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Chapter 3Variability
I. Variability – how scores differ from one another.Which set of scores has greater variability?Set 1: 8,9,5,2,1,3,1,9Set 2: 3,4,3,5,4,6,2,3Means are Set 1: 4.75 and Set 2: 3.75. Tells us nothing of
variability.Variability is more precisely how different scores are from the
mean. II. Computing the RangeSubtract the lowest score from the highest (r=h-l)What is the range of these scores? 98,86,77,56,48Answer: 50 (98-48=50)III. Computing the Standard DeviationThe standard deviation (s) is the average amount of variability in a
set of scores (average distance from mean).
A. Formula:
Compute s for the following:5,8,5,4,6,7,8,8,3,6So, an s of 1.76 tells us that each score differs from the mean by
an average of 1.76 points.*Why n-1? N represents the true population and n-1 represents
the sample. Since we are projecting onto the sample, it is better to overestimate the variability (be conservative). The larger the sample size, however, the less of a difference this will make.
B. Purpose: to compare scores between different distributions, even when the means and standard deviations are different (e.g., men and women). Larger the s the greater the variability.
IV. Computing Variance – simply s2 (really only used to compute other formulas and techniques). Difference: Variance is stated in units that are squared (not original units).
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2
n
XXs
Chapter 4Graphing
I. Why? Describes data visually, more clearly. II. Frequency DistributionA. Class Interval Column – divides the scores up into
categories (0-4, 5-9, etc.). Usually range of 2,5,10, or 25 data points. Main thing: be consistent!
B. Frequency Column – number of scores within that range or category.
III. GraphsA. Histogram – shows the distribution of scores by class
interval. Can compare different distributions on the same histogram. Shows:
1. Variability (p. 60)2. Skewness (p. 61). If the mean is greater than the median,
positive skewness. If median is greater than mean, negative skewness.
B. Column Charts – simply tells the quantity of a category according to some scale. SCALE IS IMPORTANT (CSPAN-drug use story).
C. Bar Charts – same as Column chart, but reverse the axes.
D. Line Chart – Used to show trends (e.g. rise and fall in pres. Popularity – line on website).
E. Pie Charts – Great for proportions (percent of MS budget going to each budget category).
IV. SPSS and Graphing (southern states and % evangelical-histogram; this class and % gop/dem/other – line/bar)