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TAMU PSYC 203 - Variability

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PSYC 203 1st Edition Lecture 2 Outline of Last Lecture II. Parameters and StatisticsA. Definition of eachB. ExamplesIII. Notationa. Meanb. Summation NotationIV. Sampling errora. Definitionb. ExamplesV. Types of Variablesa. Discrete b. ContinuousVI. Histogramsa. DefinitionVII. Central Tendency3 measures of central tendency Outline of Current Lecture I. Review of last class a. Parameter vs. Statistics b. Sampling errorc. Formula for Mean II. Categorical dateIII. MedianIV. PercentileV. ModeVI. Distributions & Central TendencyVII. VariabilityVIII. RangeIX. Standard DeviationCurrent LectureI. Review of last class These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.a. Parameter vs. Statistics i. Parameters are for populations ii. Statistics are for samples 1. X with a bar over it is used for samples, μ is used for populations when calculating mean b. Sampling errori. The difference between sample and population valuesc. Formula for Mean i. Μ=ΣX/N (sample mean)ii. μ=Σx/n(population mean)II. Categorical dataa. It doesn’t really make sense to use mean for thisb. Values are given a numerical value that is more of a label than anything else so getting the mean, 1.77 for example, of Democrat (assigned “value1”) Republican (assigned “value2”), or Independent(assigned “value3”) doesn’t make any sense c. Instead, use mode for thesed. Another reason that the mean doesn’t work for these instances is that someotimes the extremes offset the data. i. For example: if everyone in a class fails the test, but three people get 100s, the average may not be as bad as the majority actually was. (5 people got 50s and 2 got hundreds, the mean would be 64, when the majority of the people actually got 50s)III. Mediana.Attained by ranking a set of scores from smallest to largest (or vice versa) and getting the middle numberb.If there is an odd number of scores, the median is the one in the middlec.If the is an even number of scores, the median is the mean of the two middle numbers d.The median has 50% of the scores above it and 50% below It e.In a positively skewed dataset, the mean is higher than the median and vice versa if negatively skewedIV. Percentilea. These refer to the percentage of cases equal to and below a given point on the distribution of scores – Used in standardized testing a lot! b. Whether you want to be in the high or low percentile depends on the situation. For example, you want to be in the high percentile when it comes to tests scores, but not when it comes to death rates or illness rates. V. Modea. The most frequently occurring category or score in a distribution.b. It is important to realize that the modal is not the value. For example, if “Republican” was assigned the most commonly occurring, with 10 people. “10” isnot the modal, it is “Republican”c. It is possible to have a bimodal distribution VI. Distributions & Central Tendencya. On a graph, the mean is always attracted towards the tails in a skewed distributionb. In a negative distribution, the mode is the highest point on the graph and medianis higher than the mean c. The mode is also the highest point for a positive distribution, but the median is lower than the mean VII. Variabilitya. refers to how spread out scores are in a distribution.b. Central tendency = Central point of the distribution c. Variability = Scatter d. Together, central tendency and variability are the two primary ways of summarizing a dataset. e. Variability can be measured several ways – the range-- the standard deviation/variancef. In each case, variability is based on the distance between scoresi. if everything is bunched up, there is not much distance VIII. Rangea. The range is the total distance covered by the entire distribution, from the highest score to the lowest score.b. The formula for range is: range= Xmax-XminIX. Standard Deviationa. The most frequently reported measure of variability– Represents the average amount of variability in a set of scoresb. On average, how far away are the data points from the mean?– Low standard deviation means the data tends to be close to the mean – High standard deviation means the points tend to be far away from the mean– Which distribution would have a higher standard deviation?X. • Abbreviated s or SDXI.on the graph above, A has a higher deviation than B S^2= variance and SD=standard deviation XII. All of this is with response to the mean XIII. If below mean, negative and if above mean,


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