# collier

 Raw scores they are meaningless because we dont know whats good or bad, high or low Relative scale most test scores are judged on a relative scalerelative to other test takers Summary statistics about summarizing single variablesfocus on quantitative (numerical)variablesstart with a "bag of data" (collection of numbers)consists of one or (usually) more variables what does summarizing mean making information more concise (shorter)summarizing depends on the sample size (N)if N is large, we need to be very conciseif N is small, we can be less concise (more complete) Sorting the simpliest summary technique is to sort the dataworks with small sets of numberseasier to see the distribution when the data are sortedno information is lost; the presentation is merely simplified Histogram a bar graph of a grouped frequency distribution of quantitative variablethe apperance of a histogram can vary depending on how many categories you use how to create a histogram create categories or groups of binscount the number of people or items in each groupmake a bar graph, one bar for each group Frequency polygons the same as histograms, but midpoints connected by lines, rather than using barsnot used very much raw frequencies counts are the original numbers relative frequencies the numbers divided by N (the total)percentages are the same relative frequency, except with the decimal point shifted over two places Symmetrical left side is the mirror image of the right sidemany distributions are symmetrical Shapes of distributions SymmetricalUniformBell-shapedFloor and Ceiling effectsSkewedBimodal Uniform equal probabilities in all categoriesuniform distribution is symmetricalbars are close together in uniform Bell-shaped most commonanother examole of a symmetrical distributionbars are close togther in a bell shape Floor effects there is a lower limit to the possible numbersusually this is 0examples: incomes, which generally cannot be negative ceiling effect an upper limit to the possible numbers Skewed to the right (positively skewed)to the left (negatively skewed)skew us frequentky due to floor and ceiling effects Bimodal two humps or central pointslike two bell shaped put together Boxplots (or box-and-whisker plots) includes median (a small square)outliers (small circle)non-outlier range (in the shape of a capital I)and the percentage (a big box) measures of central tendency these measure where the "middle" or "center" is, or where most of the action is in the distributionincludes the mean, median, and mode measures of dispersion or variability theses measure how spread out the data are mean arithmetic average- add them up and divide by Nmost sensitive to outliers median middle-most number (same as the 50th percentile)if there is an even amount of numbers, average the middle twosort the numbers firstless sensitive to outliers mode the most frequently occuring number.the hump in the histogramsthe only measure that works with qualitative datathe only measure of central tendency where there can be two (eg. bimodal) when a distribution is symmetrical and bell-shaped the mean median and mode are the same when distributions are skewed mean, median, and mode are separate measures of dispersion of variability these measure how spread out the data area data set: 3 3 3 3 (0 variability)another data set: 1 2 3 4 5 (medium variability)another data set: -1 1 3 5 7 (larger variability) Ordinal measures of variability these depend only on the order of the numbersrange, interquartile range, and semi-interquartile range range highest to lowest interquartile range chop off the top 25% (upper quartile)chop off the bottom 25% (lower/bottom quartile)take the difference semi-interquartile range half of the interquartile range quantitative measures of variability these are based on the actual numbers, not just their ordersvariance and standard deviation variance average squared deviation from the mean Standard deviation square root of the variance Norms are summary statistics of test results-they tell us what is "normal" or averagewe can tell how far an individual score is from average using summary statisticsZ scores are commonly used Authorbrittanyball42 ID177812 Card Setcollier Descriptionchapter 4.1 Updated2012-10-15T18:43:46Z Show Answers