Download Variability

Chapter 3
Variability
I.
Variability – how scores differ from one another.
Which set of scores has greater variability?
Set 1: 8,9,5,2,1,3,1,9
Set 2: 3,4,3,5,4,6,2,3
Means 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 Range
Subtract the lowest score from the highest (r=h-l)
What is the range of these scores? 98,86,77,56,48
Answer: 50 (98-48=50)
III.
Computing the Standard Deviation
The standard deviation (s) is the average amount of variability in a
set of scores (average distance from mean).
A.
Formula:
s
 X
X
n 1

2
Compute s for the following:
5,8,5,4,6,7,8,8,3,6
So, 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).
SPSS (practice in class p. 43).
Chapter 4
Graphing
I. Why? Describes data visually, more clearly.
II.
Frequency Distribution
A.
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.
Graphs
A.
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.
Relative Frequency
Central Tendency and Variability
Centre
Relative Frequency
Central Tendency and Variability
Spread
Skewness
Relative Frequency
If the data set is symmetric, the mean equals
the median.
Median
Mean
Skewness
If the data set is skewed to the right, the
mean is greater than the median.
Median
Mean
Skewness
If the data set is skewed to the left, the mean
is less than the median.
Mean
Median
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)