This document discusses histograms and frequency distributions for organizing and summarizing data. It defines key terms like frequency distribution, class limits, and histograms. Histograms are described as bar graphs that visually display the shape, center, and spread of data distribution. Examples are provided to demonstrate how to construct histograms and interpret their features. Different common distribution shapes like normal, skewed left, and skewed right are illustrated. The document also introduces normal quantile plots as another tool to assess normality of data distribution by examining how closely the points follow a straight line pattern.
Time Series basic concepts and ARIMA family of models. There is an associated video session along with code in github: https://github.com/bhaskatripathi/timeseries-autoregressive-models
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Chapter 2: Exploring Data with Tables and Graphs
2.2: Histograms
Time Series basic concepts and ARIMA family of models. There is an associated video session along with code in github: https://github.com/bhaskatripathi/timeseries-autoregressive-models
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Chapter 2: Exploring Data with Tables and Graphs
2.2: Histograms
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Chapter 4: Probability
4.1: Basic Concepts of Probability
This presentation includes an introduction to statistics, introduction to sampling methods, collection of data, classification and tabulation, frequency distribution, graphs and measures of central tendency.
This presentation gives you a brief idea;
-definition of frequency distribution
- types of frequency distribution
-types of charts used in the distribution
-a problem on creating types of distribution
-advantages and limitations of the distribution
Box and whisker plot is a statistical measure to show the distribution of data. It is also called as Five Number Summary box as it consists of the median, the quartiles (lower and upper) and smallest and greatest values in distribution.
The standard deviation is a measure of the spread of scores within a set of data. Usually, we are interested in the standard deviation of a population.
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Chapter 4: Probability
4.1: Basic Concepts of Probability
This presentation includes an introduction to statistics, introduction to sampling methods, collection of data, classification and tabulation, frequency distribution, graphs and measures of central tendency.
This presentation gives you a brief idea;
-definition of frequency distribution
- types of frequency distribution
-types of charts used in the distribution
-a problem on creating types of distribution
-advantages and limitations of the distribution
Box and whisker plot is a statistical measure to show the distribution of data. It is also called as Five Number Summary box as it consists of the median, the quartiles (lower and upper) and smallest and greatest values in distribution.
The standard deviation is a measure of the spread of scores within a set of data. Usually, we are interested in the standard deviation of a population.
This slideshow describes about type of data, its tabular and graphical representation by various ways. It is slideshow is useful for bio statisticians and students.
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Chapter 2: Exploring Data with Tables and Graphs
2.1: Frequency Distributions for Organizing and Summarizing Data
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Chapter 2: Exploring Data with Tables and Graphs
2.3: Graphs that Enlighten and Graphs that Deceive
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Elementary Statistics Practice Test 4
Chapter 9: Inferences about Two Samples
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Elementary Statistics Practice Test 4
Chapter 8: Hypothesis Testing
Solution to the practice test ch 10 correlation reg ch 11 gof ch12 anovaLong Beach City College
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Elementary Statistics Practice Test 5
Module 5
Chapter 10: Correlation and Regression
Chapter 11: Goodness of Fit and Contingency Tables
Chapter 12: Analysis of Variance
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Elementary Statistics Practice Test 5
Module 5
Chapter 10: Correlation and Regression
Chapter 11: Goodness of Fit and Contingency Tables
Chapter 12: Analysis of Variance
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Elementary Statistics Practice Test 4
Module 4:
Chapter 8, Hypothesis Testing
Chapter 9: Two Populations
Solution to the practice test ch 8 hypothesis testing ch 9 two populationsLong Beach City College
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Elementary Statistics Practice Test 4
Module 4:
Chapter 8, Hypothesis Testing
Chapter 9: Two Populations
Solution to the Practice Test 3A, Chapter 6 Normal Probability DistributionLong Beach City College
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Elementary Statistics Practice Test 3
Practice Test Chapter 6 (Normal Probability Distributions)
Chapter 6: Normal Probability Distributions
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Elementary Statistics Practice Test 3
Practice Test Chapter 6 (Normal Probability Distributions)
Chapter 6: Normal Probability Distributions
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Elementary Statistics Practice Test 2 Solutions
Chapter 4: Probability
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Elementary Statistics Practice Test 2
Chapter 4: Probability
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Elementary Statistics Practice Test 1
Module 1: Chapters 1-3
Chapter 1: Introduction to Statistics.
Chapter 2: Exploring Data with Tables and Graphs.
Chapter 3: Describing, Exploring, and Comparing Data.
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Elementary Statistics Practice Test 1
Module 1: Chapters 1-3
Chapter 1: Introduction to Statistics.
Chapter 2: Exploring Data with Tables and Graphs.
Chapter 3: Describing, Exploring, and Comparing Data.
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Chapter 12: Analysis of Variance
12.2: Two-Way ANOVA
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Chapter 12: Analysis of Variance
12.1: One-Way ANOVA
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Chapter 11: Goodness-of-Fit and Contingency Tables
11.2: Contingency Tables
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Chapter 11: Goodness-of-Fit and Contingency Tables
11.1: Goodness of Fit Notation
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
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2. Chapter 2:
Exploring Data with Tables and Graphs
2.1 Frequency Distributions for Organizing and
Summarizing Data
2.2 Histograms
2.3 Graphs that Enlighten and Graphs that Deceive
2.4 Scatterplots, Correlation, and Regression
2
Objectives:
1. Organize data using a frequency distribution.
2. Represent data in frequency distributions graphically using histograms, frequency polygons, and ogives.
3. Represent data using bar graphs, Pareto charts, time series graphs, and pie graphs.
4. Draw and interpret a stem and leaf plot.
5. Draw and interpret a scatter plot for a set of paired data.
3. Recall : 2.1 Frequency Distributions for Organizing and Summarizing Data
Data collected in original form is called raw data.
Frequency Distribution (or Frequency Table)
A frequency distribution is the organization of raw data in table form, using
classes and frequencies. It Shows how data are partitioned among several
categories (or classes) by listing the categories along with the number
(frequency) of data values in each of them.
Nominal- or ordinal-level data that can be placed in categories is organized in
categorical frequency distributions.
Lower class limits: The smallest numbers that can belong to each of the
different classes
Upper class limits: The largest numbers that can belong to each of the
different classes
Class boundaries: The numbers used to separate the classes, but without the
gaps created by class limits
Class midpoints: The values in the middle of the classes Each class midpoint
can be found by adding the lower class limit to the upper class limit
and dividing the sum by 2.
Class width: The difference between two consecutive lower class limits in a
frequency distribution
Procedure for Constructing a
Frequency Distribution
1. Select the number of classes,
usually between 5 and 20.
2. Calculate the class width: 𝑊 =
𝑀𝑎𝑥−𝑀𝑖𝑛
# 𝑜𝑓 𝑐𝑙𝑎𝑠𝑠𝑒𝑠
and round up
accordingly.
3. Choose the value for the first
lower class limit by using either
the minimum value or a
convenient value below the
minimum.
4. Using the first lower class limit
and class width, list the other
lower class limits.
5. List the lower class limits in a
vertical column and then
determine and enter the upper
class limits.
6. Take each individual data value
and put a tally mark in the
appropriate class. Add the tally
marks to get the frequency.
3
4. 2.2 Histograms
While a frequency distribution is a useful tool for summarizing data and
investigating the distribution of data, an even better tool is a histogram, which
is a graph that is easier to interpret than a table of numbers.
Key Concept
Histogram:
A graph consisting of bars of equal width drawn adjacent to each other (unless
there are gaps in the data)
The horizontal scale represents classes of quantitative data values, and the vertical
scale represents frequencies. The heights of the bars correspond to frequency values.
Important Uses of a Histogram
• Visually displays the shape of the distribution of the data
• Shows the location of the center of the data
• Shows the spread of the data & Identifies outliers
4
5. 5
Example 1
Construct a histogram to
represent the data for the record
high temperatures for each of
the 50 states.
Class Limits
Class
Boundaries
Frequency
100 - 104
105 - 109
110 - 114
115 - 119
120 - 124
125 - 129
130 - 134
99.5 - 104.5
104.5 - 109.5
109.5 - 114.5
114.5 - 119.5
119.5 - 124.5
124.5 - 129.5
129.5 - 134.5
2
8
18
13
7
1
1
6. Relative Frequency Histogram
Relative Frequency
Histogram has the same shape
and horizontal scale as a
histogram, but the vertical scale
is marked with relative
frequencies instead of actual
frequencies.
Time
(seconds) Frequency
75-124 11
125-174 24
175-224 10
225-274 3
275-324 2
Example 2
Relative
Frequency = f / n
11 / 50 = 0.22
24 / 50 = 0.48
10 / 50 = 0.2
3 / 50 = 0.06
2 / 50 = 0.04
Percent
Frequency
22%
24%
20%
6%
4%
6
f = 50 rf = 1
7. Common
Distribution
Shapes
7
Critical Thinking Interpreting Histograms
Explore the data by analyzing the histogram to see what can be learned about
“CVDOT”: the Center of the data, the Variation, the shape of the Distribution,
whether there are any Outliers, and Time.
8. Normal Distribution
Because this histogram is roughly
bell-shaped, we say that the data
have a normal distribution.
8
Skewness:
A distribution of data is
skewed if it is not symmetric
and extends more to one side
than to the other.
Data skewed to the right
(positively skewed) have a
longer right tail.
Data skewed to the left
(negative skewed) have a
longer left tail.
9. 9
Example 3
Given Histogram: Find the following:
1. Estimate the number of subjects
2. The width
3. Boundaries of the 1st bar
4. Explain the gap.
5. Normal?
Find the following:
1. The number of subjects 12 + 20 + 8 + 0 + 0 + 5 + 18 + 14 + 3 = 80
2. The width; 5.6 – 5.5 = 0.1 g
3. Boundaries of the 1st bar: 5.5g & 5.6g
4. The Gap: The 1st 40 quarters are from a different era than the 2nd set of 40 quarters.
5. Not Normally Distribution
Pre 1964:
90% silver + 10 % copper
Post 1964:
Copper-Nickel alloy
10. Assessing Normality with Normal Quantile Plots
Criteria for Assessing Normality with a Normal Quantile Plot
Normal Distribution: The pattern of the points in the normal quantile plot is reasonably close to a
straight line, and the points do not show some systematic pattern that is not a straight-line pattern.
Not a Normal Distribution: The population distribution is not normal if the normal quantile plot has
either or both of these two conditions:
The points do not lie reasonably close to a straight-line pattern.
The points show some systematic pattern that is not a straight-line pattern.
10
Normal Distribution: The points are
reasonably close to a straight-line pattern, and
there is no other systematic pattern that is not
a straight-line pattern.
Not a Normal Distribution: The
points do not lie reasonably close
to a straight line.
Normal Quantile Plot:
A normal quantile plot
(or normal probability
plot) is a graph of
points (x, y) where each
x value is from the
original set of sample
data, and each y value
is the corresponding z
score that is expected
from the standard
normal distribution.