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This document provides an overview of different types of variables and methods for summarizing clinical data, including descriptive statistics. It discusses categorical variables like gender and ordinal variables like disease staging. For continuous variables it explains measures of central tendency like mean, median and mode, and measures of variation like range, standard deviation, and interquartile range. Graphs for summarizing univariate data are also covered, such as bar charts for categorical variables and histograms and box plots for continuous variables.

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Ds vs Is discuss 3.1

This document discusses descriptive and inferential statistics. Descriptive statistics summarize and organize data through frequency distributions, graphs, and summary statistics like the mean, median, mode, variance, and standard deviation. Inferential statistics allow generalization from samples to populations through hypothesis testing, where the null hypothesis is tested against the alternative hypothesis. Type I and type II errors are possible, and significance tests control the probability of type I errors through the alpha level while power analysis aims to reduce type II errors. Common inferential tests mentioned include t-tests, ANOVA, and meta-analysis.

Normal distribution

This document provides information about the normal distribution and related statistical concepts. It begins with learning objectives and definitions of key terms like the normal distribution formula and how the mean and standard deviation affect the shape of the distribution. It then discusses properties of the normal distribution like symmetry and how it extends infinitely in both directions. The next sections cover areas under the normal curve and how to calculate probabilities using the standard normal distribution table. Later sections explain how to convert variables to standard scores using z-scores and the concepts of skewness and sampling distributions. Examples and exercises are provided throughout to illustrate calculating probabilities and percentiles for the normal distribution.

introduction to biostat, standard deviation and variance

The document discusses standard deviation and variance in statistics. It defines standard deviation as a measure of how far data points are spread from the mean. A lower standard deviation indicates data points are close to the mean, while a higher standard deviation indicates data points are more spread out. It provides the formula for calculating standard deviation and explains the steps. Variance is defined as the average of the squared deviations from the mean and the formula is given. Grouped data and calculating variance from grouped data is also covered. Applications of standard deviation are listed.

Central Tendency

Central tendency refers to statistical measures that identify a central or typical value for a data set. The three main measures are the mean, median, and mode. The mean is the average value calculated by dividing the sum of all values by the number of values. The median is the middle value of the data set when sorted. The mode is the most frequently occurring value. Different measures are better suited depending on the type of data and how it is distributed.

Biostatistics i

The document discusses concepts related to measurement, scaling, and data analysis in statistics. It defines measurement as assigning numbers or symbols to characteristics of interest according to set rules. There are different types of scales (nominal, ordinal, interval, ratio) that provide varying levels of information based on their scaling properties of description, order, distance, and origin. The document also discusses topics like descriptive statistics, types of data collection and processing, methods of data presentation, and measures of relationships between variables like correlation and regression.

Variability

The document discusses variability and measures of variability. It defines variability as a quantitative measure of how spread out or clustered scores are in a distribution. The standard deviation is introduced as the most commonly used measure of variability, as it takes into account all scores in the distribution and provides the average distance of scores from the mean. Properties of the standard deviation are examined, such as how it does not change when a constant is added to all scores but does change when all scores are multiplied by a constant.

Unit iii measures of dispersion (2)

Measures of dispersion describe how similar or spread out scores in a data set are. The three main measures are:
1) The range, which is the difference between the highest and lowest scores.
2) The semi-interquartile range, which is the difference between the first and third quartiles divided by two.
3) Variance and standard deviation, which measure how far scores deviate from the mean on average, with larger values indicating more spread out data. Variance is the average of the squared deviations from the mean.

Measures of-central-tendency-dispersion

This document discusses measures of central tendency (mean, median, mode) and measures of dispersion (range, standard deviation). It explains how to calculate each measure and their strengths and weaknesses. For example, the mean is more sensitive than the median but can be skewed by outliers, while the median is not affected by outliers but is less sensitive. The document also provides examples of calculating and interpreting the mean, range, and standard deviation using sample data.

Ds vs Is discuss 3.1

This document discusses descriptive and inferential statistics. Descriptive statistics summarize and organize data through frequency distributions, graphs, and summary statistics like the mean, median, mode, variance, and standard deviation. Inferential statistics allow generalization from samples to populations through hypothesis testing, where the null hypothesis is tested against the alternative hypothesis. Type I and type II errors are possible, and significance tests control the probability of type I errors through the alpha level while power analysis aims to reduce type II errors. Common inferential tests mentioned include t-tests, ANOVA, and meta-analysis.

Normal distribution

This document provides information about the normal distribution and related statistical concepts. It begins with learning objectives and definitions of key terms like the normal distribution formula and how the mean and standard deviation affect the shape of the distribution. It then discusses properties of the normal distribution like symmetry and how it extends infinitely in both directions. The next sections cover areas under the normal curve and how to calculate probabilities using the standard normal distribution table. Later sections explain how to convert variables to standard scores using z-scores and the concepts of skewness and sampling distributions. Examples and exercises are provided throughout to illustrate calculating probabilities and percentiles for the normal distribution.

introduction to biostat, standard deviation and variance

The document discusses standard deviation and variance in statistics. It defines standard deviation as a measure of how far data points are spread from the mean. A lower standard deviation indicates data points are close to the mean, while a higher standard deviation indicates data points are more spread out. It provides the formula for calculating standard deviation and explains the steps. Variance is defined as the average of the squared deviations from the mean and the formula is given. Grouped data and calculating variance from grouped data is also covered. Applications of standard deviation are listed.

Central Tendency

Central tendency refers to statistical measures that identify a central or typical value for a data set. The three main measures are the mean, median, and mode. The mean is the average value calculated by dividing the sum of all values by the number of values. The median is the middle value of the data set when sorted. The mode is the most frequently occurring value. Different measures are better suited depending on the type of data and how it is distributed.

Biostatistics i

The document discusses concepts related to measurement, scaling, and data analysis in statistics. It defines measurement as assigning numbers or symbols to characteristics of interest according to set rules. There are different types of scales (nominal, ordinal, interval, ratio) that provide varying levels of information based on their scaling properties of description, order, distance, and origin. The document also discusses topics like descriptive statistics, types of data collection and processing, methods of data presentation, and measures of relationships between variables like correlation and regression.

Variability

The document discusses variability and measures of variability. It defines variability as a quantitative measure of how spread out or clustered scores are in a distribution. The standard deviation is introduced as the most commonly used measure of variability, as it takes into account all scores in the distribution and provides the average distance of scores from the mean. Properties of the standard deviation are examined, such as how it does not change when a constant is added to all scores but does change when all scores are multiplied by a constant.

Unit iii measures of dispersion (2)

Measures of dispersion describe how similar or spread out scores in a data set are. The three main measures are:
1) The range, which is the difference between the highest and lowest scores.
2) The semi-interquartile range, which is the difference between the first and third quartiles divided by two.
3) Variance and standard deviation, which measure how far scores deviate from the mean on average, with larger values indicating more spread out data. Variance is the average of the squared deviations from the mean.

Measures of-central-tendency-dispersion

This document discusses measures of central tendency (mean, median, mode) and measures of dispersion (range, standard deviation). It explains how to calculate each measure and their strengths and weaknesses. For example, the mean is more sensitive than the median but can be skewed by outliers, while the median is not affected by outliers but is less sensitive. The document also provides examples of calculating and interpreting the mean, range, and standard deviation using sample data.

Chapter 022

This document discusses descriptive statistics which are used to describe characteristics of a sample dataset. It covers topics such as frequency distributions, measures of central tendency, measures of dispersion, the normal curve, z-scores, sampling error, confidence intervals, and degrees of freedom. Descriptive statistics are used to initially describe variables in quantitative research and for descriptive research purposes.

Some study materials

The document presents a case study where Lisa wants to open a beauty store and needs data to support her belief that women in her local area spend more than the national average of $59 every 3 months on fragrance products. Lisa takes a random sample of 25 women in her area and finds the sample mean is $68.10 with a standard deviation of $14.46. She conducts a one-sample t-test to test if the population mean is greater than $59. The test statistic is 3.1484 with a p-value of 0.0021, which is less than the significance level of 0.05. Therefore, there is sufficient evidence to conclude that the population mean is indeed greater than $

Seminar SPSS di UM

This document summarizes an SPSS workshop held on September 6-7, 2014 at the Faculty of Science, UM. It discusses various SPSS procedures like entering and cleaning data, checking for missing values, frequencies, descriptive statistics, reliability analysis, factor analysis, t-tests, ANOVA, and linear regression. Frequency tables are presented to analyze gender distribution and responses to motivation questions. Reliability analysis and factor analysis are conducted to assess scales. T-tests are used to compare depression, satisfaction, productivity, supervisor support, and coworker support between groups. ANOVA tests for differences in these variables between multiple ethnic groups.

Chapter3

This document provides examples and explanations of various graphical methods for describing data, including frequency distributions, bar charts, pie charts, stem-and-leaf diagrams, histograms, and cumulative relative frequency plots. It demonstrates how to construct these graphs using sample data on student weights, grades, ages, and other examples. The goal is to help readers understand different ways to visually represent data distributions and patterns.

Normal distribution

The document discusses standard deviation and the normal distribution. Some key points:
- Standard deviation is a measure of how spread out values are from the mean. It is the square root of the variance.
- For a normal distribution, approximately 68% of values fall within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99% within 3 standard deviations.
- The normal distribution is the most common continuous probability distribution and is important because many variables tend toward a normal distribution as the number of trials increases. It is used in statistical quality control.

Measure of dispersion part II ( Standard Deviation, variance, coefficient of ...

This tutorial gives the detailed explanation measure of dispersion part II (standard deviation, properties of standard deviation, variance, and coefficient of variation). It also explains why std. deviation is used widely in place of variance. This tutorial also teaches the MS excel commands of calculation in excel.

Frequency Measures for Healthcare Professioanls

Frequency distributions summarize data by grouping values of a variable and counting the number of observations in each group. This document discusses measures used to describe frequency distributions, including measures of central tendency (mode, median, mean) and measures of variability. The mode is the most frequent value, median is the middle value, and mean averages all values. These measures summarize the central or typical value in a data set.

Hcai 5220 lecture notes on campus sessions fall 11(2)

This chapter discusses descriptive statistics such as measures of central tendency (mean, median, mode), measures of variation (range, variance, standard deviation, coefficient of variation), and the shape of distributions (skewness). It also covers the normal distribution and how to calculate probabilities using the normal distribution. Key points include:
1) The mean, median, and mode are measures of central tendency while the range, variance, standard deviation, and coefficient of variation measure the spread or variation of data.
2) The normal distribution is a bell-shaped symmetric distribution that is useful in inferential statistics.
3) Probabilities using the normal distribution can be calculated by transforming the data into standard normal variables (Z

Measures of dispersion

The document discusses various measures of central tendency, dispersion, and shape used to describe data numerically. It defines terms like mean, median, mode, variance, standard deviation, coefficient of variation, range, interquartile range, skewness, and quartiles. It provides formulas and examples of how to calculate these measures from data sets. The document also discusses concepts like normal distribution, empirical rule, and how measures of central tendency and dispersion do not provide information about the shape or symmetry of a distribution.

Normal curve

The document discusses the normal curve and its key properties. A normal curve is a bell-shaped distribution that is symmetrical around the mean value, with half of the data falling above and half below the mean. The standard deviation measures how spread out the data is from the mean. In a normal distribution, 68% of the data lies within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations, following the 68-95-99.7 rule.

Measures of Dispersion

This pused to find measures of dispersion.pt tells us what dispersion is, need of dispersion and the different methods

Measures of central tendency and dispersion

The document discusses various measures of central tendency and dispersion used in statistical analysis. It defines measures of central tendency like arithmetic mean, median and mode, and provides their formulas and properties. It also discusses measures of dispersion such as range, mean deviation, standard deviation, variance and their characteristics. The document provides examples and steps to calculate various averages and measures of dispersion for a given data set.

State presentation2

This document summarizes various statistical measures used to analyze and describe data distributions, including measures of central tendency (mean, median, mode), dispersion (range, standard deviation, variance), skewness, and kurtosis. It provides formulas and methods for calculating each measure along with interpretations of the results. Measures of central tendency provide a single value to represent the center of the data set. Measures of dispersion describe how spread out or varied the data values are. Skewness and kurtosis measure the symmetry and peakedness of distributions compared to the normal curve.

02a one sample_t-test

The document discusses a one-sample t-test used to compare sample data to a standard value. It provides an example comparing intelligence scores of university students to the average score of 100. The sample of 6 students had a mean of 120. Running a one-tailed t-test in SPSS, the results showed the mean score was significantly higher than 100 with t(5)=3.15, p=.02. This allows the inference that the population mean intelligence at the university is greater than the standard score of 100.

The Normal distribution

The document discusses the normal distribution and related concepts. It describes how normal distributions can vary in their mean and standard deviation. It then discusses key features of normal distributions including that they are symmetric, have equal mean, median and mode, and are denser in the center than the tails. Finally, it discusses related statistical concepts like kurtosis and skewness, describing how kurtosis measures the thickness of a distribution's tails and how skewness measures a distribution's asymmetry.

Chisquare

Chi-square is a non-parametric test used to compare observed data with expected data. It can test goodness of fit, independence of attributes, and homogeneity. The document provides an introduction to chi-square terms and calculations including contingency tables, expected and observed frequencies, degrees of freedom, and test steps. Examples demonstrate applying chi-square to test the effectiveness of chloroquine and inoculation. Both examples find the null hypothesis of no effect can be rejected, indicating the treatments were effective.

Descriptive Statistics Part II: Graphical Description

The document provides information on descriptive statistics and graphical descriptions of data, including bar charts, pie charts, histograms, and cumulative frequency distributions. It discusses how to construct these various graphs using Excel and includes examples and questions to describe and interpret the graphs. Key information that can be obtained from these graphs includes the mode, range, percentages of observations within certain classes or below/above certain values, and comparing values across categories.

3.2 measures of variation

This document discusses measures of variation used to assess how far data points are from the average or mean. It defines key terms like range, variance, and standard deviation. Variance measures the mathematical dispersion of data relative to the mean, while standard deviation gives a value in the original units of measurement, making it easier to interpret. Formulas are provided for calculating sample variance and standard deviation versus population variance and standard deviation. Chebyshev's Theorem is introduced, stating that a certain minimum percentage of data must fall within a specified number of standard deviations of the mean. An example applies these concepts.

Statistics for dummies

This document provides an overview of key statistical concepts including:
1. The average (arithmetic mean) is calculated by summing all values and dividing by the number of samples.
2. The median is the middle value of a data set when values are sorted from lowest to highest.
3. The 90th percentile represents the value where 90% of values are below it.
4. Standard deviation measures how spread out values are from the average and 68% of values fall within one standard deviation of the average in a normal distribution.

Measures of dispersion

Measures of Dispersion: Absolute and Relative Measures of Dispersion, their computation & properties.

DescriptiveStatistics.pdf

This document provides an outline and overview of descriptive statistics. It discusses the key concepts including:
- Visualizing and understanding data through graphs and charts
- Measures of central tendency like mean, median, and mode
- Measures of spread like range, standard deviation, and interquartile range
- Different types of distributions like symmetrical, skewed, and their properties
- Levels of measurement for variables and appropriate statistics for each level
The document serves as an introduction to descriptive statistics, the goals of which are to summarize key characteristics of data through numerical and visual methods.

Statistics 3, 4

This document discusses measures of central tendency and variation for numerical data. It defines and provides formulas for the mean, median, mode, range, variance, standard deviation, and coefficient of variation. Quartiles and interquartile range are introduced as measures of spread less influenced by outliers. The relationship between these measures and the shape of a distribution are also covered at a high level.

Chapter 022

This document discusses descriptive statistics which are used to describe characteristics of a sample dataset. It covers topics such as frequency distributions, measures of central tendency, measures of dispersion, the normal curve, z-scores, sampling error, confidence intervals, and degrees of freedom. Descriptive statistics are used to initially describe variables in quantitative research and for descriptive research purposes.

Some study materials

The document presents a case study where Lisa wants to open a beauty store and needs data to support her belief that women in her local area spend more than the national average of $59 every 3 months on fragrance products. Lisa takes a random sample of 25 women in her area and finds the sample mean is $68.10 with a standard deviation of $14.46. She conducts a one-sample t-test to test if the population mean is greater than $59. The test statistic is 3.1484 with a p-value of 0.0021, which is less than the significance level of 0.05. Therefore, there is sufficient evidence to conclude that the population mean is indeed greater than $

Seminar SPSS di UM

This document summarizes an SPSS workshop held on September 6-7, 2014 at the Faculty of Science, UM. It discusses various SPSS procedures like entering and cleaning data, checking for missing values, frequencies, descriptive statistics, reliability analysis, factor analysis, t-tests, ANOVA, and linear regression. Frequency tables are presented to analyze gender distribution and responses to motivation questions. Reliability analysis and factor analysis are conducted to assess scales. T-tests are used to compare depression, satisfaction, productivity, supervisor support, and coworker support between groups. ANOVA tests for differences in these variables between multiple ethnic groups.

Chapter3

This document provides examples and explanations of various graphical methods for describing data, including frequency distributions, bar charts, pie charts, stem-and-leaf diagrams, histograms, and cumulative relative frequency plots. It demonstrates how to construct these graphs using sample data on student weights, grades, ages, and other examples. The goal is to help readers understand different ways to visually represent data distributions and patterns.

Normal distribution

The document discusses standard deviation and the normal distribution. Some key points:
- Standard deviation is a measure of how spread out values are from the mean. It is the square root of the variance.
- For a normal distribution, approximately 68% of values fall within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99% within 3 standard deviations.
- The normal distribution is the most common continuous probability distribution and is important because many variables tend toward a normal distribution as the number of trials increases. It is used in statistical quality control.

Measure of dispersion part II ( Standard Deviation, variance, coefficient of ...

This tutorial gives the detailed explanation measure of dispersion part II (standard deviation, properties of standard deviation, variance, and coefficient of variation). It also explains why std. deviation is used widely in place of variance. This tutorial also teaches the MS excel commands of calculation in excel.

Frequency Measures for Healthcare Professioanls

Frequency distributions summarize data by grouping values of a variable and counting the number of observations in each group. This document discusses measures used to describe frequency distributions, including measures of central tendency (mode, median, mean) and measures of variability. The mode is the most frequent value, median is the middle value, and mean averages all values. These measures summarize the central or typical value in a data set.

Hcai 5220 lecture notes on campus sessions fall 11(2)

This chapter discusses descriptive statistics such as measures of central tendency (mean, median, mode), measures of variation (range, variance, standard deviation, coefficient of variation), and the shape of distributions (skewness). It also covers the normal distribution and how to calculate probabilities using the normal distribution. Key points include:
1) The mean, median, and mode are measures of central tendency while the range, variance, standard deviation, and coefficient of variation measure the spread or variation of data.
2) The normal distribution is a bell-shaped symmetric distribution that is useful in inferential statistics.
3) Probabilities using the normal distribution can be calculated by transforming the data into standard normal variables (Z

Measures of dispersion

The document discusses various measures of central tendency, dispersion, and shape used to describe data numerically. It defines terms like mean, median, mode, variance, standard deviation, coefficient of variation, range, interquartile range, skewness, and quartiles. It provides formulas and examples of how to calculate these measures from data sets. The document also discusses concepts like normal distribution, empirical rule, and how measures of central tendency and dispersion do not provide information about the shape or symmetry of a distribution.

Normal curve

The document discusses the normal curve and its key properties. A normal curve is a bell-shaped distribution that is symmetrical around the mean value, with half of the data falling above and half below the mean. The standard deviation measures how spread out the data is from the mean. In a normal distribution, 68% of the data lies within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations, following the 68-95-99.7 rule.

Measures of Dispersion

This pused to find measures of dispersion.pt tells us what dispersion is, need of dispersion and the different methods

Measures of central tendency and dispersion

The document discusses various measures of central tendency and dispersion used in statistical analysis. It defines measures of central tendency like arithmetic mean, median and mode, and provides their formulas and properties. It also discusses measures of dispersion such as range, mean deviation, standard deviation, variance and their characteristics. The document provides examples and steps to calculate various averages and measures of dispersion for a given data set.

State presentation2

This document summarizes various statistical measures used to analyze and describe data distributions, including measures of central tendency (mean, median, mode), dispersion (range, standard deviation, variance), skewness, and kurtosis. It provides formulas and methods for calculating each measure along with interpretations of the results. Measures of central tendency provide a single value to represent the center of the data set. Measures of dispersion describe how spread out or varied the data values are. Skewness and kurtosis measure the symmetry and peakedness of distributions compared to the normal curve.

02a one sample_t-test

The document discusses a one-sample t-test used to compare sample data to a standard value. It provides an example comparing intelligence scores of university students to the average score of 100. The sample of 6 students had a mean of 120. Running a one-tailed t-test in SPSS, the results showed the mean score was significantly higher than 100 with t(5)=3.15, p=.02. This allows the inference that the population mean intelligence at the university is greater than the standard score of 100.

The Normal distribution

The document discusses the normal distribution and related concepts. It describes how normal distributions can vary in their mean and standard deviation. It then discusses key features of normal distributions including that they are symmetric, have equal mean, median and mode, and are denser in the center than the tails. Finally, it discusses related statistical concepts like kurtosis and skewness, describing how kurtosis measures the thickness of a distribution's tails and how skewness measures a distribution's asymmetry.

Chisquare

Chi-square is a non-parametric test used to compare observed data with expected data. It can test goodness of fit, independence of attributes, and homogeneity. The document provides an introduction to chi-square terms and calculations including contingency tables, expected and observed frequencies, degrees of freedom, and test steps. Examples demonstrate applying chi-square to test the effectiveness of chloroquine and inoculation. Both examples find the null hypothesis of no effect can be rejected, indicating the treatments were effective.

Descriptive Statistics Part II: Graphical Description

The document provides information on descriptive statistics and graphical descriptions of data, including bar charts, pie charts, histograms, and cumulative frequency distributions. It discusses how to construct these various graphs using Excel and includes examples and questions to describe and interpret the graphs. Key information that can be obtained from these graphs includes the mode, range, percentages of observations within certain classes or below/above certain values, and comparing values across categories.

3.2 measures of variation

This document discusses measures of variation used to assess how far data points are from the average or mean. It defines key terms like range, variance, and standard deviation. Variance measures the mathematical dispersion of data relative to the mean, while standard deviation gives a value in the original units of measurement, making it easier to interpret. Formulas are provided for calculating sample variance and standard deviation versus population variance and standard deviation. Chebyshev's Theorem is introduced, stating that a certain minimum percentage of data must fall within a specified number of standard deviations of the mean. An example applies these concepts.

Statistics for dummies

This document provides an overview of key statistical concepts including:
1. The average (arithmetic mean) is calculated by summing all values and dividing by the number of samples.
2. The median is the middle value of a data set when values are sorted from lowest to highest.
3. The 90th percentile represents the value where 90% of values are below it.
4. Standard deviation measures how spread out values are from the average and 68% of values fall within one standard deviation of the average in a normal distribution.

Measures of dispersion

Measures of Dispersion: Absolute and Relative Measures of Dispersion, their computation & properties.

Chapter 022

Chapter 022

Some study materials

Some study materials

Seminar SPSS di UM

Seminar SPSS di UM

Chapter3

Chapter3

Normal distribution

Normal distribution

Measure of dispersion part II ( Standard Deviation, variance, coefficient of ...

Measure of dispersion part II ( Standard Deviation, variance, coefficient of ...

Frequency Measures for Healthcare Professioanls

Frequency Measures for Healthcare Professioanls

Hcai 5220 lecture notes on campus sessions fall 11(2)

Hcai 5220 lecture notes on campus sessions fall 11(2)

Measures of dispersion

Measures of dispersion

Normal curve

Normal curve

Measures of Dispersion

Measures of Dispersion

Measures of central tendency and dispersion

Measures of central tendency and dispersion

State presentation2

State presentation2

02a one sample_t-test

02a one sample_t-test

The Normal distribution

The Normal distribution

Chisquare

Chisquare

Descriptive Statistics Part II: Graphical Description

Descriptive Statistics Part II: Graphical Description

3.2 measures of variation

3.2 measures of variation

Statistics for dummies

Statistics for dummies

Measures of dispersion

Measures of dispersion

DescriptiveStatistics.pdf

This document provides an outline and overview of descriptive statistics. It discusses the key concepts including:
- Visualizing and understanding data through graphs and charts
- Measures of central tendency like mean, median, and mode
- Measures of spread like range, standard deviation, and interquartile range
- Different types of distributions like symmetrical, skewed, and their properties
- Levels of measurement for variables and appropriate statistics for each level
The document serves as an introduction to descriptive statistics, the goals of which are to summarize key characteristics of data through numerical and visual methods.

Statistics 3, 4

This document discusses measures of central tendency and variation for numerical data. It defines and provides formulas for the mean, median, mode, range, variance, standard deviation, and coefficient of variation. Quartiles and interquartile range are introduced as measures of spread less influenced by outliers. The relationship between these measures and the shape of a distribution are also covered at a high level.

2-Measures_of_Spreadddddddddddddddd-K.pptx

This document discusses various measures of spread used to quantify the variation or dispersion of data from the central location. It defines range, interquartile range, variance, and standard deviation. Range is the difference between the largest and smallest values but is affected by outliers. Interquartile range represents the central 50% of data. Variance is the average of squared deviations from the mean while standard deviation measures how closely values cluster around the mean. Examples are provided to demonstrate calculating and interpreting these measures of spread.

Basics of statistics by Arup Nama Das

This document provides an overview of biostatistics, including definitions, concepts, and methods. It defines statistics as the science of collecting, organizing, summarizing, analyzing, and interpreting data. Various statistical concepts are explained, such as variables, distributions, frequency distributions, measures of center and variability. Graphical and numerical methods for presenting data are described, including histograms, box plots, mean, median, and standard deviation. Methods for summarizing categorical and numerical variable data are also outlined.

Descriptive statistics and graphs

The document provides an overview of descriptive statistics and statistical graphs, including measures of center such as mean, median, and mode, measures of variation such as range and standard deviation, and different types of statistical graphs like histograms, boxplots, and normal distributions. It discusses key concepts like outliers, percentiles, quartiles, sampling distributions, and the central limit theorem. The document is intended to describe important statistical tools and concepts for summarizing and describing the characteristics of data sets.

Student’s presentation

This document provides an overview of basic statistics concepts. It defines statistics as the science of collecting, analyzing, and interpreting data. There are two main types of statistics: descriptive statistics which summarize data, and inferential statistics which make predictions from data. Key concepts discussed include variables, frequency distributions, measures of center such as mean and median, measures of variability such as range and standard deviation, and methods of presenting data graphically and numerically.

presentation

This document provides an overview of basic statistics concepts. It defines statistics as the science of collecting, analyzing, and interpreting data. There are two main types of statistics: descriptive statistics which summarize data, and inferential statistics which make predictions from data. Key concepts discussed include variables, frequency distributions, measures of center such as mean and median, measures of variability such as range and standard deviation, and methods of presenting data graphically and numerically.

Penggambaran Data Secara Numerik

The document summarizes key concepts in describing data with numerical measures from a statistics textbook chapter. It covers measures of center including mean, median, and mode. It also covers measures of variability such as range, variance, and standard deviation. It provides examples of calculating these measures and interpreting them, as well as using them to construct box plots.

Numerical measures stat ppt @ bec doms

This chapter discusses numerical measures used to describe data, including measures of center (mean, median, mode), location (percentiles, quartiles), and variation (range, variance, standard deviation, coefficient of variation). It defines these terms and how to calculate and interpret them, as well as how to construct and use box and whisker plots to graphically display data distributions.

Class1.ppt

The document provides an overview of the structure and content of a biostatistics class. It includes:
- Two instructors who will teach 8 classes, with 3 take-home assignments and a final exam.
- Default and contributed datasets that students can use, focusing on nominal, ordinal, interval, and ratio variables.
- Optional late topics like microarray analysis, pattern recognition, and time series analysis.

Class1.ppt

The class consists of 8 classes taught by two instructors over biostatistics and psychology. There are 3 take-home assignments due in classes 3, 5, and 7 and a final take-home exam assigned in class 8. The default dataset for class participation contains data on 60 subjects across 3-4 treatment groups and various measure types. Special topics may include microarray analysis, pattern recognition, machine learning, and hidden Markov modeling.

Class1.ppt

The document provides an overview of the structure and content of a biostatistics class. It includes:
- Two instructors who will teach 8 classes, with 3 take-home assignments and a final exam.
- Default datasets with health data that students can use for assignments, and an option for students to bring their own de-identified data.
- Possible special topics like machine learning, time series analysis, and others.

Introduction to Statistics - Basics of Data - Class 1

The document provides an overview of the structure and content of a biostatistics class. It includes:
- Two instructors who will teach 8 classes, with 3 take-home assignments and a final exam.
- Default and contributed datasets that students can use, focusing on nominal, ordinal, interval, and ratio variables.
- Optional late topics like microarray analysis, pattern recognition, and time series analysis.
- A taxonomy of statistics, covering statistical description, presentation of data through graphs and numbers, and measures of center and variability.

Class1.ppt

The class consists of 8 classes taught by two instructors over biostatistics and psychology. There are 3 take-home assignments due in classes 3, 5, and 7. A final take-home exam is assigned in class 8. The default dataset contains data on 60 subjects across 3-4 treatment groups with various measure types. Students can also bring their own de-identified datasets. The course covers topics like microarray analysis, pattern recognition, machine learning and more.

STATISTICS BASICS INCLUDING DESCRIPTIVE STATISTICS

The class consists of 8 classes taught by two instructors over biostatistics and psychology. There are 3 take-home assignments due in classes 3, 5, and 7. A final take-home exam is assigned in class 8. The default dataset contains data on 60 subjects across 3-4 treatment groups with various measure types. Students can also bring their own de-identified datasets. The course covers topics like microarray analysis, pattern recognition, machine learning and more.

Statistics

The class consists of 8 classes taught by two instructors. There are 3 take-home assignments due in classes 3, 5, and 7. A final take-home exam is assigned in class 8. The default dataset contains data from 60 subjects across 3-4 groups with different variable types. Students can also bring their own de-identified datasets. Special topics may include microarray analysis, pattern recognition, machine learning, and time series analysis.

Chapter 4Summarizing Data Collected in the Sample.docx

This document discusses the meaning of ethics. It begins by providing examples of how some business people defined ethics as following feelings, religious beliefs, laws, or social standards. However, the document argues that ethics cannot be reduced to any of these things. Ethics refers to well-founded standards of right and wrong that prescribe human obligations and duties, taking into account factors like rights, fairness, benefits to society, and virtues. True ethics can deviate from feelings, laws, religions or social acceptance at a given time.

Lab 1 intro

Here are the responses to the questions:
1. A statistical population is the entire set of individuals or objects of interest. A sample is a subset of the population selected to represent the population. The sample infers information about the characteristics, attributes, and properties of the entire population.
2. Variance is the average of the squared deviations from the mean. It is calculated as the sum of the squared deviations from the mean divided by the number of values in the data set minus 1. Standard deviation is the square root of the variance. It measures how far data values spread out from the mean.
3. No data was provided to create graphs. Additional data on the number of fish in each age group would be needed.

Stats chapter 1

This document provides an overview of different methods for displaying and describing data, including graphs, measures of center, and measures of spread. It discusses bar graphs, pie charts, stem-and-leaf plots, histograms, and calculating the mean, median, quartiles, interquartile range, and standard deviation. Examples are provided using data on football scores to demonstrate these concepts. Key terms like outliers, shape, and transformations of data are also introduced.

Measures of dispersion discuss 2.2

The document discusses various measures of central tendency, dispersion, and shape used to describe data numerically. It defines terms like mean, median, mode, variance, standard deviation, coefficient of variation, range, interquartile range, skewness, and quartiles. It provides formulas and examples of how to calculate these measures from data sets. The document also discusses concepts like normal distribution, empirical rule, and how measures of central tendency and dispersion do not provide information about the shape or symmetry of a distribution.

DescriptiveStatistics.pdf

DescriptiveStatistics.pdf

Statistics 3, 4

Statistics 3, 4

2-Measures_of_Spreadddddddddddddddd-K.pptx

2-Measures_of_Spreadddddddddddddddd-K.pptx

Basics of statistics by Arup Nama Das

Basics of statistics by Arup Nama Das

Descriptive statistics and graphs

Descriptive statistics and graphs

Student’s presentation

Student’s presentation

presentation

presentation

Penggambaran Data Secara Numerik

Penggambaran Data Secara Numerik

Numerical measures stat ppt @ bec doms

Numerical measures stat ppt @ bec doms

Class1.ppt

Class1.ppt

Class1.ppt

Class1.ppt

Class1.ppt

Class1.ppt

Introduction to Statistics - Basics of Data - Class 1

Introduction to Statistics - Basics of Data - Class 1

Class1.ppt

Class1.ppt

STATISTICS BASICS INCLUDING DESCRIPTIVE STATISTICS

STATISTICS BASICS INCLUDING DESCRIPTIVE STATISTICS

Statistics

Statistics

Chapter 4Summarizing Data Collected in the Sample.docx

Chapter 4Summarizing Data Collected in the Sample.docx

Lab 1 intro

Lab 1 intro

Stats chapter 1

Stats chapter 1

Measures of dispersion discuss 2.2

Measures of dispersion discuss 2.2

How population evolve

1) Biologists study how allele frequencies change in populations over time. In 1908, Hardy and Weinberg demonstrated that allele frequencies remain stable unless acted upon by evolutionary forces.
2) Their discovery, called the Hardy-Weinberg principle, states that allele frequencies will remain constant in a population as long as it is large, randomly mating, and not experiencing evolutionary pressures like mutation, gene flow, genetic drift, or natural selection.
3) Natural selection directly influences allele frequencies by increasing the chances of survival and reproduction of individuals with certain phenotypes, thus changing the distribution of traits in a population over multiple generations.

Ecology how population grow

Populations tend to grow exponentially at first until resources become limited, after which growth slows and the population reaches its carrying capacity. Demographers use population models like the logistic growth curve to predict how populations will change over time based on birth and death rates and factors like available resources. While some populations like bacteria and insects grow rapidly in changing environments, most species like humans and other mammals follow a logistic growth pattern of slower growth to a stable carrying capacity.

Cycling of materials in ecosystem

1) Carbon, water, nitrogen, and phosphorus cycle through ecosystems, with organisms using these elements and releasing them back into the nonliving environment through processes like respiration, decomposition, and erosion.
2) The water cycle involves water evaporating from plants and surfaces, condensing in the atmosphere, and falling as precipitation before infiltrating the ground and flowing into rivers and oceans.
3) In the carbon cycle, carbon dioxide is absorbed by plants and enters animals when they eat plants or each other, and it is released back through respiration and decomposition.

What is ecology

1) An ecosystem consists of all the living organisms (biotic factors) in a particular area, along with the nonliving (abiotic) parts like air, water, and mineral resources.
2) Primary succession occurs in new areas like land exposed by retreating glaciers, where pioneer species arrive first and help create conditions for later species.
3) Secondary succession follows disruptions to existing ecosystems, as earlier species are replaced over time, progressing towards a stable climactic community composition.

Energy flow in ecosystems

1) Energy from the sun is captured by producers like plants through photosynthesis and converted into chemical energy stored in organic molecules. 2) Primary consumers, like herbivores, obtain this energy by consuming producers. Secondary consumers eat primary consumers. 3) Energy is lost at each trophic level, with only about 10% transferred between levels. This limits the length of food chains and the number of organisms an ecosystem can support.

How organisms interact in communities

1) Organisms in an ecosystem are bound together in a web of interactions and coevolve over time to support each other.
2) Predators and prey coevolve through natural selection, with predators developing traits for hunting and prey developing defenses for escaping predators.
3) Symbiotic relationships can benefit both organisms, like aphids and ants, or benefit one organism without harming the other, like clown fish living among sea anemones.

How organisms interact in communities

1) Organisms in an ecosystem are bound together in a web of interactions and coevolve over time to support each other.
2) Predators and prey coevolve through natural selection, with predators developing traits for hunting and prey developing defenses to escape, ensuring both survive.
3) Symbiotic relationships between species can be mutualistic, benefiting both; commensalistic, benefiting one; or parasitic, harming the host.

Aquatic communities

The document discusses various aquatic biomes. It describes the three zones of freshwater ponds and lakes: the littoral, limnetic, and profundal zones. The littoral zone near shore is home to aquatic plants, insects, amphibians, and small fish. The limnetic zone farther from shore but near the surface contains algae, zooplankton, and fish. The deep profundal zone below light penetration contains bacteria and organisms eating lake bottom debris. Wetlands are diverse ecosystems exceeded in productivity only by coral reefs. They provide flood control by storing water during heavy rain. Many wetlands are threatened by development, but protection laws aim to conserve them. Shallow ocean areas including

Major biological communities

There are 7 major terrestrial biomes: tropical rainforests, savannas, taiga, tundra, deserts, temperate grasslands, and temperate forests. The two most important factors determining a biome are temperature and precipitation. Each biome has characteristic climate conditions and plant and animal communities adapted to that climate. For example, tropical rainforests have high rainfall year-round while deserts have less than 25 cm of annual precipitation.

How competition shapes communities

Competition occurs when multiple species rely on the same limited resources. Warblers avoid competition by specializing on different parts of the same trees. Species can coexist if they divide resources in their realized niches to minimize overlap with their fundamental niches. Predation also reduces competition by controlling populations that could otherwise outcompete other species. Greater biodiversity in ecosystems leads to higher productivity and stability.

Mitosis and cytokinesis

The document describes the process of mitosis and cytokinesis in cells. It discusses the four main stages of mitosis - prophase, metaphase, anaphase and telophase. During these stages, the chromosomes condense, align at the center, separate into two sets as the cell divides, and decondense as the nuclear envelope reforms. Cytokinesis then divides the cytoplasm and cell membrane, resulting in two daughter cells each with a full set of chromosomes. Cytokinesis differs between animal and plant cells, with plant cells forming a cell plate from vesicles to divide the cell.

Meiosis and reproduction

Meiosis is a type of cell division that produces haploid gametes from a diploid cell for sexual reproduction. It involves two divisions and results in four haploid cells. During meiosis, homologous chromosomes pair and may exchange genetic material through crossing over, and then separate, reducing the chromosome number. This and the independent assortment of chromosomes during gamete formation introduces genetic variation that is important for evolution.

Cellular respiration in detail

Cellular respiration involves the breakdown of glucose to extract energy through two main stages. In the first stage, glycolysis, glucose is broken down to pyruvate with a small ATP yield. The second stage involves either aerobic respiration, using oxygen to produce much more ATP through the Krebs cycle and electron transport chain, or fermentation when oxygen is absent. Aerobic respiration is much more efficient at producing ATP. The end products of cellular respiration are carbon dioxide, water, and energy in the form of ATP.

Energy and chem reactions in cells

1. Chemical reactions in cells produce and use energy. Enzymes speed up chemical reactions by lowering their activation energy.
2. Enzymes are proteins that act as catalysts. They have active sites that substrates fit into, reducing the energy needed for reactions.
3. Factors like temperature and pH can change an enzyme's shape, affecting its activity. Different cell types contain different enzyme combinations for their specific functions.

Cell organelles

The nucleus controls most cell functions and contains DNA. It is surrounded by a double membrane with nuclear pores that allow substances to pass. Ribosomes are partially assembled in the nucleolus. Ribosomes located on the endoplasmic reticulum produce proteins. Vesicles transport proteins from the ER to the Golgi apparatus, which packages and modifies proteins. Vesicles then distribute proteins and lysosomes contain digestive enzymes. Mitochondria produce ATP through cellular respiration. Plant cells also have cell walls, chloroplasts for photosynthesis, and a central vacuole for storage.

Cells

Carbon compounds are the primary components of living things. There are four main classes: carbohydrates, lipids, proteins, and nucleic acids. Carbohydrates include sugars and starches and are a key energy source. Lipids include fats and phospholipids and function in energy storage and cell membranes. Proteins have many functions including enzymes, structure, and transport. Nucleic acids DNA and RNA contain genetic information and aid in protein production. ATP temporarily stores energy to power cellular functions.

Cell features

- All living things are made of one or more cells, which are the basic units of structure and function in organisms. Cells arise only from preexisting cells.
- Cells come in two main types - prokaryotic cells which lack internal structures and a nucleus, and eukaryotic cells which have internal compartments including a nucleus.
- The cell membrane encloses the cell, separating the cytoplasm from the external environment. It regulates what enters and leaves the cell through membrane proteins.

How population evolve

How population evolve

Ecology how population grow

Ecology how population grow

Cycling of materials in ecosystem

Cycling of materials in ecosystem

What is ecology

What is ecology

Energy flow in ecosystems

Energy flow in ecosystems

How organisms interact in communities

How organisms interact in communities

How organisms interact in communities

How organisms interact in communities

Aquatic communities

Aquatic communities

Major biological communities

Major biological communities

How competition shapes communities

How competition shapes communities

Mitosis and cytokinesis

Mitosis and cytokinesis

Meiosis and reproduction

Meiosis and reproduction

Cellular respiration in detail

Cellular respiration in detail

Energy and chem reactions in cells

Energy and chem reactions in cells

Cell organelles

Cell organelles

Cells

Cells

Cell features

Cell features

- 4. Types of Variables: Overview Categorical Quantitative continuous discrete ordinal nominal binary 2 categories + more categories + order matters + numerical + uninterrupted
- 13. The first rule of statistics: USE COMMON SENSE! 90% of the information is contained in the graph.
- 16. Bar Chart: categorical variables no yes
- 17. Much easier to extract information from a bar chart than from a table! Bar Chart for SI categories Number of Patients Shock Index Category 0.0 16.7 33.3 50.0 66.7 83.3 100.0 116.7 133.3 150.0 166.7 183.3 200.0 1 2 3 4 5 6 7 8 9 10
- 19. 0.0 0.7 1.3 2.0 SI Box Plot: Shock Index Shock Index Units “ whisker” Q3 + 1.5IQR = .8+1.5(.25)=1.175 75th percentile (0.8) 25th percentile (0.55) maximum (1.7) interquartile range (IQR) = .8-.55 = .25 minimum (or Q1-1.5IQR) Outliers median (.66)
- 20. Note the “right skew” Bins of size 0.1 0.0 8.3 16.7 25.0 0.0 0.7 1.3 2.0 Histogram of SI SI Percent
- 21. 100 bins (too much detail)
- 22. 2 bins (too little detail)
- 23. Also shows the “right skew” 0.0 0.7 1.3 2.0 SI Box Plot: Shock Index Shock Index Units
- 24. 0.0 33.3 66.7 100.0 AGE Box Plot: Age Variables Years More symmetric 75th percentile 25th percentile maximum interquartile range minimum median
- 25. Histogram: Age Not skewed, but not bell-shaped either… 0.0 4.7 9.3 14.0 0.0 33.3 66.7 100.0 AGE (Years) Percent
- 26. Some histograms from last year’s class (n=18) Starting with politics…
- 29. Feelings about math and writing…
- 30. Optimism…
- 35. Mean of age in Kline’s data The balancing point 0.0 4.7 9.3 14.0 0.0 33.3 66.7 100.0 Percent
- 36. Mean of Pulmonary Embolism? (Binary variable?) 19.44% (181) 80.56% (750)
- 41. Median of age in Kline’s data 0.0 4.7 9.3 14.0 0.0 33.3 66.7 100.0 Percent 50% of mass 50% of mass
- 50. 0.0 4.7 9.3 14.0 0.0 33.3 66.7 100.0 Range of age: 94 years-15 years = 79 years AGE (Years) Percent
- 54. Interquartile Range: age Median (Q2) maximum minimum Q1 Q3 25% 25% 25% 25% 15 35 49 65 94 Interquartile range = 65 – 35 = 30
- 58. Calculation Example: Sample Standard Deviation Age data (n=8) : 17 19 21 22 23 23 23 38 n = 8 Mean = X = 23.25
- 59. 0.0 4.7 9.3 14.0 0.0 33.3 66.7 100.0 AGE (Years) Percent Std. dev is a measure of the “average” scatter around the mean. Estimation method: if the distribution is bell shaped, the range is around 6 SD, so here rough guess for SD is 79/6 = 13
- 61. 0.0 62.5 125.0 187.5 250.0 0.0 0.5 1.0 1.5 2.0 Std Dev of Shock Index SI Count Estimation method: if the distribution is bell shaped, the range is around 6 SD, so here rough guess for SD is 1.4/6 =.23 Std. dev is a measure of the “average” scatter around the mean.
- 63. Std. Dev of binary variable, PE Std. dev is a measure of the “average” scatter around the mean. 19.44% 80.56%
- 68. **The beauty of the normal curve: No matter what and are, the area between - and + is about 68%; the area between -2 and +2 is about 95%; and the area between -3 and +3 is about 99.7%. Almost all values fall within 3 standard deviations.
- 69. 68-95-99.7 Rule 68% of the data 95% of the data 99.7% of the data
- 71. Examples of bad graphics
- 72. What’s wrong with this graph? from : ER Tufte. The Visual Display of Quantitative Information. Graphics Press, Cheshire, Connecticut, 1983, p.69
- 73. From: Visual Revelations: Graphical Tales of Fate and Deception from Napoleon Bonaparte to Ross Perot Wainer, H. 1997, p.29. Notice the X-axis
- 75. Report of the Presidential Commission on the Space Shuttle Challenger Accident , 1986 (vol 1, p. 145) The graph excludes the observations where no O-rings failed.
- 77. Even better: graph all the data (including non-failures) using a logistic regression model Tappin, L. (1994). "Analyzing data relating to the Challenger disaster". Mathematics Teacher , 87, 423-426
- 78. What’s wrong with this graph? from : ER Tufte. The Visual Display of Quantitative Information. Graphics Press, Cheshire, Connecticut, 1983, p.74
- 80. What’s the message here? Diagraphics II , 1994
- 81. Diagraphics II , 1994
- 94. Where did the statistics come from? The 15%: Dummer GM, Rosen LW, Heusner WW, Roberts PJ, and Counsilman JE. Pathogenic weight-control behaviors of young competitive swimmers. Physician Sportsmed 1987; 15: 75-84. The “to”: Rosen LW, McKeag DB, O’Hough D, Curley VC. Pathogenic weight-control behaviors in female athletes. Physician Sportsmed . 1986; 14: 79-86. The 62%:Rosen LW, Hough DO. Pathogenic weight-control behaviors of female college gymnasts. Physician Sportsmed 1988; 16:140-146.

- That's really what distinguishes these from discrete numerical
- What are some others?
- Does everybody know what I mean when I say percentiles? What is the median? Anyone?
- 1. Bin sizes may be altered. 2. How many people do you think are in bin 125-135? 3. Where do you think the center of the data are (what's your best guess at the average weight)? 4. On average, how far do you think a given woman is from 127 -- the center/mean?
- Balance the Bell Curve on a point. Where is the point of balance, average mass on each side.
- 1. Bin sizes may be altered. 2. How many people do you think are in bin 125-135? 3. Where do you think the center of the data are (what's your best guess at the average weight)? 4. On average, how far do you think a given woman is from 127 -- the center/mean?
- SAY: within 1 standard deviation either way of the mean within 2 standard deviations of the mean within 3 standard deviations either way of the mean WORKS FOR ALL NORMAL CURVES NO MATTER HOW SKINNY OR FAT