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Sociology and Anthropology
SOAN 3120
Michelle Dumas

September 12, 2013 – Lecture 3 - SOAN Mean… - sigma represents the sum The Median - if n is an odd number, it’s integer – the easy way! - If n is an even number: fraction (average) o How to calculate:  Take the two middle numbers  Divide by two  That’s your median! Mean vs. Median - symmetric distribution (normal) o highest point is right in the middle - skewed distributions: the mean and the median are pulled in the direction of the skew o example: positive  mean will be larger than the median if it’s a positive skew o skewed right  the hill part is on the left, and the tail is on the right  median greater then the mean! o skewed left  the hill part is on the right, and the tail is on the left Measuring Spread: The Quartiles - how is dividied into quarters? - Quartiles are denoted with Qx - Q1: first quartile (represents ¼) - M (Q2): (1/2) o Second quartile is represented by the median (so Q2) o It’s the halfway point. - Q3: third quartile (3/4) o The point that has 75% or three quarters of the observations below it. Quartiles - finding Q1 and Q3 o order from smallest to largest o find median – the halfway point o find position - order observation - median use (n* = n/2) - position: (n+1)/2 September 12, 2013 – Lecture 3 - SOAN Example: - infant mortality o n=13, n*=6 o 13 17 21 / 22 22 24 //24 //39 42 45 / 46 58 66 - quartiles 1 and 3 o position: (6 +1)/2 = 3/5 o insert slide 20 here missed slide 21, 22, 23, 24 Boxplot - represents data of first and third quartile - draw a thick line where the median might be - draw whiskers o from the top max to the bottom minimum through the boxplot - this is to be a graphical representation of those 5 number summary - making a boxplot…………. o lay off scale to accommodate extremes of data o draw central box between q1 and q3 o draw median in central box o draw whisker from each extreme - outliers o some cases can be taken out o calculate inter-quartile range (IQR)  IQR = q3 – q1  Measure off 1.5 times the IQR  Fences  Observations between these fences are considered outliers  Most extreme non-outlying observation  These last of durations before the fence are called adjacent values  Whiskers: adjacent values Standrad deviation - the deviation from the mean - how far an observation
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