Chapter 4

Question 1

Measures of variability

Answer 1

Numbers that describe diversity or variability in the distribution of a variable.

Question 2

. The concept of variability has implications not only for describing the diversity
of social groups such as Asian American women but also for

Answer 2

issues that are important in

your everyday life

Question 3

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,

Answer 3

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

Question 4

Index of qualitative variation (IQV)

Answer 4

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.

Question 5

The index of qualitative variation (IQV) can vary from

Answer 5

0.00 to 1.00

Question 6

It is important to remember that the IQV is partially a function of the number of

Answer 6

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)

Question 7

To summarize, these are the steps we follow to calculate the IQV:

Answer 7

1. Construct a percentage distribution.
2. Square the percentages for each category.
3. Sum the squared percentages.
4. Calculate the IQV using the formula

Question 8

The IQV can also be expressed as a percentage rather than a proportion: how

Answer 8

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.

Question 9

t is estimated that by 2044, the United

States will be a minority-majority nation - explain

Answer 9

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.

Question 10

for ex, We can use the IQV to measure the amount of

Answer 10

diversity in different regions

Question 11

range

Answer 11

A measure of variation for interval-ratio variables. It is the difference between the highest (maximum)
and the lowest (minimum) scores in the distribution.

Question 12

the range can also be found in

Answer 12

percentages

Question 13

IQR d and purpose

Answer 13

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

Question 14

what is the first quartile?

Answer 14

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.

Question 15

box plot

Answer 15

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.

Question 16

The box plot provides us

with …

Answer 16

a way to visually examine the center, the variation, and the shape of distributions of
interval-ratio variables.

Question 17

What can we learn from creating a box plot? (first two things)

Answer 17

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.

Question 18

Similarly, the length of the vertical lines drawn

outside the box (on both ends) represents (in regards to a box plot)

Answer 18

the range of the distribution

Question 19

Both the IQR
and the range give us… aso what does the relative position of the box and the position of the median within the box tell us ?

Answer 19

a visual impression of the spread in the distribution. Finally, the
relative position of the box and the position of the median within the box tell us whether
the distribution is symmetrical or skewed. A perfectly symmetrical distribution would have
the box at the center of the range as well as the median in the center of the box.

Question 20

When the

distribution departs from symmetry,

Answer 20

the box and/or the median will not be centered; it will
be closer to the lower quartile when there are more cases with lower scores or to the upper
quartile when there are more cases with higher scores.

Question 21

box plots are particularly useful for…

Answer 21

comparing distributions

Question 22

IQR (illustrated by the height of the box) are much wider in the West (range =
36.2%; IQR = 14.85%) than in the Northeast (range = 18.9%; IQR = 8.7%), indicating

Answer 22

that there is more variability among states in the West than among those in the Northeast

Question 23

Another reason for using

the mean as a reference point is

Answer 23

s that more advanced measures of variation require the use of
algebraic properties that can be assumed only by using the arithmetic mean

Question 24

Variance

Answer 24

A measure of variation for interval-ratio and ordinal variables; it is the average of the squared
deviations from the mean.

Question 25

Standard deviation

Answer 25

A measure of variation for interval-ratio and ordinal variables; it is equal to the square root of the varianc

Question 26

variance formula

Answer 26

The formula for the variance | can be stated as

Question 27

This formula means | that the variance is equal to

Answer 27

the average of the squared deviations from the mean.

Question 28

One problem with the variance is that it is based on

Answer 28

squared deviations and therefore is no longer expressed in the original units of measurement. For instance, it is difficult to interpret the variance of 36.27, which represents the distribution of the percentage change in the elderly population, because this figure is expressed in squared percentages. Thus, we often take the square root of the variance and interpret it instead. This gives us the standard deviation, symbolized as s, is the square root of the variance

Question 29

stdev

Answer 29

equal to the square | root of the average of the squared deviations from the mean.

Question 30

what does the stdev mean

Answer 30

The actual number tells us very little by itself, but it allows us to evaluate the dispersion of the scores around the mean

Question 31

when is there no variation or dispersion in the scores

Answer 31

In a distribution where all the scores are identical, the standard deviation is zero (0). Zero is the lowest possible value for the standard deviation; in an identical distribution, all the points would be the same, with the same mean, mode, and median.

Question 32

how many measures of variatioan to we tend to use

Answer 32

1

Question 33

what are the five measures of variation

Answer 33

: (1) the IQV, (2) the range, (3) the | IQR, (4) the variance, and (5) the standard deviation

Question 34

Another way to interpret the standard deviation is

Answer 34

to compare it with another distribution

Question 35

a relatively low standard deviation for anything indicates

Answer 35

that this group is relatively homogenous | in wtv ur looking at (can see pg 206 for an example i think)

Question 36

nominal level measures of vblility

Answer 36

With nominal variables, your choice is restricted to the IQV as a measure of variability.

Question 37

ordinal level measures of vbility- also which are preferred?

Answer 37

The choice of measure of variation for ordinal variables is more problematic. The IQV can be used to reflect variability in the distributions of ordinal variables, but because IQV is sensitive to the rank-ordering of values implied in ordinal variables, it loses some information. Another possibility is to use the IQR, interpreting the IQR as the range of rank-ordered values that includes the middle 50% of the observations. 14 For example, if the IQR for income categories begins with the category $50,000 to $70,500 and ends with the category $100,000 to $120,500, the IQR can be reported as between $50,000 and $120,500. However, in most instances, social science researchers treat ordinal variables as interval-ratio measures, preferring to calculate variance and standard deviation

Question 38

interval ratio levels of measures of vibility- also which are preferred?

Answer 38

For interval-ratio variables, you can choose the variance, standard deviation, the range, or the IQR. Because the range, and to a lesser extent the IQR, is based on only two scores in the distribution (and therefore tends to be sensitive if either of the two points is extreme), the variance and/or standard deviation is usually preferred. However, if a distribution is extremely skewed so that the mean is no longer representative of the central tendency in the distribution, the range and the IQR can be used. The range and the IQR will also be useful when you are reading tables or quickly scanning data to get a rough idea of the extent of dispersion in the distribution.

Question 39

theres a good chart on page 208

Answer 39

ok lol

Question 40

Pope’s analysis about mentoring is based on

Answer 40

a survey measuring student perceptions about campus climate, institutional diversity, mentoring, and administrative support of diversity

Question 41

we present statements that measure mentoring from three different sources:

Answer 41

(1) staff, (2) peers, and (3) students themselves. The mean agreement scores and standard deviations vary by each group, that is to say, perceptions about mentoring differ by racial or ethnic identity.

Question 42

The standard deviations indicate the variability of responses

Answer 42

A smaller standard deviation reveals more consistency of responses clustered around the mean score, whereas a larger standard deviation indicates more variation, more spread from the mean.

Question 43

results of myron popes survey

Answer 43

The standard deviations are all above 1.0, with the most variation in responses for the group of African American students

Question 44

To find the range, | subtract the lowest from the highest score in a distribution. For an ordinal variable

Answer 44

report the | lowest and the highest values without subtracting.

Question 45

The box plot is a graphical device that visually presents the

Answer 45

e range, the interquartile range, the | median, the lowest (minimum) score, and the highest (maximum) score. The box plot provi

Question 46

The variance and the standard deviation are

Answer 46

two closely related measures of variation for intervalratio and ordinal variables that increase or decrease based on how closely the scores cluster around the mean. The variance is the average of the squared deviations from the center (mean) of the distribution; the standard deviation is the square root of the variance.