2 7 exploratory data analysis
•Download as PPT, PDF•
1 like•656 views
This document discusses box and whisker plots and the 5-number summary used to describe data distributions. A box and whisker plot depicts the minimum, lower quartile, median, upper quartile, and maximum of a dataset using a box and whiskers. Outliers are defined as values more than 1.5 times the interquartile range below the first quartile or above the third quartile. The document provides an example comparing temperatures from 2005 and 2008 using a box and whisker plot.
Report
Share
Report
Share
![5-number summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]](https://image.slidesharecdn.com/2-7exploratorydataanalysis-101005104237-phpapp02/85/2-7-exploratory-data-analysis-1-320.jpg)
![For example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Recommended
Stretching & Shrinking 2.2 Summary + Tests For Similarity
The document discusses coordinate transformations on shapes. It notes that adding or subtracting from the x-coordinate moves a shape left or right, and adding or subtracting from the y-coordinate moves a shape up or down. Multiplying both coordinates by the same number shrinks the shape, keeping it similar, while multiplying by different numbers makes the shape not similar to the original.
Calc 1.1
This document provides an overview of key concepts in calculus, including:
1) Calculus makes precalculus concepts like limits dynamic by exploring tangents to curves and areas under curves.
2) There are two main questions in calculus - what is the equation of the tangent line touching a curve at a point, and what is the area under a curve.
3) To find the equation of a tangent line, we can approximate the slope of a curve at a point using nearby secant lines, and then use the point-slope formula for a line.
Ogive presentation
Cumulative Frequency Table,Cumulative Frequency Table with Example,Ogive Curve,Two Types of Ogive Curve,Less than Ogive with Example,Greater than Ogive with Example.
(8) Lesson 8.1
Here are some key ways to tell the relationship shown in a scatter plot:
- Positive relationship: As one variable increases, the other variable also increases. The data points will fall generally above or to the right of the origin.
- Negative relationship: As one variable increases, the other decreases. The data points will fall generally below or to the left of the origin.
- No relationship: There is no consistent pattern to how the variables change together. The data points will be randomly scattered with no discernible upward or downward trend.
Some other clues:
- For positive or negative relationships, the data points tend to fall near a straight line. For no relationship, they are more randomly arranged.
-
Geometry unit 5.6
This document contains explanations and examples regarding triangle theorems and properties including: the exterior angle theorem, isosceles triangle theorem, relationship between side length and angle size, triangle inequality theorem, and determining possible third side lengths given two sides of a triangle. Examples are provided to demonstrate applying these triangle concepts to determine largest angles, longest/shortest sides, and possible side lengths.
Calc 4.6
The document discusses numerical integration techniques including the trapezoidal rule and Simpson's rule. The trapezoidal rule approximates the area under a curve using trapezoids within subintervals, while Simpson's rule uses quadratic approximations within subintervals. The document provides the formulas for approximating integrals using these rules, including the coefficient patterns and expressions used. Examples are given to demonstrate applying the rules to approximate definite integrals. The end discusses estimating the error involved when using these approximation methods.
Finding area
The document discusses how to find the area of several shapes. The area of a rectangle or square is simply the base multiplied by the height. The area of a trapezoid is 0.5 times the sum of the bases multiplied by the height. The area of a triangle is the base multiplied by the height divided by 2. The area of a parallelogram is the base multiplied by the height.
Series contribution to the numerical approximations
The document discusses using Taylor series to understand truncation errors in numerical approximations. It explains that Taylor series allow using approximations by adding additional terms to increase the order of approximation. Starting with a zero-order approximation, adding a first-order term allows a linear adjustment, and generalizing the Taylor series allows for better approximations of functions through higher-order terms in the series expansion. The Taylor series is used to estimate the characteristics of truncation errors that result from using approximations rather than exact mathematical procedures.
Recommended
Stretching & Shrinking 2.2 Summary + Tests For Similarity
The document discusses coordinate transformations on shapes. It notes that adding or subtracting from the x-coordinate moves a shape left or right, and adding or subtracting from the y-coordinate moves a shape up or down. Multiplying both coordinates by the same number shrinks the shape, keeping it similar, while multiplying by different numbers makes the shape not similar to the original.
Calc 1.1
This document provides an overview of key concepts in calculus, including:
1) Calculus makes precalculus concepts like limits dynamic by exploring tangents to curves and areas under curves.
2) There are two main questions in calculus - what is the equation of the tangent line touching a curve at a point, and what is the area under a curve.
3) To find the equation of a tangent line, we can approximate the slope of a curve at a point using nearby secant lines, and then use the point-slope formula for a line.
Ogive presentation
Cumulative Frequency Table,Cumulative Frequency Table with Example,Ogive Curve,Two Types of Ogive Curve,Less than Ogive with Example,Greater than Ogive with Example.
(8) Lesson 8.1
Here are some key ways to tell the relationship shown in a scatter plot:
- Positive relationship: As one variable increases, the other variable also increases. The data points will fall generally above or to the right of the origin.
- Negative relationship: As one variable increases, the other decreases. The data points will fall generally below or to the left of the origin.
- No relationship: There is no consistent pattern to how the variables change together. The data points will be randomly scattered with no discernible upward or downward trend.
Some other clues:
- For positive or negative relationships, the data points tend to fall near a straight line. For no relationship, they are more randomly arranged.
-
Geometry unit 5.6
This document contains explanations and examples regarding triangle theorems and properties including: the exterior angle theorem, isosceles triangle theorem, relationship between side length and angle size, triangle inequality theorem, and determining possible third side lengths given two sides of a triangle. Examples are provided to demonstrate applying these triangle concepts to determine largest angles, longest/shortest sides, and possible side lengths.
Calc 4.6
The document discusses numerical integration techniques including the trapezoidal rule and Simpson's rule. The trapezoidal rule approximates the area under a curve using trapezoids within subintervals, while Simpson's rule uses quadratic approximations within subintervals. The document provides the formulas for approximating integrals using these rules, including the coefficient patterns and expressions used. Examples are given to demonstrate applying the rules to approximate definite integrals. The end discusses estimating the error involved when using these approximation methods.
Finding area
The document discusses how to find the area of several shapes. The area of a rectangle or square is simply the base multiplied by the height. The area of a trapezoid is 0.5 times the sum of the bases multiplied by the height. The area of a triangle is the base multiplied by the height divided by 2. The area of a parallelogram is the base multiplied by the height.
Series contribution to the numerical approximations
The document discusses using Taylor series to understand truncation errors in numerical approximations. It explains that Taylor series allow using approximations by adding additional terms to increase the order of approximation. Starting with a zero-order approximation, adding a first-order term allows a linear adjustment, and generalizing the Taylor series allows for better approximations of functions through higher-order terms in the series expansion. The Taylor series is used to estimate the characteristics of truncation errors that result from using approximations rather than exact mathematical procedures.
Malimu variance and standard deviation
This document discusses variance and standard deviation. It defines variance as a measure of how data points differ from the mean. It explains that variance can show how two data sets that have the same mean and median can still be different. The document then provides formulas and examples for calculating variance and standard deviation. It states that standard deviation is a measure of variation from the mean and that a higher standard deviation indicates more spread and less consistency in the data.
The Interpretation Of Quartiles And Percentiles July 2009
The document discusses measures of central tendency and dispersion used to summarize data, including the mean, median, mode, range, quartiles, and percentiles. It explains that the mean is best for values representing magnitudes, the median for ranking, and the mode for popularity. Quartiles and percentiles divide a sorted data set into four and one hundred equal parts respectively. A high percentile is desirable for exams but not waiting times, while a low percentile is preferable for race times. Together these statistics provide a concise overview of a data set.
Variance And Standard Deviation
The document introduces the concepts of variance and standard deviation. Variance is a statistical measure that quantifies how far observations in a data set spread out from the mean or average value. It is calculated by taking the average of the squared differences from the mean. Standard deviation is the square root of variance and represents how dispersed the values in a data set are from the mean. The document provides examples of computing variance and standard deviation to illustrate these statistical concepts.
Grouped Mean Median Mode
A coffee shop conducted a two-day survey to determine the average number of cappuccinos made per hour. A histogram showed the frequency of cappuccinos made within various hourly intervals. To calculate the average, interval midpoints were determined and multiplied by the frequencies. The total of these products was divided by the total frequency, determining that the average number of cappuccinos made per hour was 10.
Mean, Median, Mode: Measures of Central Tendency
There are three common measures of central tendency: mean, median, and mode. The mean is the average value found by dividing the sum of all values by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the value that occurs most frequently. Each measure provides a single number to represent the central or typical value in a data set.
Measures of central tendency
Here are the modes for the three examples:
1. The mode is 3. This value occurs most frequently among the number of errors committed by the typists.
2. The mode is 82. This value occurs most frequently among the number of fruits yielded by the mango trees.
3. The mode is 12 and 15. These values occur most frequently among the students' quiz scores.
Standard Deviation and Variance
The document discusses how to calculate standard deviation and variance for both ungrouped and grouped data. It provides step-by-step instructions for finding the mean, deviations from the mean, summing the squared deviations, and using these values to calculate standard deviation and variance through standard formulas. Standard deviation measures how spread out numbers are from the mean, while variance is the square of the standard deviation.
Overview Of Quartile.pptx
The document discusses quartiles, which divide a dataset into four equal parts. There are three quartiles: the first quartile (Q1) divides the data so that 25% falls below it; the second quartile is the median, which halves the data; and the third quartile (Q3) divides the data so that 75% falls below it. Formulas are provided for calculating quartiles for both ungrouped and grouped data. Examples of calculating quartiles from datasets are also shown.
TSTD 6251 Fall 2014SPSS Exercise and Assignment 120 PointsI.docx
TSTD 6251 Fall 2014
SPSS Exercise and Assignment 1
20 Points
In this class, we are going to study descriptive summary statistics and learn how to construct box plot. We are still working with univariate variable for this exercise.
Practice Example:
Admission receipts (in million of dollars) for a recent season are given below for the
n =
30 major league baseball teams:
19.4 26.6 22.9 44.5 24.4 19.0 27.5 19.9 22.8 19.0 16.9 15.2 25.7 19.0 15.5 17.1 15.6 10.6 16.2 15.6 15.4 18.2 15.5 14.2 9.5 9.9
10.7 11.9 26.7 17.5
Require:
a. Compute the mean, variance and standard deviation.
b. Find the sample median, first quartile, and third quartile.
c. Construct a boxplot and interpret the distribution of the data.
d. Discuss the distribution of this set of data by examining kurtosis and skewness
statistics, such as if the distribution is skewed to one side of the distribution, and if the
distribution shows a peaked/skinny curve or a spread out/flat curve.
SPSS Procedures for Computing Summary Statistics
:
Enter the 30 data values in the first column of SPSS
Data View
Tab
Variable View
and name this variable
receipts
Adjust
Decimals
to 3 decimal points
Type
Admission Receipts
($ mn)
in the
Label
column for output viewer
Return to
Data View
and click
A
nalyze
on the menu bar
Click the second menu
D
e
scriptive Statistics
Click
F
requencies …
Move
Admission Receipts
to the
Variable(s)
list by clicking the arrow button
Click
S
tatistics …
button at the top of the dialog box
Now, you can select the descriptive statistics according to what the question requires. For this practice question, it requires central tendency, dispersion, percentile and distribution statistics, so we click all the boxes
except for
P
ercentile(s): and Va
l
ues are group midpoints
.
Click
Continue
to return to the
Frequencies
dialog box
Click
OK
to generate descriptive statistic output which is pasted below:
The first table provides summary statistics and the second table lists frequencies, relative frequencies and cumulative frequencies. The statistics required for solving this problem are highlighted in red.
Statistics
Admission Receipts
N
Valid
30
Missing
0
Mean
18.76333
Std. Error of Mean
1.278590
Median
17.30000
Mode
19.000
Std. Deviation
7.003127
Variance
49.043782
Skewness
1.734
Std. Error of Skewness
.427
Kurtosis
5.160
Std. Error of Kurtosis
.833
Range
35.000
Minimum
9.500
Maximum
44.500
Sum
562.900
Percentiles
10
10.61000
20
14.40000
25
15.35000
30
15.50000
40
15.84000
50
17.30000
60
19.00000
70
19.75000
75
22.82500
80
24.10000
90
26.69000
Admission Receipts
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
9.500
1
3.3
3.3
3.3
9.900
1
3.3
3.3
6.7
10.600
1
3.3
3.3
10.0
10.700
1
3.3
3.3
13.3
11.900
1
3.3
3.3
16.7
14.200
1
3.3
3.3
20.0
15.2.
3.3 percentiles and boxandwhisker plot
The document defines percentiles and how they divide data into hundredths, with quartiles specifically dividing data into fourths. It describes how to compute quartiles and the interquartile range. Finally, it explains how to create and interpret box-and-whisker plots using the five number summary to visually depict the spread and symmetry of a data set.
Ejercicio resuelto-de-estadc3adstica-descriptiva1
The document provides information and instructions for analyzing student exam score data. It includes:
1) A table of 80 exam scores ranging from 53 to 97.
2) Instructions to calculate descriptive statistics like minimum, maximum, range, and percentiles of the scores.
3) Directions to construct a frequency distribution table and histogram of the scores binned into intervals of 5.
4) A calculation of measures of central tendency (mean, median, mode) and dispersion (variance, standard deviation) of the scores.
5) An analysis of the distribution's asymmetry and kurtosis.
Statistic and probability 2
This is very important presentation on stem and leaf, histogram, why we use them how we use them and the tool that is used to draw these.
Lecture-2 Descriptive Statistics-Box Plot Descriptive Measures.pdf
This is a book of probability and statisticsThis is a book of probability and statisticsThis is a book of probability and statisticsThis is a book of probability and statistics
Statistics (Measures of Dispersion)
The document provides information about measures of central tendency (mean, median, mode) and measures of dispersion (range, quartiles, variance, standard deviation) using examples of data distributions. It defines key terms like mean, median, mode, range, quartiles, variance and standard deviation. It also shows how to calculate and interpret these measures of central tendency and dispersion using sample data sets.
Chapter 1 descriptive_stats_2_rev_2009
This document discusses three methods for graphically displaying data: stem-and-leaf displays, histograms, and box plots. It provides instructions on how to construct each type of graph and describes what each graph conveys visually about a dataset. Stem-and-leaf displays show the distribution of values, histograms summarize frequency distributions of quantitative variables, and box plots simultaneously describe the center, spread, and outliers of a dataset.
Summarizing Data : Listing and Grouping pdf
Introduction
Descriptive Statistics describe basic features of the data gathered from an experimental study in various ways.
They provide simple summaries about the sample via graphs and numbers, mainly measures of center and variation.
Together with graphics analysis (histograms, bar plots, pie-charts), they are the cornerstone of quantitative data analysis.
Tables (frequency distributions, stem-and-leaf plots, …) that summarize the data.
Graphical representations of the data (histograms, bar plots, pie-charts).
Summary statistics (numbers) which summarize the data
The Frequency distribution table.pptx
- A frequency distribution organizes data into classes and displays the frequency of observations in each class.
- Grouped data uses classes with cut-offs to group interval or ratio level data, while ungrouped data lists each observation individually for smaller data sets.
- To make a frequency distribution, the data's range is found and classes are determined. Each observation is tallied and frequencies per class are calculated. This displays the distribution of the data.
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.
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.
C2 st lecture 13 revision for test b handout
This document provides an outline for a lecture series revising key concepts for Test B, including:
- Pythagoras' theorem, trigonometry, sine and cosine rules, and calculating triangle areas.
- Probability, probability trees, and examples calculating probabilities of dice rolls.
- Descriptive statistics like mode, median, interquartile range, mean, absolute deviation, and standard deviation.
- Hypothesis testing using z-tests, t-tests, and chi-squared tests; including setting up hypotheses, finding critical values, calculating test statistics, and making conclusions.
The revision is in preparation for Standard Track Test B which will be held the week of April 21st.
Measures of Relative Standing and Boxplots
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 3: Describing, Exploring, and Comparing Data
3.3: Measures of Relative Standing and Boxplots
Box and-whisker-plots
This document provides instructions for constructing and interpreting box-and-whisker plots. It explains how to find the median, quartiles, interquartile range, and range using example data sets. Key steps include ordering the data, finding the median (Q2), splitting data into lower and upper halves, calculating medians for each half to determine the lower (Q1) and upper (Q3) quartiles, and using the quartiles to derive the interquartile range. Box-and-whisker plots are then introduced as a visual way to represent the spread and central tendency of data through boxes and whiskers denoting quartiles, median, and outliers.
More Related Content
Viewers also liked
Malimu variance and standard deviation
This document discusses variance and standard deviation. It defines variance as a measure of how data points differ from the mean. It explains that variance can show how two data sets that have the same mean and median can still be different. The document then provides formulas and examples for calculating variance and standard deviation. It states that standard deviation is a measure of variation from the mean and that a higher standard deviation indicates more spread and less consistency in the data.
The Interpretation Of Quartiles And Percentiles July 2009
The document discusses measures of central tendency and dispersion used to summarize data, including the mean, median, mode, range, quartiles, and percentiles. It explains that the mean is best for values representing magnitudes, the median for ranking, and the mode for popularity. Quartiles and percentiles divide a sorted data set into four and one hundred equal parts respectively. A high percentile is desirable for exams but not waiting times, while a low percentile is preferable for race times. Together these statistics provide a concise overview of a data set.
Variance And Standard Deviation
The document introduces the concepts of variance and standard deviation. Variance is a statistical measure that quantifies how far observations in a data set spread out from the mean or average value. It is calculated by taking the average of the squared differences from the mean. Standard deviation is the square root of variance and represents how dispersed the values in a data set are from the mean. The document provides examples of computing variance and standard deviation to illustrate these statistical concepts.
Grouped Mean Median Mode
A coffee shop conducted a two-day survey to determine the average number of cappuccinos made per hour. A histogram showed the frequency of cappuccinos made within various hourly intervals. To calculate the average, interval midpoints were determined and multiplied by the frequencies. The total of these products was divided by the total frequency, determining that the average number of cappuccinos made per hour was 10.
Mean, Median, Mode: Measures of Central Tendency
There are three common measures of central tendency: mean, median, and mode. The mean is the average value found by dividing the sum of all values by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the value that occurs most frequently. Each measure provides a single number to represent the central or typical value in a data set.
Measures of central tendency
Here are the modes for the three examples:
1. The mode is 3. This value occurs most frequently among the number of errors committed by the typists.
2. The mode is 82. This value occurs most frequently among the number of fruits yielded by the mango trees.
3. The mode is 12 and 15. These values occur most frequently among the students' quiz scores.
Standard Deviation and Variance
The document discusses how to calculate standard deviation and variance for both ungrouped and grouped data. It provides step-by-step instructions for finding the mean, deviations from the mean, summing the squared deviations, and using these values to calculate standard deviation and variance through standard formulas. Standard deviation measures how spread out numbers are from the mean, while variance is the square of the standard deviation.
Viewers also liked (7)
The Interpretation Of Quartiles And Percentiles July 2009
The Interpretation Of Quartiles And Percentiles July 2009
Similar to 2 7 exploratory data analysis
Overview Of Quartile.pptx
The document discusses quartiles, which divide a dataset into four equal parts. There are three quartiles: the first quartile (Q1) divides the data so that 25% falls below it; the second quartile is the median, which halves the data; and the third quartile (Q3) divides the data so that 75% falls below it. Formulas are provided for calculating quartiles for both ungrouped and grouped data. Examples of calculating quartiles from datasets are also shown.
TSTD 6251 Fall 2014SPSS Exercise and Assignment 120 PointsI.docx
TSTD 6251 Fall 2014
SPSS Exercise and Assignment 1
20 Points
In this class, we are going to study descriptive summary statistics and learn how to construct box plot. We are still working with univariate variable for this exercise.
Practice Example:
Admission receipts (in million of dollars) for a recent season are given below for the
n =
30 major league baseball teams:
19.4 26.6 22.9 44.5 24.4 19.0 27.5 19.9 22.8 19.0 16.9 15.2 25.7 19.0 15.5 17.1 15.6 10.6 16.2 15.6 15.4 18.2 15.5 14.2 9.5 9.9
10.7 11.9 26.7 17.5
Require:
a. Compute the mean, variance and standard deviation.
b. Find the sample median, first quartile, and third quartile.
c. Construct a boxplot and interpret the distribution of the data.
d. Discuss the distribution of this set of data by examining kurtosis and skewness
statistics, such as if the distribution is skewed to one side of the distribution, and if the
distribution shows a peaked/skinny curve or a spread out/flat curve.
SPSS Procedures for Computing Summary Statistics
:
Enter the 30 data values in the first column of SPSS
Data View
Tab
Variable View
and name this variable
receipts
Adjust
Decimals
to 3 decimal points
Type
Admission Receipts
($ mn)
in the
Label
column for output viewer
Return to
Data View
and click
A
nalyze
on the menu bar
Click the second menu
D
e
scriptive Statistics
Click
F
requencies …
Move
Admission Receipts
to the
Variable(s)
list by clicking the arrow button
Click
S
tatistics …
button at the top of the dialog box
Now, you can select the descriptive statistics according to what the question requires. For this practice question, it requires central tendency, dispersion, percentile and distribution statistics, so we click all the boxes
except for
P
ercentile(s): and Va
l
ues are group midpoints
.
Click
Continue
to return to the
Frequencies
dialog box
Click
OK
to generate descriptive statistic output which is pasted below:
The first table provides summary statistics and the second table lists frequencies, relative frequencies and cumulative frequencies. The statistics required for solving this problem are highlighted in red.
Statistics
Admission Receipts
N
Valid
30
Missing
0
Mean
18.76333
Std. Error of Mean
1.278590
Median
17.30000
Mode
19.000
Std. Deviation
7.003127
Variance
49.043782
Skewness
1.734
Std. Error of Skewness
.427
Kurtosis
5.160
Std. Error of Kurtosis
.833
Range
35.000
Minimum
9.500
Maximum
44.500
Sum
562.900
Percentiles
10
10.61000
20
14.40000
25
15.35000
30
15.50000
40
15.84000
50
17.30000
60
19.00000
70
19.75000
75
22.82500
80
24.10000
90
26.69000
Admission Receipts
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
9.500
1
3.3
3.3
3.3
9.900
1
3.3
3.3
6.7
10.600
1
3.3
3.3
10.0
10.700
1
3.3
3.3
13.3
11.900
1
3.3
3.3
16.7
14.200
1
3.3
3.3
20.0
15.2.
3.3 percentiles and boxandwhisker plot
The document defines percentiles and how they divide data into hundredths, with quartiles specifically dividing data into fourths. It describes how to compute quartiles and the interquartile range. Finally, it explains how to create and interpret box-and-whisker plots using the five number summary to visually depict the spread and symmetry of a data set.
Ejercicio resuelto-de-estadc3adstica-descriptiva1
The document provides information and instructions for analyzing student exam score data. It includes:
1) A table of 80 exam scores ranging from 53 to 97.
2) Instructions to calculate descriptive statistics like minimum, maximum, range, and percentiles of the scores.
3) Directions to construct a frequency distribution table and histogram of the scores binned into intervals of 5.
4) A calculation of measures of central tendency (mean, median, mode) and dispersion (variance, standard deviation) of the scores.
5) An analysis of the distribution's asymmetry and kurtosis.
Statistic and probability 2
This is very important presentation on stem and leaf, histogram, why we use them how we use them and the tool that is used to draw these.
Lecture-2 Descriptive Statistics-Box Plot Descriptive Measures.pdf
This is a book of probability and statisticsThis is a book of probability and statisticsThis is a book of probability and statisticsThis is a book of probability and statistics
Statistics (Measures of Dispersion)
The document provides information about measures of central tendency (mean, median, mode) and measures of dispersion (range, quartiles, variance, standard deviation) using examples of data distributions. It defines key terms like mean, median, mode, range, quartiles, variance and standard deviation. It also shows how to calculate and interpret these measures of central tendency and dispersion using sample data sets.
Chapter 1 descriptive_stats_2_rev_2009
This document discusses three methods for graphically displaying data: stem-and-leaf displays, histograms, and box plots. It provides instructions on how to construct each type of graph and describes what each graph conveys visually about a dataset. Stem-and-leaf displays show the distribution of values, histograms summarize frequency distributions of quantitative variables, and box plots simultaneously describe the center, spread, and outliers of a dataset.
Summarizing Data : Listing and Grouping pdf
Introduction
Descriptive Statistics describe basic features of the data gathered from an experimental study in various ways.
They provide simple summaries about the sample via graphs and numbers, mainly measures of center and variation.
Together with graphics analysis (histograms, bar plots, pie-charts), they are the cornerstone of quantitative data analysis.
Tables (frequency distributions, stem-and-leaf plots, …) that summarize the data.
Graphical representations of the data (histograms, bar plots, pie-charts).
Summary statistics (numbers) which summarize the data
The Frequency distribution table.pptx
- A frequency distribution organizes data into classes and displays the frequency of observations in each class.
- Grouped data uses classes with cut-offs to group interval or ratio level data, while ungrouped data lists each observation individually for smaller data sets.
- To make a frequency distribution, the data's range is found and classes are determined. Each observation is tallied and frequencies per class are calculated. This displays the distribution of the data.
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.
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.
C2 st lecture 13 revision for test b handout
This document provides an outline for a lecture series revising key concepts for Test B, including:
- Pythagoras' theorem, trigonometry, sine and cosine rules, and calculating triangle areas.
- Probability, probability trees, and examples calculating probabilities of dice rolls.
- Descriptive statistics like mode, median, interquartile range, mean, absolute deviation, and standard deviation.
- Hypothesis testing using z-tests, t-tests, and chi-squared tests; including setting up hypotheses, finding critical values, calculating test statistics, and making conclusions.
The revision is in preparation for Standard Track Test B which will be held the week of April 21st.
Measures of Relative Standing and Boxplots
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 3: Describing, Exploring, and Comparing Data
3.3: Measures of Relative Standing and Boxplots
Box and-whisker-plots
This document provides instructions for constructing and interpreting box-and-whisker plots. It explains how to find the median, quartiles, interquartile range, and range using example data sets. Key steps include ordering the data, finding the median (Q2), splitting data into lower and upper halves, calculating medians for each half to determine the lower (Q1) and upper (Q3) quartiles, and using the quartiles to derive the interquartile range. Box-and-whisker plots are then introduced as a visual way to represent the spread and central tendency of data through boxes and whiskers denoting quartiles, median, and outliers.
Biostat_Chapter6_Part3.pdf Bio Statistics
This document provides an overview of the Kaplan-Meier estimator for survival analysis and includes two examples. It defines the Kaplan-Meier estimator and assumptions. Example 1 derives the Kaplan-Meier estimate from study data on time to death and finds the probability of surviving past 10 years is 85%, the minimum years for 75% survival is 13, and median survival is 18 years. Example 2 estimates survival functions for a clinical trial comparing a treatment to placebo and shows higher survival for the treatment group.
Freq & Histo
The document provides examples and explanations for creating different types of data displays, including stem-and-leaf plots, frequency tables, histograms, and cumulative frequency tables. It includes sample data sets and step-by-step instructions for making each type of display. Key terms defined include stem, leaf, frequency, interval, and cumulative frequency.
lecture8.ppt
This document provides summaries of key concepts related to statistical hypothesis testing and confidence intervals involving t-distributions. It discusses when to use a t-distribution versus a standard normal distribution, specifically when the population standard deviation is unknown and must be estimated from a sample. It provides examples of hypothesis tests and confidence intervals for a single population mean when the sample size is small as well as examples involving paired data. Key formulas are presented for t-tests, confidence intervals, and the t-distribution.
Lecture8
This document provides summaries of key concepts related to statistical hypothesis testing and confidence intervals involving t-distributions. It discusses when to use a t-distribution versus a standard normal distribution, specifically when the population standard deviation is unknown and must be estimated from a sample. It provides examples of hypothesis tests and confidence intervals for a single population mean when the sample size is small as well as examples involving paired data. Key formulas are presented for t-tests, confidence intervals, and the t-distribution.
Measures of Variation (Ungrouped Data)
Measures of Variation: Range Variance and Standard Deviation (Ungrouped Data) with quiz at the last three pages.
Similar to 2 7 exploratory data analysis (20)
TSTD 6251 Fall 2014SPSS Exercise and Assignment 120 PointsI.docx
TSTD 6251 Fall 2014SPSS Exercise and Assignment 120 PointsI.docx
Lecture-2 Descriptive Statistics-Box Plot Descriptive Measures.pdf
Lecture-2 Descriptive Statistics-Box Plot Descriptive Measures.pdf
More from Ken Kretsch
Classical probability
The document defines key probability concepts like events, outcomes, sample space, classical probability, and types of probability such as geometric and experimental probability. It provides examples to illustrate concepts like calculating the probability of outcomes for events like rolling dice, drawing cards, and spinning a spinner.
2 4 measures of center
This document discusses different methods for summarizing data, including measures of central tendency. It describes four common measures: mean, median, mode, and midrange. For each measure, it provides a definition and examples of how to calculate it from a set of data.
2 6 measure of position
This document discusses different measures of position and distribution in statistics including standard scores (z-scores), quartiles, deciles, and percentiles.
It defines standard scores as measuring how many standard deviations a value is from the mean. Quartiles divide a sorted data set into four equal parts, with the lower and upper quartiles marking the boundaries between the lower/upper half of data. Deciles divide data into 10 equal parts. Percentiles indicate the percentage of values in a data set that fall below a given value.
The document provides examples of how to calculate and interpret these different measures using sample data sets.
2 5 standard deviation
The document discusses measures of central tendency and variation such as mean, median, mode, range, standard deviation, and variance. It provides examples of calculating standard deviation and using the mean and standard deviation to build a normal distribution frequency table. Standard deviation measures how far values are from the mean, with about 2/3 of values within 1 standard deviation and 95% within 2 standard deviations of the mean. Outliers are values more than 2 standard deviations from the mean.
2 1 frequency table
The document discusses various ways of summarizing and displaying quantitative data, including through frequency tables, relative frequency tables, and two-way frequency tables. It provides examples and definitions for key terms related to frequency tables such as class boundaries, class midpoints, class width, marginal frequencies, and conditional relative frequency. The document also discusses how frequency tables can be used to validate data, explore trends, compare data over time or between samples.
2 3 depicting frequency tables
This document discusses different types of charts used to visualize qualitative and quantitative data, including histograms, bar charts, pie charts, frequency polygons, ogives, dotplots, and stem-and-leaf plots. It provides examples of how to construct each type of chart and compares their uses for different types of data. Key differences between chart types are outlined, such as histograms using bars to show frequencies and pie charts showing relative frequencies as wedges.
2 1 data
The document discusses primitive data types in Java including integers, floating point numbers, Booleans, characters, and strings. It also covers variables, their scope and declaration. Variables can store primitive values or object references. The document also discusses input/output in Java using Scanner to read from input streams like the keyboard.
2 1 expressions
An expression combines operands and operators. Arithmetic operators include addition, subtraction, multiplication, division, and remainder. Operators return values that can be assigned, used in other expressions, or passed to methods. If both operands are integers, the result is an integer, otherwise it is a double. Integer division returns the integer quotient while remainder returns the integer remainder. Operators follow PEMDAS order of operations. The string concatenation operator connects strings or mixes strings and other data types. Assignment statements store the result of an expression into a variable.
\\Dc hss2\staff\kretsch k\prob and stat\class materials\chapter 1\1-4 where d...
1. The document discusses key concepts in sampling and experiments including populations, parameters, statistics, variables, treatment and control groups, placebos, and bias.
2. It provides examples of experiments that could be conducted to test claims about reading improving school performance and characteristics affecting hair color and fun.
3. Types of sampling discussed include random, stratified, clustered, as well as self-selected and convenience sampling which are more prone to bias. Sources of bias are also outlined.
R:\ap java\class slides\chapter 1\1 2 java development
- Running a program can be done through compiling or interpreting. Compiling translates source code to machine code while interpreting reads and executes source code instructions.
- Java code execution involves compiling source code (.java files) to byte code (.class files) using a compiler (javac). The byte code is then interpreted by the Java run-time program (java) or an IDE like BlueJ to execute the program.
- Key aspects of Java development include the Java Development Kit (JDK), which includes the compiler and libraries, and BlueJ as an integrated development environment for designing, developing and testing Java software.
1 2 java development
- Running a program can be done through compiling or interpreting. Compiling translates source code to machine code while interpreting reads and executes source code instructions.
- Java code execution involves compiling source code (.java files) to byte code (.class files) using a compiler (javac). The byte code is then interpreted by the Java run-time program (java) or an IDE like BlueJ to execute the program.
- Key aspects of Java development include the Java Development Kit (JDK) which includes the compiler and libraries, and BlueJ as an integrated development environment for designing, developing and testing Java software.
Science, invention, and engineering
Science uncovers principles of nature through observation, experimentation, and theory to develop models and extend human understanding. Invention applies scientific discoveries to produce useful effects, devices, and processes. Engineering makes inventions practical for manufacture and widespread use through efficient and cost-effective designs that consider safety, durability, and mass production.
1 4 where do we get the data
The document discusses different methods for collecting data including observation, experiments, and surveys. It explains key concepts in experimental design such as variables, treatment and control groups, random assignment, placebos, sampling techniques, and potential sources of bias. Specifically, it covers census vs sample data collection, controlling and varying variables, strategies for random and stratified sampling, and how selection bias can influence results.
1 1 data
The document discusses the steps involved in conducting a statistical investigation to test a claim:
1) State the specific, measurable, and comparable claim and identify an appropriate benchmark
2) Collect relevant data from the population or a representative sample
3) Calculate appropriate statistical values from the data
4) Run statistical tests to determine whether to accept or reject the initial claim
It also provides definitions and classifications that are important for statistical analysis, such as the differences between populations and samples, parameters and statistics, and nominal, ordinal, interval, and ratio data types.
Programming model
The document discusses programming models and provides examples. It outlines common programming elements like input data, output, processing, and data storage. It then gives homework to describe the specific inputs, outputs, processing, and data used for a programmable thermostat, Facebook, and a chosen game.
More from Ken Kretsch (15)
\\Dc hss2\staff\kretsch k\prob and stat\class materials\chapter 1\1-4 where d...
\\Dc hss2\staff\kretsch k\prob and stat\class materials\chapter 1\1-4 where d...
R:\ap java\class slides\chapter 1\1 2 java development
R:\ap java\class slides\chapter 1\1 2 java development
2 7 exploratory data analysis
- 8. Two Ways to Characterize Data x i < X – 2s x i > X + 2x x i < Q1 – 1.5 IQR x i > Q3 + 1.5 IQR Outliers Distribution spread, frequency diagram, bar chart and Box and whiskers diagram Picture X and s Minimum, first quartile, median, third quartile, maximum Statistics Mean and standard deviation 5-number summary