Outliers and Data Representations (02:47)
See an irregularity in weather data on a graph. Investigate the cause of an outlier. Correct or discard data that is likely erroneous or account for data that you can legitimize.
Outliers— Far Out Waves and Surfers (03:20)
In this example, view a graph of wave height data collected by an offshore weather buoy. Use a box-and-whisker plot on a histogram to determine whether or not a value is an outlier.
Representing and Interpreting Outliers— Winds and Skyscrapers (02:51)
Engineers need to consider wind force data when constructing a skyscraper. In this example, view graphs of average wind speeds that contain outliers.
Outliers in Relationships between Variables— Waves and Winds (03:19)
An offshore weather buoy measures wind and waves before they reach surfers. In this example, consider a graph that shows a correlation between wind speed and wave height and three outliers. Overlay a least-squares regression line and a median-fit line.
Misinterpreting Data (02:56)
Bias is an opinion based on previous ideas without independent assessment. Bias and measurement error can affect the interpretation of data. Compare two graphs in an example of display distortion.
Bias— Sharks (02:32)
In this example, consider the role of bias. Ron Lydeck has seen a steep rise in the number of sharks killed in Palauan waters and fears the shark population is over-fished; bias can lead to over interpretation of data.
Measurement Error— Weight, Vision, and Election (02:05)
Measurement accuracy depends on the tool and how well it is used. In this example, see how calibration, light, and sample exclusion can result in faulty data.
Misleading Data Displays— Temperature and Music (03:16)
In this example, see how display distortion could provide a misleading view of data. Graphs can minimize or emphasize changes.
The Statistics of Sampling, or By Any Means (01:26)
Development threatens African wildlife; scientists monitor population sizes and characteristics. Sampling is the use of a subset to represent the larger population. Several factors affect how well a sample represents the population and how it is interpreted.
Sampling Distributions— Elephant Ages (01:57)
In this example, scientists use a sample to better understand the distribution of ages. Statistics of larger samples are likely to be more representative of the population as a whole.
Central Limit Theorem— Giraffe Graphs (03:56)
In this example, a graph illustrates distributions of height frequencies in a bell shape; sample randomness and size are important. In the central limit theorem, the means will tend to be normally distributed and vary less for larger samples.
Confidence Intervals— Running Cheetahs (03:08)
In this example, see hypothetical results for the top speed of individual cheetahs and the confidence interval for the population mean. The standard error of the mean equals the standard deviation divided by the square root of the sample size.
Sampling Techniques (02:18)
Every ten years, the federal government takes a census and develops statistical summaries on the U.S. population; one in every 10 households receives a detailed questionnaire. See how sampling is used in marketing.
Random and Biased Samples— Luggage (02:11)
In this example, see a hypothetical situation where airport checkers locate banned items in six out of 400 bags inspected by hand. A biased sample over represents or under represents part of a population.
Stratified Samples— Phone Survey (02:33)
In this example, a market research firm conducts a phone survey to learn how young Americans spend their disposable income; they excluded three groups of people. The firm could divided the population into subgroups for its survey.
Representative Samples— Students with Phones (02:39)
In this example, a wireless company polled 100 college students with cell phones about their spending habits; see a frequency histogram. The samples were not representative of the entire population of the target age group.
Uncertainty in Statistical Inferences (02:02)
Statisticians study trends. Sampling error is unavoidable but one can estimate the level of uncertainty. Hear examples of non-sampling errors.
Sampling Error and Confidence Interval— High School Completion (02:27)
Officials monitor high school dropout rates. In this example, the sampling group included 60,000 households throughout the U.S. Identify the sampling error percentage and the confidence interval.
Percents— Unemployment Rates (03:01)
At the beginning of the 21st century, the unemployment rate in the U.S. was approximately 5%. In this example, consider the unemployment rates of high school graduates, high school dropouts, and college graduates and identify the uncertainties.
Means— Average Salaries and Education (03:53)
In this example, consider a 2005 study indicated the financial value of a college education. Standard deviation and sample size are two factors important to estimating uncertainty for a sample mean.
Credits: Discovering Math: Advanced—Statistics and Data Analysis: Part 2 (00:45)
Credits: Discovering Math: Advanced—Statistics and Data Analysis: Part 2
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