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Measures of Dispersion boxplots

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RANGE difference between highest and lowest value; gives us some idea of how much variation there is in the categories of a variable (some variables have more response categories than others) generally, the higher the range, the more variation in the categories of response; the smaller the range, the less variation in the categories of response

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Quartiles divides data into four groups: Q1 = the bottom 25% of scores; Q2 = median, or 50% of scores, and Q3 = 75% of all scores. 50% of scores fall between Q1 and Q3

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InterQuartile Range (IQR) measure of dispersion that tells us about the distribution of responses to a variable in relation to the median can be used with ordinal or numerical variables, and tells us the range of values that encompass the middle 50% of the respondents to a variable

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BOXPLOTS also known as box-and-whiskers, is a graphical representation of the five- number summary. Plot the quartiles on a graph, and make a box around Q1 and Q3, with a line for the median (Q2) in the middle. Plot the lowest and highest points, and connect these with ‘whiskers’.

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Example - Here are the pulse rates of 22 smokers. Find the five number summary and create a boxplot. 3152606060606363 66 6768 6971727375 78808283110140 Lowest: 31 Q1: 22 x.25 = 5.5 – 6th term = 60 (we will always round up) Q2: 22 x.5 = 11 – between 11+12th terms = 68.5 Q3: 22 x.75 = 16.5 – 17th term = 78 (we will always round up) Highest: 140 IQR = 78-60=18 Mild outliers – (IQR) x 1.5 --- 18x1.5 = 27 60 – 27 = 33 and 78+27=105 Extreme outliers – (IQR) x 3 --- 18x3 = 54 60 – 54 = 6 and 78 + 54 =132

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