Measures of Dispersion

1. Measures of Dispersion boxplots

2. 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

3. 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

4. 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

5. 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’.

6. Example - Here are the pulse rates of 22 smokers. Find the five number summary and create a boxplot. 31 52 60 60 60 60 63 63 66 67 68 69 71 72 73 75 78 80 82 83 110 140 • 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