Very complete explanation of mean, standard deviation, etc. including an online calcluator for these statistics.

This lesson will explain expected value. It is 2 of 3 in the series titled "Expected Value." [3:18]

This lesson will explain expected value. It is 3 of 3 in the series titled "Expected Value." [8:00]

In this activity, students compute statistical measures like the mean, standard deviation, and variance of the data set. They understand how measures of variability can be interpreted.

Students learn about the statistical analysis of measurements and error propagation, reviewing concepts of precision, accuracy and error types. This is done through calculations related to the concept of density. Students work in teams to each measure the dimensions and mass of five identical cubes, compile the measurements into small data sets, calculate statistics including the mean and standard deviation of these measurements, and use the mean values of the measurements to calculate density of the cubes. Then they use this calculated density to determine the mass of a new object made of the same material. This is done by measuring the appropriate dimensions of the new object, calculating its volume, and then calculating its mass using the density value. Next, the mass of the new object is measured by each student group and the standard deviation of the measurements is calculated. Finally, students determine the accuracy of the calculated mass by comparing it to the measured mass, determining whether the difference in the measurements is more or less than the standard deviation.

This lesson looks at the different measures of center and variability that are used when analyzing the spread of data in a distribution. Includes downloadable study guide with exercises - guide also covers other topics. [17:21]

This lesson discusses the normal distribution and the use of z-scores. Includes downloadable study guide with exercises - guide also covers other topics. [14:58]

In this activity, students use simulation to justify the concept of the Law of Large Numbers. They understand that as the sample size increases, the relative frequency of which an event occurs approaches the probability of that event happening. Students investigate the binomial and geometric probability functions, and determine the mean and standard deviation.

Psychology is designed to meet scope and sequence requirements for the single-semester introduction to psychology course. The book offers a comprehensive treatment of core concepts, grounded in both classic studies and current and emerging research. The text also includes coverage of the DSM-5 in examinations of psychological disorders. Psychology incorporates discussions that reflect the diversity within the discipline, as well as the diversity of cultures and communities across the globe.Senior Contributing AuthorsRose M. Spielman, Formerly of Quinnipiac UniversityContributing AuthorsKathryn Dumper, Bainbridge State CollegeWilliam Jenkins, Mercer UniversityArlene Lacombe, Saint Joseph's UniversityMarilyn Lovett, Livingstone CollegeMarion Perlmutter, University of Michigan

By the end of this section, you will be able to:

Explain how intelligence tests are developed
Describe the history of the use of IQ tests
Describe the purposes and benefits of intelligence testing

This video goes over the formulas for the mean and standard deviation of a sampling distribution of sample proportions. [9:56]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This set contains questions about simulating sampling distributions. Students see graphs of simulated distributions enabling them to reach conclusions about mean, shape, and standard deviation.

Students apply pre-requisite statistics knowledge and concepts learned in an associated lesson to a real-world state-of-the-art research problem that asks them to quantitatively analyze the effectiveness of different cracked steel repair methods. As if they are civil engineers, students statistically analyze and compare 12 sets of experimental data from seven research centers around the world using measurements of central tendency, five-number summaries, box-and-whisker plots and bar graphs. The data consists of the results from carbon-fiber-reinforced polymer patched and unpatched cracked steel specimens tested under the same stress conditions. Based on their findings, students determine the most effective cracked steel repair method, create a report, and present their results, conclusions and recommended methods to the class as if they were presenting to the mayor and city council. This activity and its associated lesson are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note for details.

Working as if they are engineers aiming to analyze and then improve data collection devices for precision agriculture, students determine how accurate temperature sensors are by comparing them to each other. Teams record soil temperature data during a class period while making changes to the samples to mimic real-world crop conditions—such as the addition of water and heat and the removal of the heat. Groups analyze their collected data by finding the mean, median, mode, and standard deviation. Then, the class combines all the team data points in order to compare data collected from numerous devices and analyze the accuracy of their recording devices by finding the standard deviation of temperature readings at each minute. By averaging the standard deviations of each minute’s temperature reading, students determine the accuracy of their temperature sensors. Students present their findings and conclusions, including making recommendations for temperature sensor improvements.

This 15-minute video lesson looks at the margin of error--finding the 95% confidence interval for the proportion of a population voting for a candidate .[Statistics playlist: Lesson 43 of 85]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 10-minute video lesson continues the discussion of margin of error--finding the 95% confidence interval for the proportion of a population voting for a candidate. [Statistics playlist: Lesson 44 of 85]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 11-minute video lesson shows how to construct small sample size confidence intervals using t-distributions. [Statistics playlist: Lesson 46 of 85]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This lesson looks at what effects changing the standard deviation, confidence level, and/or sample size have on the width of a confidence interval. Includes downloadable study guide with exercises - guide also covers other topics. [11:26]

Students build on their existing air quality knowledge and a description of a data set to each develop a hypothesis around how and why air pollutants vary on a daily and seasonal basis. Then they are guided by a worksheet through an Excel-based analysis of the data. This includes entering formulas to calculate statistics and creating plots of the data. As students complete each phase of the analysis, reflection questions guide their understanding of what new information the analysis reveals. At activity end, students evaluate their original hypotheses and “put all of the pieces together.” The activity includes one carbon dioxide worksheet/data set and one ozone worksheet/data set; providing students and/or instructors with a content option. The activity also serves as a good standalone introduction to using Excel.