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Head First Statistics - Helion

Head First Statistics
ebook
Autor: Dawn Griffiths
ISBN: 978-14-493-3156-6
stron: 718, Format: ebook
Data wydania: 2008-08-26
Księgarnia: Helion

Cena książki: 101,15 zł (poprzednio: 117,62 zł)
Oszczędzasz: 14% (-16,47 zł)

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Wouldn't it be great if there were a statistics book that made histograms, probability distributions, and chi square analysis more enjoyable than going to the dentist? Head First Statistics brings this typically dry subject to life, teaching you everything you want and need to know about statistics through engaging, interactive, and thought-provoking material, full of puzzles, stories, quizzes, visual aids, and real-world examples.

Whether you're a student, a professional, or just curious about statistical analysis, Head First's brain-friendly formula helps you get a firm grasp of statistics so you can understand key points and actually use them. Learn to present data visually with charts and plots; discover the difference between taking the average with mean, median, and mode, and why it's important; learn how to calculate probability and expectation; and much more.

Head First Statistics is ideal for high school and college students taking statistics and satisfies the requirements for passing the College Board's Advanced Placement (AP) Statistics Exam. With this book, you'll:

  • Study the full range of topics covered in first-year statistics
  • Tackle tough statistical concepts using Head First's dynamic, visually rich format proven to stimulate learning and help you retain knowledge
  • Explore real-world scenarios, ranging from casino gambling to prescription drug testing, to bring statistical principles to life
  • Discover how to measure spread, calculate odds through probability, and understand the normal, binomial, geometric, and Poisson distributions
  • Conduct sampling, use correlation and regression, do hypothesis testing, perform chi square analysis, and more

Before you know it, you'll not only have mastered statistics, you'll also see how they work in the real world. Head First Statistics will help you pass your statistics course, and give you a firm understanding of the subject so you can apply the knowledge throughout your life.

Dodaj do koszyka Head First Statistics

 

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Spis treści

Head First Statistics. A Brain-Friendly Guide eBook -- spis treści

  • Head First Statistics
  • Dedication
  • A Note Regarding Supplemental Files
  • Advance Praise for Head First Statistics
  • Praise for other Head First books
  • Author of Head First Statistics
  • How to use this Book: Intro
    • Who is this book for?
      • Who should probably back away from this book?
    • We know what youre thinking
    • We know what your brain is thinking
    • Metacognition: thinking about thinking
    • Heres what WE did
      • Heres what YOU can do to bend your brain into submission
    • Read Me
    • The technical review team
    • Acknowledgments
    • Safari Books Online
  • 1. Visualizing Information: First Impressions
    • Statistics are everywhere
    • But why learn statistics?
    • A tale of two charts
    • Manic Mango needs some charts
    • The humble pie chart
      • So when are pie charts useful?
    • Chart failure
    • Bar charts can allow for more accuracy
    • Vertical bar charts
    • Horizontal bar charts
    • Its a matter of scale
      • Using percentage scales
    • Using frequency scales
    • Dealing with multiple sets of data
      • The split-category bar chart
      • The segmented bar chart
    • Your bar charts rock
    • Categories vs. numbers
      • Categorical or qualitative data
      • Numerical or quantitative data
    • Dealing with grouped data
    • To make a histogram, start by finding bar widths
    • Manic Mango needs another chart
      • A histograms bar area must be proportional to frequency
    • Make the area of histogram bars proportional to frequency
    • Step 1: Find the bar widths
    • Step 2: Find the bar heights
    • Step 3: Draw your charta histogram
    • Histograms cant do everything
    • Introducing cumulative frequency
      • So what are the cumulative frequencies?
    • Drawing the cumulative frequency graph
    • Choosing the right chart
    • Manic Mango conquered the games market!
  • 2. Measuring Central Tendency: The Middle Way
    • Welcome to the Health Club
    • A common measure of average is the mean
    • Mean math
      • Letters and numbers
    • Dealing with unknowns
    • Back to the mean
      • The mean has its own symbol
    • Handling frequencies
    • Back to the Health Club
    • Everybody was Kung Fu fighting
    • Our data has outliers
    • The butler outliers did it
    • Watercooler conversation
    • Finding the median
    • Business is booming
    • The Little Ducklings swimming class
    • Frequency Magnets
    • Frequency Magnets
    • What went wrong with the mean and median?
    • Introducing the mode
      • It even works with categorical data
    • Congratulations!
  • 3. Measuring Variability and Spread: Power Ranges
    • Wanted: one player
    • We need to compare player scores
    • Use the range to differentiate between data sets
      • Measuring the range
    • The problem with outliers
    • We need to get away from outliers
    • Quartiles come to the rescue
    • The interquartile range excludes outliers
    • Quartile anatomy
      • Finding the position of the lower quartile
      • Finding the position of the upper quartile
    • Were not just limited to quartiles
    • So what are percentiles?
      • Percentile uses
      • Finding percentiles
    • Box and whisker plots let you visualize ranges
    • Variability is more than just spread
    • Calculating average distances
    • We can calculate variation with the variance...
    • ...but standard deviation is a more intuitive measure
      • Standard deviation know-how
    • A quicker calculation for variance
    • What if we need a baseline for comparison?
    • Use standard scores to compare values across data sets
      • Calculating standard scores
    • Interpreting standard scores
      • So what does this tell us about the players?
    • Statsville All Stars win the league!
  • 4. Calculating Probabilities: Taking Chances
    • Fat Dans Grand Slam
    • Roll up for roulette!
    • Your very own roulette board
    • Place your bets now!
    • What are the chances?
    • Find roulette probabilities
    • You can visualize probabilities with a Venn diagram
      • Complementary events
    • Its time to play!
    • And the winning number is...
    • Lets bet on an even more likely event
    • You can also add probabilities
    • You win!
    • Time for another bet
    • Exclusive events and intersecting events
    • Problems at the intersection
    • Some more notation
    • Another unlucky spin...
    • ...but its time for another bet
    • Conditions apply
    • Find conditional probabilities
    • You can visualize conditional probabilities with a probability tree
    • Trees also help you calculate conditional probabilities
    • Bad luck!
    • We can find P(Black l Even) using the probabilities we already have
    • Step 1: Finding P(Black Even)
    • So where does this get us?
    • Step 2: Finding P(Even)
    • Step 3: Finding P(Black l Even)
    • These results can be generalized to other problems
    • Use the Law of Total Probability to find P(B)
    • Introducing Bayes Theorem
    • We have a winner!
    • Its time for one last bet
    • If events affect each other, they are dependent
    • If events do not affect each other, they are independent
    • More on calculating probability for independent events
    • Winner! Winner!
  • 5. Using Discrete Probability Distributions: Manage Your Expectations
    • Back at Fat Dans Casino
    • We can compose a probability distribution for the slot machine
    • Expectation gives you a prediction of the results...
    • ... and variance tells you about the spread of the results
    • Variances and probability distributions
      • So how do we calculate E(X )2?
    • Lets calculate the slot machines variance
    • Fat Dan changed his prices
    • Theres a linear relationship between E(X) and E(Y)
    • Slot machine transformations
    • General formulas for linear transforms
    • Every pull of the lever is an independent observation
    • Observation shortcuts
      • Expectation
      • Variance
    • New slot machine on the block
    • Add E(X) and E(Y) to get E(X + Y)...
    • ... and subtract E(X) and E(Y) to get E(X Y)
    • You can also add and subtract linear transformations
      • Adding aX and bY
      • Subtracting aX and bY
    • Jackpot!
  • 6. Permutations and Combinations: Making Arrangements
    • The Statsville Derby
    • Its a three-horse race
    • How many ways can they cross the finish line?
    • Calculate the number of arrangements
      • So what if there are n horses?
    • Going round in circles
    • Its time for the novelty race
    • Arranging by individuals is different than arranging by type
    • We need to arrange animals by type
    • Generalize a formula for arranging duplicates
    • Its time for the twenty-horse race
    • How many ways can we fill the top three positions?
    • Examining permutations
    • What if horse order doesnt matter
    • Examining combinations
    • Its the end of the race
  • 7. Geometric, Binomial, and Poisson Distributions: Keeping Things Discrete
    • Meet Chad, the hapless snowboarder
    • We need to find Chads probability distribution
    • Theres a pattern to this probability distribution
    • The probability distribution can be represented algebraically
    • The pattern of expectations for the geometric distribution
    • Expectation is 1/p
    • Finding the variance for our distribution
    • Youve mastered the geometric distribution
    • Should you play, or walk away?
    • Generalizing the probability for three questions
      • Whats the missing number?
    • Lets generalize the probability further
    • Whats the expectation and variance?
      • Lets look at one trial
    • Binomial expectation and variance
    • The Statsville Cinema has a problem
      • Its a different sort of distribution
      • So how do we find probabilities?
    • Expectation and variance for the Poisson distribution
      • What does the Poisson distribution look like?
    • So whats the probability distribution?
    • Combine Poisson variables
    • The Poisson in disguise
    • Anyone for popcorn?
  • 8. Using the Normal Distribution: Being Normal
    • Discrete data takes exact values...
    • ... but not all numeric data is discrete
    • Whats the delay?
    • We need a probability distribution for continuous data
    • Probability density functions can be used for continuous data
    • Probability = area
    • To calculate probability, start by finding f(x)...
    • ... then find probability by finding the area
    • Weve found the probability
    • Searching for a soul sole mate
    • Male modelling
    • The normal distribution is an ideal model for continuous data
    • So how do we find normal probabilities?
    • Three steps to calculating normal probabilities
    • Step 1: Determine your distribution
    • Step 2: Standardize to N(0, 1)
    • To standardize, first move the mean...
    • ... then squash the width
    • Now find Z for the specific value you want to find probability for
    • Step 3: Look up the probability in your handy table
      • So how do you use probability tables?
    • Julies probability is in the table
    • And they all lived happily ever after
      • But it doesnt stop there.
  • 9. Using the Normal Distribution ii: Beyond Normal
    • Love is a roller coaster
    • All aboard the Love Train
    • Normal bride + normal groom
    • Its still just weight
    • Hows the combined weight distributed?
    • Finding probabilities
    • More people want the Love Train
    • Linear transforms describe underlying changes in values...
      • So whats the distribution of a linear transform?
    • ...and independent observations describe how many values you have
    • Expectation and variance for independent observations
    • Should we play, or walk away?
    • Normal distribution to the rescue
    • When to approximate the binomial distribution with the normal
      • Finding the mean and variance
    • Revisiting the normal approximation
    • The binomial is discrete, but the normal is continuous
    • Apply a continuity correction before calculating the approximation
    • All aboard the Love Train
    • When to approximate the binomial distribution with the normal
      • When is small...
      • When is large...
      • So how large is large enough?
    • A runaway success!
  • 10. Using Statistical Sampling: Taking Samples
    • The Mighty Gumball taste test
    • Theyre running out of gumballs
    • Test a gumball sample, not the whole gumball population
      • Gumball populations
      • Gumball samples
    • How sampling works
    • When sampling goes wrong
    • How to design a sample
      • Define your target population
      • Define your sampling units
    • Define your sampling frame
    • Sometimes samples can be biased
      • Unbiased Samples
      • Biased Samples
    • Sources of bias
    • How to choose your sample
    • Simple random sampling
      • Sampling with replacement
      • Sampling without replacement
    • How to choose a simple random sample
      • Drawing lots
      • Random number generators
    • There are other types of sampling
    • We can use stratified sampling...
    • ...or we can use cluster sampling...
    • ...or even systematic sampling
    • Mighty Gumball has a sample
      • So whats next?
  • 11. Estimating Populations and Samples: Making Predictions
    • So how long does flavor really last for?
    • Lets start by estimating the population mean
    • Point estimators can approximate population parameters
    • Lets estimate the population variance
    • We need a different point estimator than sample variance
      • So what is the estimator?
    • Which formulas which?
    • Mighty Gumball has done more sampling
    • Its a question of proportion
      • Predicting population proportion
    • Buy your gumballs here!
      • Introducing new jumbo boxes
    • So how does this relate to sampling?
    • The sampling distribution of proportions
    • So whats the expectation of Ps?
    • And whats the variance of Ps?
    • Find the distribution of Ps
    • Ps follows a normal distribution
      • Pscontinuity correction required
    • How many gumballs?
      • Theres just one more problem...
    • We need probabilities for the sample mean
    • The sampling distribution of the mean
    • Find the expectation for X
    • What about the the variance of X?
    • So how is X distributed?
    • If n is large, X can still be approximated by the normal distribution
      • Introducing the Central Limit Theorem
    • Using the central limit theorem
      • The binomial distribution
      • The Poisson distribution
      • Finding probabilities
    • Sampling saves the day!
      • Youve made a lot of progress
  • 12. Constructing Confidence Intervals: Guessing with Confidence
    • Mighty Gumball is in trouble
      • They need you to save them
    • The problem with precision
    • Introducing confidence intervals
    • Four steps for finding confidence intervals
    • Step 1: Choose your population statistic
    • Step 2: Find its sampling distribution
    • Point estimators to the rescue
    • Weve found the distribution for X
    • Step 3: Decide on the level of confidence
    • How to select an appropriate confidence level
    • Step 4: Find the confidence limits
    • Start by finding Z
    • Rewrite the inequality in terms of
    • Finally, find the value of X
    • Youve found the confidence interval
    • Lets summarize the steps
    • Handy shortcuts for confidence intervals
      • Whats the interval in general?
    • Just one more problem...
    • Step 1: Choose your population statistic
    • Step 2: Find its sampling distribution
    • X follows the t-distribution when the sample is small
    • Find the standard score for the t-distribution
    • Step 3: Decide on the level of confidence
    • Step 4: Find the confidence limits
    • Using t-distribution probability tables
    • The t-distribution vs. the normal distribution
    • Youve found the confidence intervals!
  • 13. Using Hypothesis Tests: Look At The Evidence
    • Statsvilles new miracle drug
    • So whats the problem?
    • Resolving the conflict from 50,000 feet
    • The six steps for hypothesis testing
    • Step 1: Decide on the hypothesis
      • The drug companys claim
      • So whats the null hypothesis for SnoreCull?
    • So whats the alternative?
      • The doctors perspective
      • The alternate hypothesis for SnoreCull
    • Step 2: Choose your test statistic
      • Whats the test statistic for SnoreCull?
    • Step 3: Determine the critical region
      • At what point can we reject the drug company claims?
    • To find the critical region, first decide on the significance level
      • So what significance level should we use?
    • Step 4: Find the p-value
      • How do we find the p-value?
    • Weve found the p-value
    • Step 5: Is the sample result in the critical region?
    • Step 6: Make your decision
    • So what did we just do?
    • What if the sample size is larger?
    • Lets conduct another hypothesis test
    • Step 1: Decide on the hypotheses
      • Its still the same problem
    • Step 2: Choose the test statistic
    • Use the normal to approximate the binomial in our test statistic
    • Step 3: Find the critical region
    • SnoreCull failed the test
    • Mistakes can happen
    • Lets start with Type I errors
      • So whats the probability of getting a Type I error?
    • What about Type II errors?
      • So how do we find ?
    • Finding errors for SnoreCull
      • Lets start with the Type I error
      • So what about the Type II error?
    • We need to find the range of values
    • Find P(Type II error)
    • Introducing power
      • So whats the power of SnoreCull?
    • The doctors happy
      • But it doesnt stop there
  • 14. The 2 Distribution: Theres Something Going On...
    • There may be trouble ahead at Fat Dans Casino
    • Lets start with the slot machines
    • The 2 test assesses difference
    • So what does the test statistic represent?
    • Two main uses of the 2 distribution
      • When v is 1 or 2
      • When v is greater than 2
    • v represents degrees of freedom
      • So whats v?
    • Whats the significance?
      • How to use 2 probability tables
    • Hypothesis testing with 2
    • Youve solved the slot machine mystery
    • Fat Dan has another problem
    • the 2 distribution can test for independence
    • You can find the expected frequencies using probability
    • So what are the frequencies?
      • How do we find the frequencies in general?
    • We still need to calculate degrees of freedom
    • Generalizing the degrees of freedom
    • And the formula is...
    • Youve saved the casino
  • 15. Correlation and Regression: Whats My Line?
    • Never trust the weather
    • Lets analyze sunshine and attendance
    • Exploring types of data
      • All about bivariate data
    • Visualizing bivariate data
    • Scatter diagrams show you patterns
    • Correlation vs. causation
      • We need to predict the concert attendance
    • Predict values with a line of best fit
    • Your best guess is still a guess
      • We need to find the equation of the line
    • We need to minimize the errors
    • Introducing the sum of squared errors
    • Find the equation for the line of best fit
      • Lets start with b
    • Finding the slope for the line of best fit
      • We use x and to help us find b
    • Finding the slope for the line of best fit, part ii
    • Weve found b, but what about a?
    • Youve made the connection
    • Lets look at some correlations
      • Accurate linear correlation
      • No linear correlation
    • The correlation coefficient measures how well the line fits the data
    • Theres a formula for calculating the correlation coefficient, r
    • Find r for the concert data
    • Find r for the concert data, continued
    • Youve saved the day!
    • Leaving town...
    • Its been great having you here in Statsville!
  • A. Leftovers: The Top Ten Things (we didnt cover)
    • #1. Other ways of presenting data
      • Dotplots
      • Stemplots
    • #2. Distribution anatomy
      • The empirical rule for normal distributions
      • Chebyshevs rule for any distribution
    • #3. Experiments
      • So what makes for a good experiment?
    • Designing your experiment
      • Completely randomized design
      • Randomized block design
      • Matched pairs design
    • #4. Least square regression alternate notation
    • #5. The coefficient of determination
      • Calculating r2
    • #6. Non-linear relationships
    • #7. The confidence interval for the slope of a regression line
      • The margin of error for b
    • #8. Sampling distributions the difference between two means
    • #9. Sampling distributions the difference between two proportions
    • #10. E(X) and Var(X) for continuous probability distributions
    • Finding E(X)
    • Finding Var(X)
  • B. Statistics Tables: Looking Things Up
    • #1. Standard normal probabilities
    • #2. t-distribution critical values
    • #3. X2 critical values
  • Index
  • About the Author
  • Copyright

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