### 26 Episodes

** What Is Statistics?** #101
**[TV-G]**

Using historical anecdotes and contemporary applications, this introduction to the series explores the vital links between statistics and our everyday world and examines the evolution of the discipline.

** Picturing Distributions** #102
**[TV-G]**

Explores how key characteristics in the distribution of a histogram—shape, center, and spread—help professionals make decisions in such diverse fields as meteorology, television programming, health care, and air traffic control. A discussion of the advantages of back-to-back stem plots emphasizes the importance of seeking explanations for gaps and outliers in small data sets.

** Describing Distributions** #103
**[TV-G]**

Examines the difference between mean and median, explains the use of quartiles to describe a distribution, and illustrates the use of boxplots and the five-number summary for comparing and describing data. A city government uses statistical methods to correct inequity between men's and women's salaries.

** Normal Distributions** #104
**[TV-G]**

Shows ways to describe the shape of a distribution using progressively simpler methods, from histograms through smooth curves to normal curves and finally to a single normal curve for standardized measurement. A lesson on creating a density curve explains why, under steadily decreasing deviation, today's baseball players are less likely to achieve a .400 batting average.

** Normal Calculations** #105
**[TV-G]**

How to convert the standard normal and use the standard deviation, how to use a table of areas to compute relative frequencies, how to find any percentile, and how a computer creates a normal quartile plot to determine whether a distribution is normal. Vehicle emissions standards and medical studies of cholesterol provide real-life examples.

** Time Series** #106
**[TV-G]**

Statistics can reveal patterns over time. Using the concept of seasonal variation, this program shows ways to present smooth data and recognize whether a particular pattern is meaningful. Stock market trends and sleep cycles are used to explore the topics of deriving a time series and using the 68-95-99.7 rule to determine the control limits.

** Models for Growth** #107
**[TV-G]**

A study of growth problems in children serves to illustrate the use of the logarithm function to transform an exponential pattern into a line, while an examination of world oil production over time helps illustrate such topics as linear growth, least squares, exponential growth, and straightening an exponential growth curve by logic.

** Describing Relationships** #108
**[TV-G]**

Using a scatter plot to display relationships between variables; patterns in variables (positive, negative, and linear association) and the importance of outliers. Examples include calculating the least squares regression line of metabolic rate *y* on lean body mass *x* for a group of subjects and examining the fit of the regression line by plotting residuals.

** Correlation** #109
**[TV-G]**

The relationship between a baseball player's salary and his home run statistics provides an example of deriving and interpreting the correlation coefficient and then using its square to measure the strength and direction of the relationship between two variables. A study comparing identical twins raised together and apart illustrates the concept of correlation.

** Multidimensional Data Analysis** #110
**[TV-G]**

An examination of computer graphics for statistical analysis at Bell Communications Research shows how the computer can graph multivariate data as well as various ways of presenting it. Data on many variables is used to get a picture of overall environmental stresses in the Chesapeake Bay.

** The Question of Causation** #111
**[TV-G]**

Explores common and confounding responses, the use of two-way tables of percents to calculate marginal distribution, a segmented bar as a way to visually compare sets of conditional distributions, and Simpson's Paradox. The relationship between smoking and lung cancer provides a clear example.

** Experimental Design** #112
**[TV-G]**

Looks at how statistics can be used to evaluate anecdotal evidence; distinguishes between observational studies and experiments; and reviews basic principles of experiment design, including comparison, randomization, and replication. Case material on heart disease from the Physician's Health Study demonstrates the advantages of a double-blind experiment.

** Blocking and Sampling** #113
**[TV-G]**

Looks at how sound conclusions about a population can be drawn from a tiny sample through random sampling and the census method. Topics include single- and multi-factor experiments and the kinds of questions each can answer. Agriculturalists' efforts to find a better strawberry illustrate randomized block design.

** Samples and Surveys** #114
**[TV-G]**

How to improve the accuracy of a survey by using stratified random sampling and how to avoid sampling errors such as bias. A 1936 Gallup poll provides a striking illustration of the perils of undercoverage.

** What Is Probability?** #115
**[TV-G]**

Distinguishes between deterministic phenomena and random sampling; introduces the concepts of sample space, events, and outcomes; and demonstrates how to use them to create a probability model. A discussion of statistician Persi Diaconis' work with probability theory covers many of the central ideas about randomness and probability.

** Random Variables** #116
**[TV-G]**

Demonstrates how to determine the probability of any number of independent events, incorporating many of the same concepts used in previous programs. An interview with a statistician who helped to investigate the space shuttle *Challenger* accident shows how probability can be used to estimate the reliability of equipment.

** Binomial Distributions** #117
**[TV-G]**

Presents the definition and criteria of a binomial distribution and describes a simple way to calculate its mean and standard deviation. The quincunx, a randomizing device at the Boston Museum of Science, provides a real-life example.

** The Sample Mean and Control Charts** #118
**[TV-G]**

Success stories from casino owners and the manufacturing industry demonstrate the use of the central limit theorem and show how control charts allow effective monitoring of random variation. Topics include how to create x-bar charts and the definitions of control limits and out-of-control limits.

** Confidence Intervals** #119
**[TV-G]**

Lays out the parts of the confidence interval and gives an example of how it is used to measure the accuracy of long-term mean blood pressure. An example from politics and population surveys shows how margin of error and confidence levels are interpreted. After an explanation of the use of a formula to convert the *z** values into values on the sampling distribution curve, the concepts are applied to an issue of animal ethics.

** Significance Tests** #120
**[TV-G]**

Explains the basic reasoning behind tests of significance and the concept of null hypothesis and shows how a z-test is carried out when the hypothesis concerns the mean of a normal population with known standard deviation. These ideas are explored by determining whether a poem "fits Shakespeare as well as Shakespeare fits Shakespeare." Court battles over discrimination in hiring provide additional illustration.

** Inference for One Mean** #121
**[TV-G]**

Illustrates an improved technique for statistical problems that involve a population mean and the *t* statistic for use when *?* is not known, emphasizing paired samples and the *t* confidence test and interval; covers the precautions associated with these robust *t* procedures as well as their distribution characteristics and broad applications.

** Comparing Two Means** #122
**[TV-G]**

How to recognize a two-sample problem and how to distinguish such problems from one- and paired-sample situations. A confidence interval is given for the difference between two means, using the two-sample *t* statistic with conservative degrees of freedom.

** Inference for Proportions** #123
**[TV-G]**

Introduces the use of statistical analysis to make inferences about the proportion or percent of a population that has a certain characteristic. Examples include the use of confidence intervals and tests for comparing proportions applied in government estimates of unemployment rates.

** Inference for Two-Way Tables** #124
**[TV-G]**

The use of the *chi*-square test and null hypothesis in determining the relationship between two ways of classifying a case. The methods are used to investigate a possible relationship between a worker's gender and the type of job he or she holds.

** Inference for Relationships** #125
**[TV-G]**

An examination of inference for simple linear regression and prediction presents the two most important kinds of inference: inference about the slope of the population line and prediction of the response for a given *x.* Although the formulas are more complicated, the ideas are similar to *t* procedures for the mean *?* of a population.

** Case Study** #126
**[TV-G]**

Presents a detailed case study of statistics at work, tracing the process from planning the data collection to collecting and picturing the data, drawing inferences from it, and deciding how reliable the conclusions are.