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This document provides an introduction and overview of descriptive statistics and measures of dispersion. It discusses summarizing data through numbers and histograms. It then defines common measures of dispersion like range, interquartile range, and sample standard deviation. For standard deviation, it provides the formula and explains that it averages the squared deviations from the mean divided by N-1 rather than N. It also mentions mean absolute deviation as another measure of dispersion.
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2.pdf
This document provides an introduction to descriptive statistics and measures of central tendency. It discusses how data can be summarized numerically through histograms and measures like mean, median, and mode. The mean is the average value calculated by summing all values and dividing by the number of values. The median is the middle value when data is arranged in order. The mode is the value that appears most frequently. The document explains how to determine which measure of central tendency to use depending on factors like outliers and the type of data.
Ee184405 statistika dan stokastik statistik deskriptif 2 numerik
Statistika adalah suatu bidang ilmu yang mempelajari cara-cara mengumpulkan data untuk selanjutnya dapat dideskripsikan dan diolah, kemudian melakukan induksi/inferensi dalam rangka membuat kesimpulan, agar dapat ditentukan keputusan yang akan diambil berdasarkan data yang dimiliki.
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Statistik Deskriptif adalah suatu cara menggambarkan persoalan yang berdasarkan data yang dimiliki yakni dengan cara menata data tersebut sedemikian rupa agar karakteristik data dapat dipahami dengan mudah sehingga berguna untuk keperluan selanjutnya.
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This document provides an introduction to descriptive statistics and measures of central tendency. It discusses how data can be summarized numerically through histograms and measures like mean, median, and mode. The mean is the average value calculated by summing all values and dividing by the number of values. The median is the middle value when data is arranged in order. The mode is the value that appears most frequently. The document explains how to determine which measure of central tendency to use depending on factors like outliers and the type of data.
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This document discusses texture formation processes in metals and alloys, including deformation, annealing, and transformation textures. It focuses on deformation textures and the mechanisms of slip and twinning. The key factors that determine the dominant deformation mechanism are crystal structure and stacking fault energy. Materials with high stacking fault energy deform primarily through slip, while those with low stacking fault energy experience more twinning. The document also examines differences in slip systems for BCC, FCC, and HCP crystals and how deformation leads to the development of crystallographic texture through grain rotation.
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To calculate ODFs:
- Measure multiple pole figures experimentally
- Express pole figures and ODF using spherical harmonic functions
- Use the fundamental equation relating pole figure coefficients to ODF coefficients to calculate the ODF coefficients via "pole figure inversion"
Advantages of ODF plots include:
- Represent the full 3D orientation space
- Allow identification of orientation
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q.pdf
This document discusses texture formation processes in metals and alloys, including deformation, annealing, and transformation textures. It focuses on deformation textures and the mechanisms of slip and twinning. The key factors that determine the dominant deformation mechanism are crystal structure and stacking fault energy. Materials with high stacking fault energy deform primarily through slip, while those with low stacking fault energy experience more twinning. The document also examines differences in slip systems for BCC, FCC, and HCP crystals and how deformation leads to the development of crystallographic texture through grain rotation.
p.pdf
Here are the key points about representing orientations in ODF vs pole figures:
- ODF describes the volume/number fraction of all possible orientations in 3D space using the orientation distribution function f(g).
- Pole figures only describe orientations along certain crystallographic directions (poles), not the full 3D orientation space.
To calculate ODFs:
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The document discusses different methods for describing crystallographic orientations with respect to specimen axes, specifically the Euler angle representation. It describes the Bunge method for determining Euler angles, which involves three rotations - the first about the normal direction, the second about the transformed reference direction, and the third about the new normal direction. Euler angles provide a convenient way to uniquely describe each crystal orientation. A new coordinate system can be constructed with the three Euler angles as axes, with each point representing a specific crystal orientation.
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The document discusses different methods for describing the orientation of a crystal structure with respect to a reference frame or specimen axes. It explains that at least three parameters are needed to fully describe the three-dimensional orientation of a crystal. Pole figures are described as an incomplete method that only provides information about a single crystal direction. Direct description of orientation using crystal and specimen coordinate systems and a rotation matrix relating the two is presented as a more complete method. The key steps of defining the coordinate systems, establishing the rotation relation between them, and extracting Miller
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EBSD can be used to determine various microstructural parameters such as grain size, texture, nature of grain boundaries, and strained/unstrained regions. It works by scanning an electron beam over a sample on a grid and obtaining a diffraction pattern at each point to measure crystal orientation. The resulting data can be displayed as orientation maps and processed to provide information about the microstructure like grain structure, texture, and phase identification. Pattern quality maps can reveal features like grains, grain boundaries, and surface damage. EBSD is a versatile technique for microstructural characterization of materials.
l.pdf
EBSD uses electron diffraction patterns (Kikuchi patterns) formed via backscattered electrons in an SEM to determine the crystallographic orientation of materials. The sample must be tilted to around 70 degrees to optimize the diffraction pattern resolution. Kikuchi band positions are indexed using their angles and spacings compared to reference diffraction data to determine the crystal structure and orientation at each measurement point. Automated analysis uses Hough transforms to detect band positions in Hough parameter space and calculate orientations by comparing interplanar angles to reference crystal structures. Tilting and beam conditions must be optimized to ensure high resolution diffraction patterns for accurate microstructure analysis.
k.pdf
Microtexture refers to the crystallographic orientation of individual grains within a polycrystalline material. It is determined through spatially resolved microstructural analysis techniques like electron backscatter diffraction (EBSD) in SEM or microdiffraction in TEM. These techniques produce diffraction patterns from each sampled volume, allowing the crystallographic orientation to be determined on a grain-by-grain basis. Interpreting the Kikuchi patterns generated in these techniques involves identifying the crystallographic indices of bands in the pattern and determining their relative position to deduce the orientation of each sampled volume.
j.pdf
The document discusses limitations of texture measurement procedures using X-ray diffraction and ways to overcome them. It describes issues like defocusing error that occurs at large tilt angles, limitations of the Schultz method related to divergence slit width and receiving slit width, and how to perform corrections for defocusing error, background subtraction, and normalization. It also provides example questions to test understanding of pole figures and related concepts.
i.pdf
The document discusses texture measurement using X-ray diffraction. It describes the Schulz reflection method for measuring pole figures using a 5-axis goniometer. The key steps are to first identify diffraction peaks via a Bragg scan, then fix the Bragg angle and measure intensity while rotating the sample through angles φ and ψ to map the intensity distribution on a pole figure for the chosen diffraction plane. Intensity variations reveal the texture components present in the material.
h.pdf
X-ray diffraction is the most common method for measuring macrotexture, providing information about the average texture over penetration depths of micrometers. Neutron diffraction can measure average bulk texture over centimeters by penetrating thicker samples. Electron backscatter diffraction has the best spatial resolution for local microtexture over nanometers but is limited to surface analysis. These techniques work by fixing the diffraction condition for crystal planes and rotating the sample to measure variations in intensity, which are represented as pole figures mapping orientations.
g.pdf
The document discusses the difference between bulk/macrotexture and microtexture. Bulk texture provides information about the overall orientation distribution in a material but not the spatial location of orientations. Microtexture provides information about individual grain orientations and neighbors from EBSD mapping. Bulk texture is represented by pole figures and ODFs from XRD, while microtexture uses orientation image maps from EBSD. The document also explains how pole figures are obtained from XRD by rotating the sample to satisfy Bragg's law for different crystal planes and orientations.
f.pdf
Here are the answers to the questions:
1. A pole figure is a graphical representation of the orientation of crystallites in a polycrystalline material. It shows the distribution of crystal orientations with respect to sample axes.
2. The figures shown are:
- The first figure is a (111) pole figure. It represents a brass texture with preferred orientations around the (111) poles.
- The second figure is an inverse pole figure (IPF). It represents the texture of a drawn wire, with preferred orientations around the (110) direction.
3. Pole figures represent the orientation of crystals with respect to the sample frame of reference.
4. The statement is true. In a 111 pole figure
c.pdf
Here are the answers to the questions:
1. a, b, d are correct. Grain boundary character cannot be measured using XRD.
2. d is incorrect. Crystallite sizes below 1000 Å have errors greater than 20% when using Scherrer equation to calculate size from XRD peak broadening.
3. FCC structure:
1) 2θ = 44.7°, (111)
2) 2θ = 51.8°, (200)
3) 2θ = 75.5°, (220)
4. Use Scherrer equation:
B = Kλ / t cosθ
For 10°: t = 880 Å
For 45°
a.pdf
This document provides an introduction to texture in polycrystalline materials. It defines texture as the orientations of crystals in a polycrystalline material. Texture is described using Miller indices of directions aligned with sample axes. Texture develops during processes like deformation, annealing, and phase transformations due to changes in crystal orientations. Diffraction patterns can indicate texture, with non-uniform Debye-Scherrer rings observed for textured polycrystals versus uniform rings for random orientations. Texture is important because it influences material properties and performance.
20.pdf
This document discusses two approaches to data modeling and algorithmic modeling: regression techniques and K-Nearest Neighbors (K-NN) techniques. Regression finds a function to relate independent and dependent variables, while K-NN is an algorithmic approach that relates variables based on proximity in a multi-dimensional space. K-NN is described for both regression and classification problems, where the response is predicted based on the K closest training examples in feature space.
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This document provides an introduction to performing simple and multiple regression analyses in Excel and Matlab. It discusses using Excel to conduct multiple regression with a demonstration, going beyond ordinary least squares regression with another demonstration, how to choose input variables, the impact of adding and removing variables, best subsets regression, and forward, backward, and hybrid stepwise regression approaches with another demonstration.
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The document provides an introduction to ordinary least squares (OLS) regression. It discusses how OLS regression finds the best fitting line to describe the relationship between an explanatory variable (x) and response variable (y) by minimizing the sum of the squared differences between the actual and estimated y values. The derivation shows taking the partial derivative of this sum of squared errors (SSE) function with respect to the slope (b1) and intercept (b0) and setting each equal to 0 to find the OLS estimates. Solving these equations results in formulas that calculate the OLS slope and intercept in terms of the sample means and covariances.
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This document discusses two unsupervised learning techniques: clustering and association rule mining. Clustering involves analyzing unlabeled data and grouping similar examples together to discover inherent groupings or patterns. Association rule mining aims to find relationships between variables in large datasets and extract rules to describe large portions of a dataset. Some applications of these techniques mentioned include discovering customer segments, image segmentation, finding word synonyms, and identifying topics in documents.
16.pdf
This document discusses supervised learning. Supervised learning uses labeled training data to learn a function that maps inputs to outputs. The training data contains examples of inputs along with the desired outputs, allowing an algorithm to learn by example how to map new examples. The process involves a training algorithm that learns from the labeled training data and produces a classifier, which can then be used to predict the labels of new unlabeled data. Some common applications of supervised learning mentioned include credit card fraud detection, sentiment analysis, churn prediction, and medical diagnoses.
15.pdf
This document provides an introduction to machine learning, including definitions of machine learning, different machine learning paradigms such as supervised learning, unsupervised learning, and reinforcement learning. It discusses common machine learning tasks such as classification, regression, clustering, and association. It also outlines some challenges in machine learning such as evaluating model performance, selecting the right model, dealing with issues related to data quantity and quality, and correctly representing the data.
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Information and Communication Technology in Education
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 2)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐈𝐂𝐓 𝐢𝐧 𝐞𝐝𝐮𝐜𝐚𝐭𝐢𝐨𝐧:
Students will be able to explain the role and impact of Information and Communication Technology (ICT) in education. They will understand how ICT tools, such as computers, the internet, and educational software, enhance learning and teaching processes. By exploring various ICT applications, students will recognize how these technologies facilitate access to information, improve communication, support collaboration, and enable personalized learning experiences.
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐫𝐞𝐥𝐢𝐚𝐛𝐥𝐞 𝐬𝐨𝐮𝐫𝐜𝐞𝐬 𝐨𝐧 𝐭𝐡𝐞 𝐢𝐧𝐭𝐞𝐫𝐧𝐞𝐭:
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skeleton System.pdf (skeleton system wow)
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إضغ بين إيديكم من أقوى الملازم التي صممتها
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تتميز هذهِ الملزمة بعِدة مُميزات :
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3- دقة الكتابة والصور عالية جداً جداً جداً
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5- الملزمة تشرح نفسها ب نفسها بس تكلك تعال اقراني
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واخيراً هذهِ الملزمة حلالٌ عليكم وإتمنى منكم إن تدعولي بالخير والصحة والعافية فقط
كل التوفيق زملائي وزميلاتي ، زميلكم محمد الذهبي 💊💊
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- 1. Introduction to Data Analytics Lecture: Descriptive Statistics: Summary Statistics: Measures of Dispersion NPTEL MOOC By Prof. Nandan Sudarsanam, DoMS, IIT-M and Prof. B. Ravindran, CS&E, IIT-M
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- 3. Measures of Dispersion • Data set: 3,4,3,1,2,3,9,5,6,7,4,8 • Range (Max-Min) (9-1 = 8) • Inter Quartile Range: 3rd quartile -1st quartile (75th Percentile – 25th Percentile) (6.5 – 3 = 3.5) • Sample Standard deviation 1 𝑁 − 1 (𝑥𝑖 − 𝑥)2 𝑁 𝑖=1 = 1 12 − 1 ((3 − 4.58)2 + (4 − 4.58)2 … )
- 4. Measures of Dispersion • Questions that go with Standard deviation • Why do we use the square function on the deviations? What are its implications? • Why do we work on standard deviation and not the variance? • Why do we average by dividing by N-1 and not N? • Mean absolute Deviation and its variants • Use 𝑥𝑖 − 𝑥 instead of (𝑥𝑖 − 𝑥)2