Head First Statistics

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.

Copyright
Dedication
Author of Head First Statistics
how to use this book
Chapter 1. visualizing information
Section 1.1. Statistics are everywhere
Section 1.2. But why learn statistics?
Section 1.3. A tale of two charts
Section 1.4. The humble pie chart
Section 1.5. Bar charts can allow for more accuracy
Section 1.6. Vertical bar charts
Section 1.7. Horizontal bar charts
Section 1.8. It's a matter of scale
Section 1.9. Using frequency scales
Section 1.10. Dealing with multiple sets of data
Section 1.11. Categories vs. numbers
Section 1.12. Dealing with grouped data
Section 1.13. To make a histogram, start by finding bar widths
Section 1.14. Step 1: Find the bar widths
Section 1.15. Step 2: Find the bar heights
Section 1.16. Step 3: Draw your chart?a histogram
Section 1.17. Introducing cumulative frequency
Section 1.18. Drawing the cumulative frequency graph
Section 1.19. Choosing the right chart
Chapter 2. measuring central tendency
Section 2.1. Welcome to the...Copyright
Dedication
Author of Head First Statistics
how to use this book
Chapter 1. visualizing information
Section 1.1. Statistics are everywhere
Section 1.2. But why learn statistics?
Section 1.3. A tale of two charts
Section 1.4. The humble pie chart
Section 1.5. Bar charts can allow for more accuracy
Section 1.6. Vertical bar charts
Section 1.7. Horizontal bar charts
Section 1.8. It's a matter of scale
Section 1.9. Using frequency scales
Section 1.10. Dealing with multiple sets of data
Section 1.11. Categories vs. numbers
Section 1.12. Dealing with grouped data
Section 1.13. To make a histogram, start by finding bar widths
Section 1.14. Step 1: Find the bar widths
Section 1.15. Step 2: Find the bar heights
Section 1.16. Step 3: Draw your chart?a histogram
Section 1.17. Introducing cumulative frequency
Section 1.18. Drawing the cumulative frequency graph
Section 1.19. Choosing the right chart
Chapter 2. measuring central tendency
Section 2.1. Welcome to the Health Club
Section 2.2. A common measure of average is the mean
Section 2.3. Mean math
Section 2.4. Dealing with unknowns
Section 2.5. Back to the mean
Section 2.6. Back to the Health Club
Section 2.7. Everybody was Kung Fu fighting
Section 2.8. Our data has outliers
Section 2.9. The butler outliers did it
Section 2.10. Watercooler conversation
Section 2.11. Finding the median
Section 2.12. How to find the median in three steps:
Section 2.13. Business is booming
Section 2.14. The Little Ducklings swimming class
Section 2.15. What went wrong with the mean and median?
Section 2.16. What should we do for data like this?
Section 2.17. The Mean Exposed
Section 2.18. Introducing the mode
Section 2.19. Three steps for finding the mode:
Chapter 3. measuring variability and spread
Section 3.1. Wanted: one player
Section 3.2. We need to compare player scores
Section 3.3. Use the range to differentiate between data sets
Section 3.4. The problem with outliers
Section 3.5. We need to get away from outliers
Section 3.6. Quartiles come to the rescue
Section 3.7. The interquartile range excludes outliers
Section 3.8. Quartile anatomy
Section 3.9. We're not just limited to quartiles
Section 3.10. So what are percentiles?
Section 3.11. Box and whisker plots let you visualize ranges
Section 3.12. Variability is more than just spread
Section 3.13. Calculating average distances
Section 3.14. We can calculate variation with the variance...
Section 3.15. ...but standard deviation is a more intuitive measure
Section 3.16. Standard Deviation Exposed
Section 3.17. A quicker calculation for variance
Section 3.18. What if we need a baseline for comparison?
Section 3.19. Use standard scores to compare values across data sets
Section 3.20. Interpreting standard scores
Section 3.21. Statsville All Stars win the league!
Chapter 4. calculating probabilities
Section 4.1. Fat Dan's Grand Slam
Section 4.2. Roll up for roulette!
Section 4.3. What are the chances?
Section 4.4. Find roulette probabilities
Section 4.5. You can visualize probabilities with a Venn diagram
Section 4.6. You can also add probabilities
Section 4.7. Exclusive events and intersecting events
Section 4.8. Problems at the intersection
Section 4.9. Some more notation
Section 4.10. Another unlucky spin...
Section 4.11. Conditions apply
Section 4.12. Find conditional probabilities
Section 4.13. Trees also help you calculate conditional probabilities
Section 4.14. Handy hints for working with trees
Section 4.15. Step 1: Finding P(Black Even)
Section 4.16. Step 2: Finding P(Even)
Section 4.17. Step 3: Finding P(Black l Even)
Section 4.18. Use the Law of Total Probability to find P(B)
Section 4.19. Introducing Bayes' Theorem
Section 4.20. If events affect each other, they are dependent
Section 4.21. If events do not affect each other, they are independent
Section 4.22. More on calculating probability for independent events
Chapter 5. using discrete probability distributions
Section 5.1. Back at Fat Dan's Casino
Section 5.2. We can compose a probability distribution for the slot machine
Section 5.3. Expectation gives you a prediction of the results...
Section 5.4. ...and variance tells you about the spread of the results
Section 5.5. Variances and probability distributions
Section 5.6. Let's calculate the slot machine's variance
Section 5.7. Fat Dan changed his prices
Section 5.8. There's a linear relationship between E(X) and E(Y)
Section 5.9. Slot machine transformations
Section 5.10. General formulas for linear transforms
Section 5.11. Every pull of the lever is an independent observation
Section 5.12. Observation shortcuts
Section 5.13. New slot machine on the block
Section 5.14. Add E(X) and E(Y) to get E(X + Y)...
Section 5.15. ...and subtract E(X) and E(Y) to get E(X - Y)
Section 5.16. You can also add and subtract linear transformations
Section 5.17. Jackpot!
Chapter 6. permutations and combinations
Section 6.1. The Statsville Derby
Section 6.2. It's a three-horse race
Section 6.3. How many ways can they cross the finish line?
Section 6.4. Calculate the number of arrangements
Section 6.5. Going round in circles
Section 6.6. It's time for the novelty race
Section 6.7. Arranging by individuals is different than arranging by type
Section 6.8. We need to arrange animals by type
Section 6.9. Generalize a formula for arranging duplicates
Section 6.10. It's time for the twenty-horse race
Section 6.11. How many ways can we fill the top three positions?
Section 6.12. Examining permutations
Section 6.13. What if horse order doesn't matter
Section 6.14. Examining combinations
Section 6.15. Combination Exposed
Section 6.16. Does order really matter?
Section 6.17. It's the end of the race
Chapter 7. geometric, binomial, and poisson distributions
Section 7.1. We need to find Chad's probability distribution
Section 7.2. There's a pattern to this probability distribution
Section 7.3. The probability distribution can be represented algebraically
Section 7.4. The geometric distribution also works with inequalities
Section 7.5. The pattern of expectations for the geometric distribution
Section 7.6. Expectation is 1/p
Section 7.7. Finding the variance for our distribution
Section 7.8. A quick guide to the geometric distribution
Section 7.9. You've mastered the geometric distribution
Section 7.10. Who Wants To Win A Swivel Chair!
Section 7.11. Should you play, or walk away?
Section 7.12. Generalizing the probability for three questions
Section 7.13. Let's generalize the probability further
Section 7.14. What's the expectation and variance?
Section 7.15. Binomial expectation and variance
Section 7.16. Your quick guide to the binomial distribution
Section 7.17. Expectation and variance for the Poisson distribution
Section 7.18. So what's the probability distribution?
Section 7.19. Combine Poisson variables
Section 7.20. The Poisson in disguise
Section 7.21. Your quick guide to the Poisson distribution
Chapter 8. using the normal distribution
Section 8.1. Discrete data takes exact values...
Section 8.2. ...but not all numeric data is discrete
Section 8.3. What's the delay?
Section 8.4. We need a probability distribution for continuous data
Section 8.5. Probability density functions can be used for continuous data
Section 8.6. Probability = area
Section 8.7. To calculate probability, start by finding f(x)...
Section 8.8. ...then find probability by finding the area
Section 8.9. We've found the probability
Section 8.10. Searching for a soul sole mate
Section 8.11. Male modelling
Section 8.12. The normal distribution is an "ideal" model for continuous data
Section 8.13. So how do we find normal probabilities?
Section 8.14. Three steps to calculating normal probabilities
Section 8.15. Step 1: Determine your distribution
Section 8.16. Step 2: Standardize to N(0, 1)
Section 8.17. To standardize, first move the mean...
Section 8.18. ...then squash the width
Section 8.19. Now find Z for the specific value you want to find probability for
Section 8.20. Step 3: Look up the probability in your handy table
Chapter 9. using the normal distribution ii
Section 9.1. All aboard the Love Train
Section 9.2. Normal bride + normal groom
Section 9.3. It's still just weight
Section 9.4. How's the combined weight distributed?
Section 9.5. Finding probabilities
Section 9.6. More people want the Love Train
Section 9.7. Linear transforms describe underlying changes in values...
Section 9.8. ...and independent observations describe how many values you have
Section 9.9. Expectation and variance for independent observations
Section 9.10. Should we play, or walk away?
Section 9.11. Normal distribution to the rescue
Section 9.12. When to approximate the binomial distribution with the normal
Section 9.13. Revisiting the normal approximation
Section 9.14. The binomial is discrete, but the normal is continuous
Section 9.15. Apply a continuity correction before calculating the approximation
Section 9.16. The Normal Distribution Exposed
Section 9.17. All aboard the Love Train
Section 9.18. When to approximate the binomial distribution with the normal
Section 9.19. A runaway success!
Chapter 10. using statistical sampling
Section 10.1. The Mighty Gumball taste test
Section 10.2. They're running out of gumballs
Section 10.3. Test a gumball sample, not the whole gumball population
Section 10.4. How sampling works
Section 10.5. When sampling goes wrong
Section 10.6. How to design a sample
Section 10.7. Define your sampling frame
Section 10.8. Sometimes samples can be biased
Section 10.9. Sources of bias
Section 10.10. How to choose your sample
Section 10.11. Simple random sampling
Section 10.12. How to choose a simple random sample
Section 10.13. There are other types of sampling
Section 10.14. We can use stratified sampling...
Section 10.15. ...or we can use cluster sampling...
Section 10.16. ...or even systematic sampling
Section 10.17. Mighty Gumball has a sample
Chapter 11. estimating populations and samples
Section 11.1. So how long does flavor really last for?
Section 11.2. Let's start by estimating the population mean
Section 11.3. Point estimators can approximate population parameters
Section 11.4. Let's estimate the population variance
Section 11.5. We need a different point estimator than sample variance
Section 11.6. Which formula's which?
Section 11.7. It's a question of proportion
Section 11.8. So how does this relate to sampling?
Section 11.9. The sampling distribution of proportions
Section 11.10. So what's the expectation of Ps?
Section 11.11. And what's the variance of Ps?
Section 11.12. Find the distribution of Ps
Section 11.13. Ps follows a normal distribution
Section 11.14. We need probabilities for the sample mean
Section 11.15. The sampling distribution of the mean
Section 11.16. Find the expectation for
Section 11.17. What about the the variance of ?
Section 11.18. So how is distributed?
Section 11.19. If n is large, can still be approximated by the normal distribution
Section 11.20. Using the central limit theorem
Chapter 12. constructing confidence intervals
Section 12.1. Mighty Gumball is in trouble
Section 12.2. The problem with precision
Section 12.3. Introducing confidence intervals
Section 12.4. Four steps for finding confidence intervals
Section 12.5. Step 1: Choose your population statistic
Section 12.6. Step 2: Find its sampling distribution
Section 12.7. Step 3: Decide on the level of confidence
Section 12.8. Step 4: Find the confidence limits
Section 12.9. Start by finding Z
Section 12.10. Rewrite the inequality in terms of ¥ì
Section 12.11. Finally, find the value of
Section 12.12. You've found the confidence interval
Section 12.13. Let's summarize the steps
Section 12.14. Handy shortcuts for confidence intervals
Section 12.15. Step 1: Choose your population statistic
Section 12.16. Step 2: Find its sampling distribution
Section 12.17. Step 3: Decide on the level of confidence
Section 12.18. Step 4: Find the confidence limits
Section 12.19. The t-distribution vs. the normal distribution
Chapter 13. using hypothesis tests
Section 13.1. Statsville's new miracle drug
Section 13.2. Resolving the conflict from 50,000 feet
Section 13.3. The six steps for hypothesis testing
Section 13.4. Step 1: Decide on the hypothesis
Section 13.5. Step 2: Choose your test statistic
Section 13.6. Step 3: Determine the critical region
Section 13.7. Step 4: Find the p-value
Section 13.8. Step 5: Is the sample result in the critical region?
Section 13.9. Step 6: Make your decision
Section 13.10. What if the sample size is larger?
Section 13.11. Let's conduct another hypothesis test
Section 13.12. Step 1: Decide on the hypotheses
Section 13.13. Step 2: Choose the test statistic
Section 13.14. Use the normal to approximate the binomial in our test statistic
Section 13.15. Step 3: Find the critical region
Section 13.16. Let's start with Type I errors
Section 13.17. What about Type II errors?
Section 13.18. Finding errors for SnoreCull
Section 13.19. We need to find the range of values
Section 13.20. Find P(Type II error)
Section 13.21. Introducing power
Chapter 14. the x2 distribution
Section 14.1. There may be trouble ahead at Fat Dan's Casino
Section 14.2. Let's start with the slot machines
Section 14.3. The x2 test assesses difference
Section 14.4. So what does the test statistic represent?
Section 14.5. Two main uses of the x2 distribution
Section 14.6. ¥í represents degrees of freedom
Section 14.7. What's the significance?
Section 14.8. Hypothesis testing with ¥ö2
Section 14.9. You've solved the slot machine mystery
Section 14.10. Fat Dan has another problem
Section 14.11. the x2 distribution can test for independence
Section 14.12. You can find the expected frequencies using probability
Section 14.13. So what are the frequencies?
Section 14.14. We still need to calculate degrees of freedom
Section 14.15. Generalizing the degrees of freedom
Section 14.16. And the formula is...
Section 14.17. You've saved the casino
Chapter 15. correlation and regression
Section 15.1. Let's analyze sunshine and attendance
Section 15.2. Exploring types of data
Section 15.3. Visualizing bivariate data
Section 15.4. Scatter diagrams show you patterns
Section 15.5. Correlation vs. causation
Section 15.6. Predict values with a line of best fit
Section 15.7. Your best guess is still a guess
Section 15.8. We need to minimize the errors
Section 15.9. Introducing the sum of squared errors
Section 15.10. Find the equation for the line of best fit
Section 15.11. Finding the slope for the line of best fit
Section 15.12. Finding the slope for the line of best fit, part ii
Section 15.13. We've found b, but what about a?
Section 15.14. You've made the connection
Section 15.15. Let's look at some correlations
Section 15.16. The correlation coefficient measures how well the line fits the data
Section 15.17. There's a formula for calculating the correlation coefficient, r
Section 15.18. Find r for the concert data
Section 15.19. Find r for the concert data, continued
Appendix A. leftovers
Section A.1. #1. Other ways of presenting data
Section A.2. #2. Distribution anatomy
Section A.3. #3. Experiments
Section A.4. #4. Least square regression alternate notation
Section A.5. #5. The coefficient of determination
Section A.6. #6. Non-linear relationships
Section A.7. #7. The confidence interval for the slope of a regression line
Section A.8. #8. Sampling distributions - the difference between two means
Section A.9. #9. Sampling distributions - the difference between two proportions
Section A.10. #10. E(X) and Var(X) for continuous probability distributions
Appendix B. Statistics tables
Section B.1. #1. Standard normal probabilities
Section B.2. #2. t-distribution critical values
Section B.3. #3. X2 critical values
Index