Binomial distributions
•
0 likes•410 views
The document discusses the binomial distribution and its key properties: 1) Outcomes are success or not success, with a fixed probability of success. 2) The number of trials is fixed. 3) Trials are independent. It provides the mean and standard deviation formulas, and explains how to calculate the probability of a binomial event occurring exactly, at least, or at most a certain number of times using the binomial probability formula. An example calculates the probability of a team winning 6 or more games in 8 tries with a 40% chance of winning each game.
Report
Share
Report
Share
Download to read offline
Recommended
4.5 multiplying and dividng by powers of 10
This document discusses multiplying and dividing by powers of ten. It provides examples of multiplying and dividing whole numbers and decimals by powers of ten. The key rules are:
1) For multiplication, move the decimal point to the right when multiplying by a whole number power of ten, and to the left when multiplying by a decimal power of ten.
2) For division, move the decimal point to the left when dividing by a whole number power of ten, and to the right when dividing by a decimal power of ten.
3) Examples are provided to demonstrate applying these rules to calculate answers through mental math.
Multiplication phone
The document discusses the mathematical operation of multiplication. Multiplication is defined as the operation where a number indicates how many times another number is added to itself. The document then provides tables showing the multiplication facts for multiplying any single digit number from 0 to 12 by any other single digit number from 0 to 12.
Multiplication
The document discusses learning multiplication facts through a multiplication chart and games. It provides options to review tricks for multiplying by 6s, 7s, 8s, 9s, and 10s or to play games to practice multiplication facts. Clicking on different areas of the chart or games allows the user to learn facts and get practice with multiplication.
Multiply divide scientific notation edmodo 2013 14
This document provides instructions and examples for performing calculations using scientific notation. It explains how to multiply and divide terms in scientific notation by multiplying or dividing the coefficients and using exponent properties. It then provides examples of multiplying and dividing terms in scientific notation, such as 4 x 103 • 3 x 104 = 12 x 107, and their simplified forms.
Day 9 factoring with gcf
This document provides instructions and examples for factoring polynomials using the greatest common factor (GCF) method. It begins with examples to factor, then provides steps for finding the GCF of terms and factoring a polynomial using the GCF. Examples are worked through, factoring polynomials with variables like x, q, a. The document concludes by discussing how factoring relates to graphing polynomials and finding roots.
PUZZLE IN C PROGRAMMING
# N queens problem in c using BACK TRACKING
NO two queens are in the same row,same column,same diagonal.
using the c program to find the solution for N queens problem through back tracking.
queens problem is an example for back tracking in c langauage
Puzzle in c program
This document discusses solving the N Queens problem using backtracking in C. It presents the N Queens problem, which involves placing N queens on an N x N chessboard so that no two queens share the same row, column, or diagonal. It then provides the C code for a backtracking algorithm to find all solutions to the N Queens problem for a given board size N. The code uses a recursive function to try placing queens one by one, checking for conflicts, and backtracking when it reaches a dead end.
Lesson 7 multiplying decimals by 10, 100, 1000, 10 000
This document discusses multiplying decimals by powers of ten. It explains that multiplying a decimal by 10 moves the decimal point one place to the right, multiplying by 100 moves it two places to the right, and multiplying by 1000 moves it three places to the right. Examples are provided of multiplying various decimals by 10, 100, 1000 and 10,000 to demonstrate this pattern. Conversions between meters, decimeters, centimeters and millimeters are also explained.
Recommended
4.5 multiplying and dividng by powers of 10
This document discusses multiplying and dividing by powers of ten. It provides examples of multiplying and dividing whole numbers and decimals by powers of ten. The key rules are:
1) For multiplication, move the decimal point to the right when multiplying by a whole number power of ten, and to the left when multiplying by a decimal power of ten.
2) For division, move the decimal point to the left when dividing by a whole number power of ten, and to the right when dividing by a decimal power of ten.
3) Examples are provided to demonstrate applying these rules to calculate answers through mental math.
Multiplication phone
The document discusses the mathematical operation of multiplication. Multiplication is defined as the operation where a number indicates how many times another number is added to itself. The document then provides tables showing the multiplication facts for multiplying any single digit number from 0 to 12 by any other single digit number from 0 to 12.
Multiplication
The document discusses learning multiplication facts through a multiplication chart and games. It provides options to review tricks for multiplying by 6s, 7s, 8s, 9s, and 10s or to play games to practice multiplication facts. Clicking on different areas of the chart or games allows the user to learn facts and get practice with multiplication.
Multiply divide scientific notation edmodo 2013 14
This document provides instructions and examples for performing calculations using scientific notation. It explains how to multiply and divide terms in scientific notation by multiplying or dividing the coefficients and using exponent properties. It then provides examples of multiplying and dividing terms in scientific notation, such as 4 x 103 • 3 x 104 = 12 x 107, and their simplified forms.
Day 9 factoring with gcf
This document provides instructions and examples for factoring polynomials using the greatest common factor (GCF) method. It begins with examples to factor, then provides steps for finding the GCF of terms and factoring a polynomial using the GCF. Examples are worked through, factoring polynomials with variables like x, q, a. The document concludes by discussing how factoring relates to graphing polynomials and finding roots.
PUZZLE IN C PROGRAMMING
# N queens problem in c using BACK TRACKING
NO two queens are in the same row,same column,same diagonal.
using the c program to find the solution for N queens problem through back tracking.
queens problem is an example for back tracking in c langauage
Puzzle in c program
This document discusses solving the N Queens problem using backtracking in C. It presents the N Queens problem, which involves placing N queens on an N x N chessboard so that no two queens share the same row, column, or diagonal. It then provides the C code for a backtracking algorithm to find all solutions to the N Queens problem for a given board size N. The code uses a recursive function to try placing queens one by one, checking for conflicts, and backtracking when it reaches a dead end.
Lesson 7 multiplying decimals by 10, 100, 1000, 10 000
This document discusses multiplying decimals by powers of ten. It explains that multiplying a decimal by 10 moves the decimal point one place to the right, multiplying by 100 moves it two places to the right, and multiplying by 1000 moves it three places to the right. Examples are provided of multiplying various decimals by 10, 100, 1000 and 10,000 to demonstrate this pattern. Conversions between meters, decimeters, centimeters and millimeters are also explained.
Binomial Probability Distributions
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 5: Discrete Probability Distribution
5.2 - Binomial Probability Distributions
Practice Test 2 Solutions
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 2 Solutions
Chapter 4: Probability
Stats chapter 8
The document summarizes key concepts about the binomial and geometric distributions:
The binomial distribution models the number of successes in a fixed number of yes/no trials where the probability of success is constant. The geometric distribution models the number of trials until the first success. Both have calculators functions and follow patterns for mean, standard deviation, and normal approximations. Formulas for probability mass and cumulative distribution functions are provided.
Stats chapter 8
The document summarizes key concepts about the binomial and geometric distributions:
The binomial distribution models the number of successes in a fixed number of yes/no trials where the probability of success is constant. The geometric distribution models the number of trials until the first success. Both have calculators functions and follow patterns for mean, standard deviation, and normal approximations. Formulas for probability mass and cumulative distribution functions are provided.
Final examexamplesapr2013
The document contains statistics lab report scores for 8 students who spent varying amounts of time preparing. It includes the regression equation relating hours spent to score and predicts a score for someone who spent 1 hour. It also defines the correlation coefficient and explains it measures the strength of the linear relationship between two variables.
sample space formation.pdf
This document discusses counting techniques and probability distributions. It introduces counting rules for permutations, combinations, and power principle when arranging objects. It then covers the binomial probability distribution and its application to Bernoulli trials. The Poisson distribution is presented as the limiting form of the binomial distribution. Finally, the normal distribution and standard normal distribution are described. Examples are provided to demonstrate calculating probabilities and areas under the normal curve.
Binomial probability distributions
The document provides information about binomial probability distributions including:
- Binomial experiments have a fixed number (n) of independent trials with two possible outcomes and a constant probability (p) of success.
- The binomial probability distribution gives the probability of getting exactly x successes in n trials. It is calculated using the binomial coefficient and p and q=1-p.
- The mean, variance and standard deviation of a binomial distribution are np, npq, and √npq respectively.
- Examples demonstrate calculating probabilities of outcomes for binomial experiments and determining if results are significantly low or high using the range rule of μ ± 2σ.
Use of binomial probability distribution
The document provides examples of using the binomial probability distribution. It first gives an example of calculating the probability of a certain number of customers paying by credit card out of a sample of 10 customers. Another example calculates the probability of getting exactly 2 fours when a die is tossed 5 times. Further examples demonstrate calculating the mean and variance of a binomial distribution given n and p, and calculating n and p given the mean and variance.
Chapter 5.pptx
This document provides information about binomial and Poisson distributions. It includes examples of calculating probabilities for binomial distributions using the binomial probability formula and binomial tables. It also provides the key characteristics and formula for the Poisson distribution. The mean, variance and standard deviation are defined for binomial distributions. Examples are provided to demonstrate calculating these values.
Pattern recognition binoy 05-naive bayes classifier
The Naive Bayes classifier is a simple probabilistic classifier that assumes independence between features. It is easy to build and performs well even when the independence assumption is violated. The algorithm involves estimating the probability of each feature value for each class from the training data. To classify new examples, it calculates the probability of the example for each class using the Bayes rule and assumes the class with the highest probability. Despite its simplicity, Naive Bayes often performs surprisingly well and is widely used for tasks like text and spam classification.
Stat 130 chi-square goodnes-of-fit test
- The chi-square goodness-of-fit test can be used to determine if a frequency distribution fits a specific pattern or theoretical distribution. It compares observed frequencies to expected frequencies.
- To perform the test, the chi-square statistic is calculated using the formula (O-E)^2/E, where O is the observed frequency and E is the expected frequency. This value is then compared to a critical value from the chi-square distribution based on the degrees of freedom.
- If the chi-square statistic exceeds the critical value, the null hypothesis that the observed and expected frequencies are the same is rejected, indicating a poor fit between the observed and expected distributions.
Probability QA 8
JEE Mathematics / Lakshmikanta Satapathy / Questions and Answers on probability part 8 which includes Bernoulli trials and Binomial distribution
binomialprobabilitydistribution-200508182110 (1).pdf
The document discusses the binomial probability distribution. It defines a binomial experiment as having n repeated trials with two possible outcomes (success/failure), a constant probability p of success on each trial, and independent trials. It provides examples of binomial experiments and defines binomial random variables and distributions. It also gives examples of calculating probabilities of outcomes using the binomial distribution formula and solving for n and p given the mean and variance.
Genetic algorithm
The document describes using a genetic algorithm to solve the problem of coloring a checkboard with no adjacent squares having the same color. It initializes a population of random colorings, calculates their fitness based on constraints, performs selection, crossover and mutation to generate a new population, and iterates until finding a solution with optimal fitness. After 47 generations, it achieves the optimal solution of no adjacent squares having the same color.
discrete and continuous probability distributions pptbecdoms-120223034321-php...
This document discusses various probability distributions including discrete and continuous distributions. It covers the binomial, hypergeometric, Poisson, and normal distributions. For each distribution, it provides the characteristics and formulas, and examples of how to calculate probabilities using the distributions and probability tables or software. It also illustrates how the parameters impact the shape of the distributions. The goal is to help readers apply different probability distributions to problems and compute probabilities.
Probability unit2.pptx
Probability is a numerical measure of how likely an event is to occur. It is used in business to quantify uncertainty and make predictions. Some common applications in business include predicting sales based on price changes, estimating increases in productivity from new methods, and assessing the likelihood of investments being profitable. Probability is calculated on a scale of 0 to 1, with values closer to 1 indicating an event is more certain or likely to occur.
Binomial probability distribution
The document discusses the binomial probability distribution. It defines a binomial experiment as having n repeated trials with two possible outcomes (success/failure), a constant probability p of success on each trial, and independent trials. It provides examples of binomial experiments like coin tosses and MCQ questions. The number of successes is a binomial random variable with possible values from 0 to n. The binomial distribution gives the probability of x successes based on n, p, and the formula P(x) = (nCx) * px * q(n-x). It demonstrates calculating probabilities for different values of x.
Statistics Methods and Probability Presentation - Math 201.pptx
The document discusses various statistical concepts including frequency distribution, histograms, pie charts, mean, median, and probability. It provides examples and solutions to demonstrate how to calculate and interpret these concepts. For example, it shows how to calculate the median height from a grouped frequency table with 51 observations distributed across various height ranges. It also calculates the probability of rolling an even number on a standard six-sided die.
Sampling means
This document discusses key concepts related to sampling means, including that bias can occur if sample proportions or means are skewed from the population values, the central limit theorem states that sample means will follow a normal distribution as sample size increases, and the sampling distribution of sample means from any population will be approximately normal in shape with standard deviation equal to the population standard deviation divided by the square root of the sample size.
Sampling distributions
This document defines key terms related to sampling distributions, including population, parameters, statistics, population proportion, and sample proportion. It explains that as more samples are taken from a population, the sample proportions will begin to form a bell-shaped curve centered around the true population proportion. The mean of all sample proportions equals the population proportion. Under certain conditions where the sample size is large enough and neither the sample proportion or population proportion is too close to 0 or 1, the sampling distribution can be approximated as a normal distribution, allowing us to calculate a z-score to determine how many standard deviations a sample proportion is from the population proportion.
More Related Content
Similar to Binomial distributions
Binomial Probability Distributions
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 5: Discrete Probability Distribution
5.2 - Binomial Probability Distributions
Practice Test 2 Solutions
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 2 Solutions
Chapter 4: Probability
Stats chapter 8
The document summarizes key concepts about the binomial and geometric distributions:
The binomial distribution models the number of successes in a fixed number of yes/no trials where the probability of success is constant. The geometric distribution models the number of trials until the first success. Both have calculators functions and follow patterns for mean, standard deviation, and normal approximations. Formulas for probability mass and cumulative distribution functions are provided.
Stats chapter 8
The document summarizes key concepts about the binomial and geometric distributions:
The binomial distribution models the number of successes in a fixed number of yes/no trials where the probability of success is constant. The geometric distribution models the number of trials until the first success. Both have calculators functions and follow patterns for mean, standard deviation, and normal approximations. Formulas for probability mass and cumulative distribution functions are provided.
Final examexamplesapr2013
The document contains statistics lab report scores for 8 students who spent varying amounts of time preparing. It includes the regression equation relating hours spent to score and predicts a score for someone who spent 1 hour. It also defines the correlation coefficient and explains it measures the strength of the linear relationship between two variables.
sample space formation.pdf
This document discusses counting techniques and probability distributions. It introduces counting rules for permutations, combinations, and power principle when arranging objects. It then covers the binomial probability distribution and its application to Bernoulli trials. The Poisson distribution is presented as the limiting form of the binomial distribution. Finally, the normal distribution and standard normal distribution are described. Examples are provided to demonstrate calculating probabilities and areas under the normal curve.
Binomial probability distributions
The document provides information about binomial probability distributions including:
- Binomial experiments have a fixed number (n) of independent trials with two possible outcomes and a constant probability (p) of success.
- The binomial probability distribution gives the probability of getting exactly x successes in n trials. It is calculated using the binomial coefficient and p and q=1-p.
- The mean, variance and standard deviation of a binomial distribution are np, npq, and √npq respectively.
- Examples demonstrate calculating probabilities of outcomes for binomial experiments and determining if results are significantly low or high using the range rule of μ ± 2σ.
Use of binomial probability distribution
The document provides examples of using the binomial probability distribution. It first gives an example of calculating the probability of a certain number of customers paying by credit card out of a sample of 10 customers. Another example calculates the probability of getting exactly 2 fours when a die is tossed 5 times. Further examples demonstrate calculating the mean and variance of a binomial distribution given n and p, and calculating n and p given the mean and variance.
Chapter 5.pptx
This document provides information about binomial and Poisson distributions. It includes examples of calculating probabilities for binomial distributions using the binomial probability formula and binomial tables. It also provides the key characteristics and formula for the Poisson distribution. The mean, variance and standard deviation are defined for binomial distributions. Examples are provided to demonstrate calculating these values.
Pattern recognition binoy 05-naive bayes classifier
The Naive Bayes classifier is a simple probabilistic classifier that assumes independence between features. It is easy to build and performs well even when the independence assumption is violated. The algorithm involves estimating the probability of each feature value for each class from the training data. To classify new examples, it calculates the probability of the example for each class using the Bayes rule and assumes the class with the highest probability. Despite its simplicity, Naive Bayes often performs surprisingly well and is widely used for tasks like text and spam classification.
Stat 130 chi-square goodnes-of-fit test
- The chi-square goodness-of-fit test can be used to determine if a frequency distribution fits a specific pattern or theoretical distribution. It compares observed frequencies to expected frequencies.
- To perform the test, the chi-square statistic is calculated using the formula (O-E)^2/E, where O is the observed frequency and E is the expected frequency. This value is then compared to a critical value from the chi-square distribution based on the degrees of freedom.
- If the chi-square statistic exceeds the critical value, the null hypothesis that the observed and expected frequencies are the same is rejected, indicating a poor fit between the observed and expected distributions.
Probability QA 8
JEE Mathematics / Lakshmikanta Satapathy / Questions and Answers on probability part 8 which includes Bernoulli trials and Binomial distribution
binomialprobabilitydistribution-200508182110 (1).pdf
The document discusses the binomial probability distribution. It defines a binomial experiment as having n repeated trials with two possible outcomes (success/failure), a constant probability p of success on each trial, and independent trials. It provides examples of binomial experiments and defines binomial random variables and distributions. It also gives examples of calculating probabilities of outcomes using the binomial distribution formula and solving for n and p given the mean and variance.
Genetic algorithm
The document describes using a genetic algorithm to solve the problem of coloring a checkboard with no adjacent squares having the same color. It initializes a population of random colorings, calculates their fitness based on constraints, performs selection, crossover and mutation to generate a new population, and iterates until finding a solution with optimal fitness. After 47 generations, it achieves the optimal solution of no adjacent squares having the same color.
discrete and continuous probability distributions pptbecdoms-120223034321-php...
This document discusses various probability distributions including discrete and continuous distributions. It covers the binomial, hypergeometric, Poisson, and normal distributions. For each distribution, it provides the characteristics and formulas, and examples of how to calculate probabilities using the distributions and probability tables or software. It also illustrates how the parameters impact the shape of the distributions. The goal is to help readers apply different probability distributions to problems and compute probabilities.
Probability unit2.pptx
Probability is a numerical measure of how likely an event is to occur. It is used in business to quantify uncertainty and make predictions. Some common applications in business include predicting sales based on price changes, estimating increases in productivity from new methods, and assessing the likelihood of investments being profitable. Probability is calculated on a scale of 0 to 1, with values closer to 1 indicating an event is more certain or likely to occur.
Binomial probability distribution
The document discusses the binomial probability distribution. It defines a binomial experiment as having n repeated trials with two possible outcomes (success/failure), a constant probability p of success on each trial, and independent trials. It provides examples of binomial experiments like coin tosses and MCQ questions. The number of successes is a binomial random variable with possible values from 0 to n. The binomial distribution gives the probability of x successes based on n, p, and the formula P(x) = (nCx) * px * q(n-x). It demonstrates calculating probabilities for different values of x.
Statistics Methods and Probability Presentation - Math 201.pptx
The document discusses various statistical concepts including frequency distribution, histograms, pie charts, mean, median, and probability. It provides examples and solutions to demonstrate how to calculate and interpret these concepts. For example, it shows how to calculate the median height from a grouped frequency table with 51 observations distributed across various height ranges. It also calculates the probability of rolling an even number on a standard six-sided die.
Similar to Binomial distributions (20)
Pattern recognition binoy 05-naive bayes classifier
Pattern recognition binoy 05-naive bayes classifier
binomialprobabilitydistribution-200508182110 (1).pdf
binomialprobabilitydistribution-200508182110 (1).pdf
discrete and continuous probability distributions pptbecdoms-120223034321-php...
discrete and continuous probability distributions pptbecdoms-120223034321-php...
Statistics Methods and Probability Presentation - Math 201.pptx
Statistics Methods and Probability Presentation - Math 201.pptx
More from Ulster BOCES
Sampling means
This document discusses key concepts related to sampling means, including that bias can occur if sample proportions or means are skewed from the population values, the central limit theorem states that sample means will follow a normal distribution as sample size increases, and the sampling distribution of sample means from any population will be approximately normal in shape with standard deviation equal to the population standard deviation divided by the square root of the sample size.
Sampling distributions
This document defines key terms related to sampling distributions, including population, parameters, statistics, population proportion, and sample proportion. It explains that as more samples are taken from a population, the sample proportions will begin to form a bell-shaped curve centered around the true population proportion. The mean of all sample proportions equals the population proportion. Under certain conditions where the sample size is large enough and neither the sample proportion or population proportion is too close to 0 or 1, the sampling distribution can be approximated as a normal distribution, allowing us to calculate a z-score to determine how many standard deviations a sample proportion is from the population proportion.
Geometric distributions
This document defines and provides examples of a geometric distribution. It explains that a geometric distribution models outcomes of repeated Bernoulli trials where the probability of success is constant and each trial is independent. The key properties are that the trials continue until the first success occurs and there is no fixed number of trials. It gives the mean and standard deviation formulas for a geometric distribution and provides examples calculating probabilities of sequences of outcomes like having 5 boys before the first girl.
Means and variances of random variables
This document discusses means, variances, and standard deviations of random variables. It provides the formulas for calculating the mean and variance of a random variable. For the mean, it is the sum of each outcome multiplied by its probability. For the variance, it is the sum of the squared differences of each outcome from the mean multiplied by its probability. An example is provided to demonstrate calculating the standard deviation of outcomes from selling cars. The document also outlines rules for how the mean and variance are affected when combining or transforming random variables through addition, subtraction, multiplication, and addition of a constant.
Simulation
1) The document defines simulation as imitating chance behavior based on an accurate model of a random phenomenon.
2) It outlines the steps of simulation: stating the problem, assumptions, assigning digits to represent outcomes, simulating many repetitions, and stating a conclusion based on experimental evidence.
3) As an example, it considers the probability that a female student will be chosen from an AP Stats class to bring candy, assuming 80% of the class is male. It shows how digits could be assigned to represent the male and female outcomes.
General probability rules
This document defines key probability terms and provides 6 general probability rules. The rules state that: 1) A probability is between 0 and 1, 2) The probabilities of all possible outcomes sum to 1, 3) The probability of events A or B is the sum of their individual probabilities minus their intersection, 4) The probability of the complement of an event is 1 minus the original probability, 5) The probability of independent events occurring together is the product of their individual probabilities, and 6) The probability of disjoint events is the sum of their individual probabilities.
Planning and conducting surveys
This document discusses key concepts related to survey sampling including populations, samples, random selection, and sources of bias. It defines a population as the entire group being studied, and a sample as the subset used to make inferences about the population. Random selection is described as a process that gives all members of the population an equal chance of being selected to reduce bias. Common sources of bias like convenience samples and voluntary response samples are discussed. Strategies for reducing bias like simple random sampling, stratified random sampling, and cluster sampling are also outlined.
Overview of data collection methods
This document discusses different methods for collecting data for studies, including censuses, sample surveys, experiments, and observational studies. It notes that the method must be chosen based on clarifying the research question and deciding on a plan for data collection and analysis. It also outlines three main factors to consider when selecting a data collection method: the purpose of the evaluation, the evaluation design, and available project resources.
Exploring bivariate data
This document discusses analyzing and summarizing relationships between two quantitative variables (bivariate data) using scatterplots. It covers key topics like correlation, linear regression lines, residuals, outliers and influential points. Scatterplots display the relationship between two variables and can show positive or negative linear associations or no relationship. Correlation coefficients measure the strength and direction of linear relationships, while regression lines predict variable relationships. Residual plots assess linearity and outliers.
Normal probability plot
A normal probability plot provides an assessment of whether a normal distribution model fits a data set well. It involves arranging data from smallest to largest, finding the percentile and z-score for each value, and plotting the data points against their z-scores. The closer the plot forms a straight line, the better the normal model fits the data.
Exploring data stemplot
This document discusses different graphical methods for displaying categorical and quantitative data distributions, including pie charts, bar graphs, stem-and-leaf plots, back-to-back stem-and-leaf plots, and modifications to stem-and-leaf plots like splitting stems or trimming digits. It provides instructions on how to construct stem-and-leaf plots, including separating data into stems and leaves and ordering them, and notes that stem-and-leaf plots work best for smaller, less spread out data sets.
Exploring data other plots
This document discusses different types of graphs for describing data distributions: relative frequency histograms show the percent of counts in each bin while cumulative relative frequency histograms called ogives show the cumulative percents; time plots display observations over time with the horizontal axis always being time and can reveal trends over multiple observations.
Exploring data histograms
Histograms are used to graphically represent the distribution of data by dividing it into intervals and counting the frequency of data points within each interval. To construct a histogram, the data is divided into bins of equal width and a frequency table is made listing the count in each bin. The bins are then graphed on the x-axis with their corresponding frequencies on the y-axis. Patterns in histograms can reveal the center, shape, spread and skewness of the distribution through characteristics like peaks, symmetry, outliers and the range of values.
Calculating percentages from z scores
This document provides instructions for calculating percentages from z-scores. It explains how to find a percentile using a normal density curve by first calculating the z-score and then using a table or calculator to find the percentile. It also describes how to find the percent of data between two z-scores by calculating each z-score, finding the percentile value for each, and subtracting the percentiles.
Density curve
A density curve is a smooth curve drawn over a histogram that represents a probability distribution, with an area of 1. It can take different shapes like a normal bell curve or a uniform rectangle. A normal distribution is a bell-shaped density curve where we can use z-scores to determine population properties or the percentile rank of a data point. If data fits a normal distribution, the 68-95-99.7 rule applies, meaning 68%, 95%, and 99.7% of data falls within 1, 2, and 3 standard deviations of the mean, respectively.
Standardizing scores
The document discusses how to calculate z-scores, which measure how many standard deviations a data point is from the mean. It provides examples of calculating z-scores for test scores when given the class mean of 80, standard deviation of 6.07. A score of 89 is 1.482 standard deviations above the mean, while a score of 69 is 1.812 standard deviations below the mean.
Intro to statistics
Statistics is the science and art of learning from data. It involves collecting and analyzing data to describe variables and examine relationships between variables. There are different types of variables, including categorical and quantitative variables, and different ways of collecting data, such as surveys, experiments, and observational studies. Graphs and numerical summaries are used to organize and make sense of the data. Statistical inference allows conclusions to be drawn from a sample to a larger population with some degree of uncertainty.
Describing quantitative data with numbers
1. Quantitative data can be summarized using measures of center (mean, median), spread (range, IQR, standard deviation), and position (quartiles, percentiles, z-scores).
2. The mean is more affected by outliers than the median. The median is more resistant to outliers and a better measure of center for skewed data.
3. Additional summaries like the five-number summary and boxplots provide a graphical view of the distribution and identify potential outliers.
Displaying quantitative data
This document provides guidance on visualizing and interpreting quantitative data using various graph types, including dot plots, stemplots, histograms, ogives, and time plots. It discusses how to construct each graph type and what features to examine, such as shape, outliers, center, and spread. Examples are provided for each graph type along with questions to check understanding.
A.2 se and sd
The document discusses standard error and standard deviation. It defines parameters as describing populations using Greek letters, while statistics describe samples using non-Greek letters. Standard error estimates the standard deviation of a statistic and is used to calculate confidence intervals and margin of error. It relies on sample statistics rather than population parameters. The central limit theorem states that for a large enough sample size from any population, the sampling distribution of the sample mean will be approximately normally distributed.
More from Ulster BOCES (20)
Binomial distributions
- 2. 4 Parts of a Binomial Distribution 1. Outcomes are success or not success 2. Probability of Success is Fixed 3. Fixed number of trials 4. Trials are Independent Notation: B(𝜇,𝜎) Mean of Binomial Distribution: Number of trials * Probability of Success E(X)= 𝜇 = 𝑛𝑝 Standard Deviation of Binomial Distribution: 𝜎 = 𝑛𝑝(1 − 𝑝) n= number of trials p=probability of success
- 3. Probability of a Binomial Event Occurring k times 𝑛 P(X=k) = ( 𝑘 )𝑝 𝑘 (1 − 𝑝) 𝑛−𝑘 Ex. The probability the team will win is 40%. What is the probability the team will win 6 of its next 8 games? Identify n,p,k n= number of trials (games) = 8 p = probability of success (winning) = 0.4 k= # of times event occurs (# wins) = 6 Apply to formula: 𝑛 P(X=k) = ( 𝑘 )𝑝 𝑘 (1 − 𝑝) 𝑛−𝑘 P(X=6) = (8 )0.46 (1 − 0.4)8−6 = 0.0412 6 You may use the Binomial Pdf function on your calculator for this.
- 4. Probability of a Binomial Event occurring at least or at most k times This is done the same way as for exactly, except we need to do this calculation multiple times and then add them up. Ex. The probability the team will win is 40%. What is the probability the team will win at least 6 of its next 8 games? Identify n, p, and k n=8 p = 0.4 k = 6,7,and 8 (at least means include 6 and higher) Calculation: 𝑛 P(X=k) = ( 𝑘 )𝑝 𝑘 (1 − 𝑝) 𝑛−𝑘 P(X≥6) = (8 )0.46 (1 − 0.4)8−6 +(8 )0.47 (1 − 0.4)8−7 +(8 )0.48 (1 − 0.4)8−8 7 6 8 = 0.041288 + 0.007864 + 0.000655 = 0.049807 =0.050 You may also use the Binomial Cdf function on your calculator If the questions asks for at most you do all of the values at or below the given value For questions asking less than or more than, do not include the given value