and the standard deviations of both variables, the two regression lines and the coefficients of correlation and determination over a scatter plot. By showing all relevant summary statistics simultaneously, a shutter plot captures all aspects of a linear relationship, including flagging potential outliers, and helps the readers make good decisions.