Publisher: O'Reilly Media Released: August 2008 Pages: 718
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 thoughtprovoking material, full of puzzles, stories, quizzes, visual aids, and realworld examples.
Whether you're a student, a professional, or just curious about statistical analysis, Head First's brainfriendly 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 firstyear statistics
 Tackle tough statistical concepts using Head First's dynamic, visually rich format proven to stimulate learning and help you retain knowledge
 Explore realworld 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.


Chapter 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 
Chart failure 
Bar charts can allow for more accuracy 
Vertical bar charts 
Horizontal bar charts 
It’s a matter of scale 
Using frequency scales 
Dealing with multiple sets of data 
Your bar charts rock 
Categories vs. numbers 
Dealing with grouped data 
To make a histogram, start by finding bar widths 
Manic Mango needs another chart 
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 chart—a histogram 
Histograms can’t do everything 
Introducing cumulative frequency 
Drawing the cumulative frequency graph 
Choosing the right chart 
Manic Mango conquered the games market! 
Chapter 2 Measuring Central Tendency: The Middle Way 
Welcome to the Health Club 
A common measure of average is the mean 
Mean math 
Dealing with unknowns 
Back to the mean 
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 
Congratulations! 
Chapter 3 Measuring Variability and Spread: Power Ranges 
Wanted: one player 
We need to compare player scores 
Use the range to differentiate between data sets 
The problem with outliers 
We need to get away from outliers 
Quartiles come to the rescue 
The interquartile range excludes outliers 
Quartile anatomy 
We’re not just limited to quartiles 
So what are 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 
A quicker calculation for variance 
What if we need a baseline for comparison? 
Use standard scores to compare values across data sets 
Interpreting standard scores 
Statsville All Stars win the league! 
Chapter 4 Calculating Probabilities: Taking Chances 
Fat Dan’s 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 
It’s time to play! 
And the winning number is... 
Let’s 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 it’s 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! 
It’s 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! 
Chapter 5 Using Discrete Probability Distributions: Manage Your Expectations 
Back at Fat Dan’s 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 
Let’s calculate the slot machine’s variance 
Fat Dan changed his prices 
There’s 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 
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 
Jackpot! 
Chapter 6 Permutations and Combinations: Making Arrangements 
The Statsville Derby 
It’s a threehorse race 
How many ways can they cross the finish line? 
Calculate the number of arrangements 
Going round in circles 
It’s 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 
It’s time for the twentyhorse race 
How many ways can we fill the top three positions? 
Examining permutations 
What if horse order doesn’t matter 
Examining combinations 
It’s the end of the race 
Chapter 7 Geometric, Binomial, and Poisson Distributions: Keeping Things Discrete 
Meet Chad, the hapless snowboarder 
We need to find Chad’s probability distribution 
There’s 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 
You’ve mastered the geometric distribution 
Should you play, or walk away? 
Generalizing the probability for three questions 
Let’s generalize the probability further 
What’s the expectation and variance? 
Binomial expectation and variance 
The Statsville Cinema has a problem 
Expectation and variance for the Poisson distribution 
So what’s the probability distribution? 
Combine Poisson variables 
The Poisson in disguise 
Anyone for popcorn? 
Chapter 8 Using the Normal Distribution: Being Normal 
Discrete data takes exact values... 
... but not all numeric data is discrete 
What’s 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 
We’ve 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 
Julie’s probability is in the table 
And they all lived happily ever after 
Chapter 9 Using the Normal Distribution ii: Beyond Normal 
Love is a roller coaster 
All aboard the Love Train 
Normal bride + normal groom 
It’s still just weight 
How’s the combined weight distributed? 
Finding probabilities 
More people want the Love Train 
Linear transforms describe underlying changes in values... 
...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 
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 
A runaway success! 
Chapter 10 Using Statistical Sampling: Taking Samples 
The Mighty Gumball taste test 
They’re running out of gumballs 
Test a gumball sample, not the whole gumball population 
How sampling works 
When sampling goes wrong 
How to design a sample 
Define your sampling frame 
Sometimes samples can be biased 
Sources of bias 
How to choose your sample 
Simple random sampling 
How to choose a simple random sample 
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 
Chapter 11 Estimating Populations and Samples: Making Predictions 
So how long does flavor really last for? 
Let’s start by estimating the population mean 
Point estimators can approximate population parameters 
Let’s estimate the population variance 
We need a different point estimator than sample variance 
Which formula’s which? 
Mighty Gumball has done more sampling 
It’s a question of proportion 
Buy your gumballs here! 
So how does this relate to sampling? 
The sampling distribution of proportions 
So what’s the expectation of Ps? 
And what’s the variance of Ps? 
Find the distribution of Ps 
Ps follows a normal distribution 
How many gumballs? 
We need probabilities for the sample mean 
The sampling distribution of the mean 
Find the expectation for X̄ 
What about the the variance of X̄? 
So how is X̄ distributed? 
If n is large, X̄ can still be approximated by the normal distribution 
Using the central limit theorem 
Sampling saves the day! 
Chapter 12 Constructing Confidence Intervals: Guessing with Confidence 
Mighty Gumball is in trouble 
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 
We’ve found the distribution for X̄ 
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 μ 
Finally, find the value of X̄ 
You’ve found the confidence interval 
Let’s summarize the steps 
Handy shortcuts for confidence intervals 
Just one more problem... 
Step 1: Choose your population statistic 
Step 2: Find its sampling distribution 
X̄ follows the tdistribution when the sample is small 
Find the standard score for the tdistribution 
Step 3: Decide on the level of confidence 
Step 4: Find the confidence limits 
Using tdistribution probability tables 
The tdistribution vs. the normal distribution 
You’ve found the confidence intervals! 
Chapter 13 Using Hypothesis Tests: Look At The Evidence 
Statsville’s new miracle drug 
So what’s the problem? 
Resolving the conflict from 50,000 feet 
The six steps for hypothesis testing 
Step 1: Decide on the hypothesis 
So what’s the alternative? 
Step 2: Choose your test statistic 
Step 3: Determine the critical region 
To find the critical region, first decide on the significance level 
Step 4: Find the pvalue 
We’ve found the pvalue 
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? 
Let’s conduct another hypothesis test 
Step 1: Decide on the hypotheses 
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 
Let’s start with Type I errors 
What about Type II errors? 
Finding errors for SnoreCull 
We need to find the range of values 
Find P(Type II error) 
Introducing power 
The doctor’s happy 
Chapter 14 The χ2 Distribution: There’s Something Going On... 
There may be trouble ahead at Fat Dan’s Casino 
Let’s start with the slot machines 
The χ2 test assesses difference 
So what does the test statistic represent? 
Two main uses of the χ2 distribution 
v represents degrees of freedom 
What’s the significance? 
Hypothesis testing with χ2 
You’ve solved the slot machine mystery 
Fat Dan has another problem 
the χ2 distribution can test for independence 
You can find the expected frequencies using probability 
So what are the frequencies? 
We still need to calculate degrees of freedom 
Generalizing the degrees of freedom 
And the formula is... 
You’ve saved the casino 
Chapter 15 Correlation and Regression: What’s My Line? 
Never trust the weather 
Let’s analyze sunshine and attendance 
Exploring types of data 
Visualizing bivariate data 
Scatter diagrams show you patterns 
Correlation vs. causation 
Predict values with a line of best fit 
Your best guess is still a guess 
We need to minimize the errors 
Introducing the sum of squared errors 
Find the equation for the line of best fit 
Finding the slope for the line of best fit 
Finding the slope for the line of best fit, part ii 
We’ve found b, but what about a? 
You’ve made the connection 
Let’s look at some correlations 
The correlation coefficient measures how well the line fits the data 
There’s a formula for calculating the correlation coefficient, r 
Find r for the concert data 
Find r for the concert data, continued 
You’ve saved the day! 
Leaving town... 
It’s been great having you here in Statsville! 
Appendix Leftovers: The Top Ten Things (we didn’t cover) 
#1. Other ways of presenting data 
#2. Distribution anatomy 
#3. Experiments 
Designing your experiment 
#4. Least square regression alternate notation 
#5. The coefficient of determination 
#6. Nonlinear relationships 
#7. The confidence interval for the slope of a regression line 
#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) 
Appendix Statistics Tables: Looking Things Up 
#1. Standard normal probabilities 
#2. tdistribution critical values 
#3. X2 critical values 
 Title:
 Head First Statistics
 By:
 Dawn Griffiths
 Publisher:
 O'Reilly Media
 Formats:

 Print
 Ebook
 Safari Books Online
 Print:
 August 2008
 Ebook:
 June 2009
 Pages:
 718
 Print ISBN:
 9780596527587
  ISBN 10:
 0596527586
 Ebook ISBN:
 9780596558727
  ISBN 10:
 0596558724


Dawn Griffiths Dawn Griffiths started life as a mathematician at a top UK university. She was awarded a FirstClass Honours degree in Mathematics, and was offered a university scholarship to undertake a PhD studying particularly rare breeds of differential equations. She moved away from academia when she realized that people would stop talking to her at parties, and went on to pursue a career in software development instead. She currently combines IT consultancy with writing and mathematics. When Dawn's not working on Head First books, you'll find her honing her Tai Chi skills, making bobbin lace or cooking nice meals. She hasn't yet mastered the art of doing all three at the same time. She also enjoys traveling, and spending time with her lovely husband, David. View Dawn Griffiths's full profile page. 
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