Distribution of Quantitative Variables:The next quiz is up on Moodle from Sunday February 9 to Monday February 10.Review:Histogram- visual representation of the distribution of quantitative variablesMean- measure of central tendencyStandard deviation and variance- measure of spreadMedian- measure of central tendencyDifference between mean and median- median is less sensitive to the presence of outliersWhich is better? There’s no answer; it depends on what you’re measuringTo find typical value (for example: income)- use medianStats- use the meanNew Material:Q1- first quartile- median of the lower half of the distribution (lowest 25% of the distribution)Q3- third quartile-median of the upper half of the distributionCompute- take the numbers that fall below the median and take the median of those numbers (Q1)Ex: if you have 17 values, the overall median will be with 9th value and there will be 8 values below the overall median and 8 values above the overall median. Q1- mean of value 4 and value 5 and Q3- mean of 13 and 14Ex: if you have 16 values, the overall median will be the average of value 8 and 9. Q1- because the overall median is 8.5, count values 8 and 9 in the bottom and top sets which would put an even number in the bottom and top set and make Q1 fall between value 4 and 5. Q3- fall between 12 and 13.Ex number set: 1,2,3,4,5,6,7 2-Q1, 4-med, 6-Q3Ex number set: 1,2,3,4,5,6 2-Q1, 4.5-med, 5-Q3Range from Q1-Q3 is called the interquartile rangeAnother type of graph: boxplot or box-and-whisker plotLine through the main box: medianUpper edge of the box- Q3Lower edge of the box- Q1Lower whisker- minUpper whisker- maxIf values are bunched up in a central area- the distance between Q1 and Q3 is not very far but the distance between min and Q1 and Q3 and max is much larger because the values vary more off to the left and right sidesSkews will show up in the boxplot (example, slide 53) and this is shown in the boxplot by the fact that the min and Q1 are close to each other as compared to the long distance between Q3 and the maxOn boxplots, outliers are represented as circles beyond the max or below the minA histogram with a rectangular distribution would make a boxplot that has a large box (distances of min to Q1, and of Q3 to the max would be the same)Slide 55- the answer is D because all of them have different medians (the red line), they don't have the same mean (they are all pretty symmetrical), one boxplot has outliers, but they are all spread out about the same amountSlide 56- the answer is A because there are spread out values below the median and more values on the left sideDistribution with a long box and short whiskers- histograms with two humps- a bimodal distribution (the middle 50% would be very spread out compared to Q1 and Q3)Review all the terms on the last page of the powerpoint!Next Unit: Relationships between quantitative variablesPsych 240 Lecture February 7, 2014 02/08/2014-Distribution of Quantitative Variables:-The next quiz is up on Moodle from Sunday February 9 to Monday February 10.Review: -Histogram- visual representation of the distribution of quantitative variables-Mean- measure of central tendency-Standard deviation and variance- measure of spread -Median- measure of central tendency-Difference between mean and median- median is less sensitive to the presence of outliers -Which is better? There’s no answer; it depends on what you’re measuring-To find typical value (for example: income)- use median-Stats- use the meanNew Material:-Q1- first quartile- median of the lower half of the distribution (lowest 25% of the distribution)-Q3- third quartile-median of the upper half of the distribution -Compute- take the numbers that fall below the median and take the median of those numbers (Q1)-Ex: if you have 17 values, the overall median will be with 9th value and there will be 8 values below the overall median and 8 values above the overall median. Q1- mean of value 4 and value 5 and Q3- mean of 13 and 14-Ex: if you have 16 values, the overall median will be the average of value 8 and 9. Q1- because the overall median is 8.5, count values 8 and 9 in the bottom and top sets which would put an even number in the bottom and top set and make Q1 fall between value 4 and 5. Q3- fall between 12 and 13. -Ex number set: 1,2,3,4,5,6,7 2-Q1, 4-med, 6-Q3-Ex number set: 1,2,3,4,5,6 2-Q1, 4.5-med, 5-Q3-Range from Q1-Q3 is called the interquartile range -Another type of graph: boxplot or box-and-whisker plot-Line through the main box: median-Upper edge of the box- Q3-Lower edge of the box- Q1-Lower whisker- min-Upper whisker- max -If values are bunched up in a central area- the distance between Q1 and Q3 is not very far but the distance between min and Q1 and Q3 and max is much larger because the values vary more off to the left and right sides-Skews will show up in the boxplot (example, slide 53) and this is shown in the boxplot by the fact that the min and Q1 are close to each other as compared to the long distance between Q3 and the max-On boxplots, outliers are represented as circles beyond the max or below the min -A histogram with a rectangular distribution would make a boxplot that hasa large box (distances of min to Q1, and of Q3 to the max would be the same)-Slide 55- the answer is D because all of them have different medians (the red line), they don't have the same mean (they are all pretty symmetrical), one boxplot has outliers, but they are all spread out about the same amount -Slide 56- the answer is A because there are spread out values below the median and more values on the left side -Distribution with a long box and short whiskers- histograms with two humps- a bimodal distribution (the middle 50% would be very spread out compared to Q1 and Q3)-Review all the terms on the last page of the powerpoint!-Next Unit: Relationships between quantitative