Unit 4: Accentuate the Negative Investigation 1

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Our objective today:Learn about statistics and why they are important Explore how we can gain information about a population by examining a sample populationStatistics2Statistics is the study of the collection, organization, analysis of data.Statistics

3A statistical population is a set of entities concerning which statistical inferences are to be drawn.Examples: Population of a school A sports teamStatistics

4A statistical sample is a subset of the statistical population that should represent the statistical population. A sample is valid only if the sample is representative of the populationStatistics

5Random sampling tends to produce representative samples and support valid inferences.Statistics

6Variability a measure of how far a set of numbers is spread out.Measures of Central Tendency relates to the way in which data tends to cluster around some valueMeanMedianModeRange

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7

http://www.youtube.com/watch?v=qpxtBghmvvsData Set: 11, 26, 22, 15, 18, 26, 16

MeanMedianModeRangeData Set: 5, 12, 6, 15, 7, 10, 4, 8

MeanMedianModeRange

http://www.youtube.com/watch?v=1jVZi0cNHls

Can you think of any ways that Statistics are used in life?Statistics

Can you think of data distributions and statistics kept in sports?Who cares about these?Would variability matter in Tim Duncans earnings?CAN YOU THINK OF OTHER SPORTS STATISTICS ?StatisticsStatistics

RBIERA15StatisticsFree-ThrowPercentage

16Statistics & ProbabilityYards Per Game

17Can you think of data distributions and statistics kept for music?Who cares about these?Would variability matter in Rihannas statistics?

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Can you think of data distributions and statistics kept that will effect your application to college?Who cares about these?Would variability matter ?StatisticsStatistical Data can be1. Categorical2. NumericalStatistics

Categorical Data data that fall into specific labels or categories.Categorical data is data that is defined by words or as a limited number of answer options.StatisticsStatistics

GreenYellowOrangeBlueBrownRedTotalNumber51444191258PercentCategorical data is reported in the FREQUENCY. It is recorded by how many or what percentage fall into each category.For example, if you counted the number of each color of M&Ms found a bag, you may find. Statistics

GreenYellowOrangeBlueBrownRedTotalBag 151444191258Bag 251527151054Bag 331355191055If you counted several bags, you might find.StatisticsThis data can also be reported in other forms, such as bar graphs that show the frequency.What patterns do you see?

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GreenYellowOrangeBlueBrownRedTotalNumber92449109905764151,731PercentThe following is actual data of colors found in a sampling of 30 bags of M&Ms. Find the percentage of each color. Sketch a bar graph showing the percentages.StatisticsDo you think the sample of 30 bags have any more statistical reliability than the earlier sample of 3 bags?30 Bags Percent of Each Color40%35%30%25%20%15%10%5%0%Green Yellow Orange Blue Brown RedNumerical Data data that are counts or measures.For example, we count people to find the population of each state in the United States in order to answer the question, How much do state populations vary in size?Statistics

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What are other examples of numerical data?

28StatisticsIn decade from 1901 to 1910, how many immigrants came from Europe? What else can you say about this decade?DecadeImmigrants FromEuropeTotalImmigrantsPercent of ImmigrantsFrom Europe188118904,735,4845,246,61390%189119003,555,3523,687,56496%190119108,056,0408,795,38692%191119204,321,8875,735,81175%192119302,463,1944,107,20960%19311940347,566528,43166%19411950 621,1471,035,03960%195119601,325,7272,515,47953%196119701,123,4923,321,67734%19711980 800,3684,493,31418%19811990 761,5507,338,06210%199120001,359,7379,095,41715%29Categorical vs. Numerical ? Age Month you were born. Weight Favorite Singer Eye Color Height Favorite Ice Cream

StatisticsThe school food service wants to increase the number of students who eat lunch in the cafeteria.The student council has been asked to conduct a survey of the student body to determine the students preferences for hot lunch. They are considering several methods to do the survey.Statistics & Probability31Lets look at the methods and determine if they would provide a random sample. Which method should the council use?Write all the students names on cards and pull them out in a draw to determine who will complete the survey.Survey the first 20 students that enter the lunchroom.Survey every 3rd student who gets off a bus.Statistics32Now, lets devise a sampling method in our class for conducting the following surveys.Do 7th Grade Students prefer Coke or Pepsi products ?What is the average shoe size for students at Quail Hollow?Statistics