پاورپوینت کامل Statistics 52 اسلاید در PowerPoint

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پاورپوینت کامل Statistics 52 اسلاید در PowerPoint

اسلاید ۴: پاورپوینت کامل Statistics 52 اسلاید در PowerPoint deals with numbersNeed to know nature of numbers collectedContinuous variables: type of numbers associated with measuring or weighing; any value in a continuous interval of measurement.Examples:Weight of students, height of plants, time to floweringDiscrete variables: type of numbers that are counted or categoricalExamples:Numbers of boys, girls, insects, plants

اسلاید ۵: Can you figure out…Which type of numbers (discrete or continuous)Numbers of persons preferring Brand X in 5 different townsThe weights of high school seniorsThe lengths of oak leavesThe number of seeds germinating35 tall and 12 dwarf pea plantsAnswers: all are discrete except the 2nd and 3rd examples are continuous.

اسلاید ۶: Populations and SamplesPopulation includes all members of a groupExample: all 9th grade students in AmericaNumber of 9th grade students at SRNo absolute numberSampleUsed to make inferences about large populationsSamples are a selection of the populationExample: 6th period Accelerated BiologyWhy the need for statisticsپاورپوینت کامل Statistics 52 اسلاید در PowerPoint are used to describe sample populations as estimators of the corresponding populationMany times, finding complete information about a population is costly and time consuming. We can use samples to represent a population.

اسلاید ۷: Sample Populations avoiding BiasIndividuals in a sample populationMust be a fair representation of the entire pop.Therefore sample members must be randomly selected (to avoid bias)Example: if you were looking at strength in students: picking students from the football team would NOT be random

اسلاید ۸: Is there biasA cage has 1000 rats, you pick the first 20 you can catch for your experimentA public opinion poll is conducted using the telephone directoryYou are conducting a study of a new diabetes drug; you advertise for participants in the newspaper and TVAll are biased: Rats-you grab the slower rats. Telephone-you call only people with a phone (wealth) and people who are listed (responsible). Newspaper/TV-you reach only people with newspaper (wealth/educated) and TV( wealth).

اسلاید ۹: Statistical Computations (the Math)If you are using a sample populationArithmetic Mean (average)The mean shows that ½ the members of the pop fall on either side of an estimated value: meanThe sum of all the scores divided by the total number of scores.http://en.wi/wiki/Table_of_mathematical_symbols

اسلاید ۱۰: Looking at profile of data: DistributionWhat is the frequency of distribution, where are the data points Class (height of plants-cm)Number of plants in each class0.0-0.931.0-1.9102.0-2.9213.0-3.9304.0-4.9205.0-5.9146.0-6.92Distribution Chart of Heights of 100 Control PlantsDistribution Chart of Heights of 100 Control Plants

اسلاید ۱۱: Histogram-Frequency Distribution ChartsThis is called a “normal” curve or a bell curveThis is an “idealized” curve and is theoretical based on an infinite number derived from a sample

اسلاید ۱۲: Mode and MedianMode: most frequently seen value (if no numbers repeat then the mode = 0)Median: the middle number If you have an odd number of data then the median is the value in the middle of the setIf you have an even number of data then the median is the average between the two middle values in the set.

اسلاید ۱۳: Variance (s2)Mathematically expressing the degree of variation of scores (data) from the meanA large variance means that the individual scores (data) of the sample deviate a lot from the mean.A small variance indicates the scores (data) deviate little from the mean

اسلاید ۱۴: http://e.edu/wasson/ed602calcvardevs.htmCalculating the variance for a whole population = sum of; X = score, value, µ = mean, N= total of scores or valuesOR use the VAR function in Excel

اسلاید ۱۵: http://e.edu/wasson/ed602calcvardevs.htmCalculating the variance for a Biased SAMPLE population = sum of; X = score, value, n -1 = total of scores or values-1 (often read as “x bar”) is the mean (average value of xi). Note the sample variance is larger…why

اسلاید ۱۶: Heights in Centimeters of Five Randomly Selected Pea Plants Grown at 8-10 °CPlantHeight (cm)Deviations from meanSquares of deviation from mean(xi)(xi- x) (xi- x)2A1024B7-11C6-24D800E911 xi = 40 (xi- x) = 0 (xi- x)2 = 10Xi = score or value; X (bar) = mean; = sum of

اسلاید ۱۷: Variance helps to characterize the data concerning a sample by indicating the degree to which individual members within the sample vary from the meanFinish Calculating the Variance xi = 40 (xi- x) = 0 (xi- x)2 = 10There were five plants; n=5; therefore n-1=4So 10/4= 2.5

اسلاید ۱۸: Standard DeviationAn important statistic that is also used to measure variation in biased samples.S is the symbol for standard deviationCalculated by taking the square root of the varianceSo from the previous example of pea plants: The square root of 2.5 ; s=1.6Which means the measurements vary plus or minus +/- 1.6 cm from the mean

اسلاید ۱۹: What does “S” meanWe can predict the probability of finding a pea plant at a predicted height… the probability of finding a pea plant above 12.8 cm or below 3.2 cm is less than 1% S is a valuable tool because it reveals predicted limits of finding a particular value

اسلاید ۲۰: Pea Plant Normal Distribution Curve with Std Dev

اسلاید ۲۱: The Normal Curve and Standard Deviationhttp://classes.kumc.edu/sah/resources/sensory_processing/images/bell_curve.gifA normal curve:Each vertical line is a unit of standard deviation68% of values fall within +1 or -1 of the mean95% of values fall within +2 & -2 unitsNearly all members (>99%) fall within 3 std dev units

اسلاید ۲۲: Standard Error of the Sample Means AKA Standard ErrorThe mean, the variance, and the std dev help estimate characteristics of the population from a single sampleSo if many samples were taken then the means of t