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description= 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 … - Selection from Head First Statistics [Book];
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Text of the page (random words):
rts 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 histogram s 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 chart a histogram histograms can t 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 we re 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 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 complementary events 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 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 so how do we calculate e x μ 2 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 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 it s 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 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 twenty horse 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 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 what s the missing number let s generalize the probability further what s the expectation and variance let s look at one trial binomial expectation and variance the statsville cinema has a problem it s 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 what s 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 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 so how do you use probability tables julie s probability is in the table and they all lived happily ever after but it doesn t stop there 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 so what s 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 λ is small when λ is large so how large is large enough a runaway success 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 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 what s next 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 so what is the estimator which formula s which mighty gumball has done more sampling it s 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 what s the expectation of ps and what s the variance of ps find the distribution of ps ps follows a normal distribution ps continuity correction required how many gumballs there s just one more problem 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 introducing the central limit theorem using the central limit theorem the binomial distribution the poisson distribution finding probabilities sampling saves the day you ve 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 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 what s the interval in general just one more problem step 1 choose your population statistic step 2 find its sampling distribution x̄ 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 you ve found the confidence intervals 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 the drug company s claim so what s the null hypothesis for snorecull so what s the alternative the doctor s perspective the alternate hypothesis for snorecull step 2 choose your test statistic what s 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 we ve 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 let s conduct another hypothesis test step 1 decide on the hypotheses it s 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 let s start with type i errors so what s the probability of getting a type i error what about type ii errors so how do we find β finding errors for snorecull let s 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 what s the power of snorecull the doctor s happy but it doesn t stop there 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 when v is 1 or 2 when v is greater than 2 v represents degrees of freedom so what s v what s the significance how to use χ2 probability tables 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 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 you ve saved the casino 15 correlation and regression what s my line never trust the weather let s 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 let s start with b finding the slope for the line of best fit we use x̄ and ȳ to help us find b 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 accurate linear correlation no linear correlation 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 a leftovers the top ten things we didn t cover 1 other ways of presenting data dotplots stemplots 2 distribution anatomy the empirical rule for normal distributions chebyshev s 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...
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