Chapter 4 Flashcards
Measures of variability
Numbers that describe diversity or variability in the distribution of a variable.
. The concept of variability has implications not only for describing the diversity
of social groups such as Asian American women but also for
issues that are important in
your everyday life
These
changes challenge us to rethink every conceptualization of society based solely on the
experiences of European populations and force us to ask questions that focus on the
experiences of different racial/ethnic groups. For instance,
we may want to compare the
racial/ethnic diversity in different cities, regions, or states or may want to find out if a
group has become more racially and ethnically diverse over time
Index of qualitative variation (IQV)
A measure of variability for nominal variables. It is based on the ratio
of the total number of differences in the distribution to the maximum number of possible differences within
the same distribution.
The index of qualitative variation (IQV) can vary from
0.00 to 1.00
It is important to remember that the IQV is partially a function of the number of
In this example, there were four and five racial/ethnic categories in Maine and
Hawaii, respectively. Had we used more categories, the IQV for both states would have
been considerably more (pg 184)
To summarize, these are the steps we follow to calculate the IQV:
- Construct a percentage distribution.
- Square the percentages for each category.
- Sum the squared percentages.
- Calculate the IQV using the formula
The IQV can also be expressed as a percentage rather than a proportion: how
Simply multiply
the IQV by 100. Expressed as a percentage, the IQV would reflect the percentage of
racial/ethnic differences relative to the maximum possible differences in each distribution.
t is estimated that by 2044, the United
States will be a minority-majority nation - explain
While the non-Hispanic white population will
still be the largest group, no racial or ethnic group will have the majority share of the
population.
for ex, We can use the IQV to measure the amount of
diversity in different regions
range
A measure of variation for interval-ratio variables. It is the difference between the highest (maximum)
and the lowest (minimum) scores in the distribution.
the range can also be found in
percentages
IQR d and purpose
To remedy the limitation of the range, we can employ an alternative—the interquartile
range. The interquartile range (IQR), a measure of variation for interval-ratio and ordinal
variables, is the width of the middle 50% of the distribution. It is defined as the difference
between the lower and upper quartiles (Q1 and Q3
).
IQR = Q3 − Q1
what is the first quartile?
Recall that the first quartile (Q1
) is the 25th percentile, the point at which 25% of the cases
fall below it and 75% above it.
box plot
A graphic device called the box plot can visually present the range, the IQR, the median, the lowest (minimum) score, and the highest (maximum) score.
The box plot provides us
with …
a way to visually examine the center, the variation, and the shape of distributions of
interval-ratio variables.
What can we learn from creating a box plot? (first two things)
We can obtain a visual impression of the
following properties: First, the center of the distribution is easily identified by the solid line
inside the box. Second, since the box is drawn between the lower and upper quartiles, the
IQR is reflected in the height of the box.
Similarly, the length of the vertical lines drawn
outside the box (on both ends) represents (in regards to a box plot)
the range of the distribution