Chapter 3

Question 1

what are frequency distribs useful for? what is a main advntage of using f using frequency distributions or graphs is to summarize quantitative
information

Answer 1

Frequency distributions and graphical techniques are useful tools for describing data. The
main advantage of using frequency distributions or graphs is to summarize quantitative
information in ways that can be easily understood even by a lay audience

Question 2

Measures of central tendency

Answer 2

y Categories or scores that describe what is average or typical of the
distribution.

Question 3

We will see that the choice of an appropriate measure of central tendency for representing a
distribution depends on three factors:

Answer 3

(1) the way the variables are measured (their level of

measurement) , (2) the shape of the distribution, and (3) the purpose of the research.

Question 4

mode and what level of measurement is it used in

Answer 4

The mode is the category or score with the largest frequency or percentage in the
distributionThe mode is the only measure of central tendency that can be used with nominal-level
variables

Question 5

what is the mode - a category/score or a frequency?

Answer 5

a category/score, The mode
is not necessarily the category with the majority (i.e., more than 50%) of cases, as it is in
Table 3.1; it is simply the category in which the largest number (or proportion) of cases fall

Question 6

why is the mode the only measure of CT to be used with nominal level vbles

Answer 6

Recall that with nominal variables—such as foreign languages spoken in the
United States, race/ethnicity, or religious affiliation—we are only able to classify
respondents based on a qualitative and not on a quantitative property. However, the mode
can also be used to describe the most commonly occurring category in any distribution

Question 7

what is bimodal? what should you report in these situations?

Answer 7

When two
scores or categories with the highest frequencies are quite close (but not identical) in
frequency, the distribution is still “essentially” bimodal. In these situations, you should not
rely on merely reporting the (true) mode, but instead report the two highest frequency
categories.

Question 8

median

Answer 8

The score that divides the distribution into two equal parts so that half the cases are above it and
half below it.

Question 9

what does the median represent

Answer 9

the exact middle of a
distribution; it is the score that divides the distribution into two equal parts so that half the
cases are above it and half below it.

Question 10

The median is a suitable measure for those variables whose

…

Answer 10

categories or scores can be arranged in order of magnitude from the lowest to the highest.

Question 11

what happens with a median (for ex, for the fair example on pgs 132-133)

Answer 11

Notice that the median divides the distribution exactly into
half so that there are two respondents who are more satisfied and two respondents who are
less satisfied.

Question 12

what happens when data is ordinal

Answer 12

As a note of caution, when data are ordinal, averaging the middle two scores is no longer
appropriate. The median simply falls between two middle values.

Question 13

how to find the median? what is it always?

Answer 13

To find the median, we need to identify the category associated with the observation
located at the middle of the distribution. This may seem odd; however, the median is always the
value of the response category, not the frequency.

Question 14

We can also locate the median in a frequency distribution by using the cumulative
percentages column - how?

Answer 14

To find
the median, we identify the response category that contains a cumulative percentage value
equal to 50%. The median is the value of the category associated with this observation.

Question 15

how to find the percentage value = to 50%?

Answer 15

If you are not sure
why the middle of the distribution—the 50% point—is associated with the category
“moderate,” look again at the cumulative percentage column (C%). Notice that 33% of the
observations are accumulated below the category “moderate” and that 66% are
accumulated up to and including the category “moderate.” We know, then, that the
percentage value equal to 50% is located somewhere within the “moderate” category.

Question 16

what is a percentile? how is it connected to a median?

Answer 16

The median is a special case of a more general set of measures of location called percentiles.
A percentile is a score at or below which a specific percentage of the distribution falls

Question 17

explain the 75th percentile

Answer 17

The
nth percentile is a score below which n% of the distribution falls. For example, the 75th
percentile is a score that divides the distribution so that 75% of the cases are below it

Question 18

like the median, what do percentiles requie? when are they easy to identify?

Answer 18

Like the median, percentiles require that data be ordinal or higher in
level of measurement. Percentiles are easy to identify when the data are arranged in
frequency distributions.

Question 19

explain how ACT percentiles work

Answer 19

e. Suppose for a moment that
90% of all students received a lower ACT score than you (and 10% scored above you).
Your percentile rank would have been 90

Question 20

what is a quartile? what is the lower and upper ones?

Answer 20

Another widely used measure of location is the quartile. The lower quartile is equal to the
25th percentile and the upper quartile is equal to the 75th percentile

Question 21

how would colleges calculate and use quartiles

Answer 21

A college admissions office interested in accepting the top
25% of its applicants based on their SAT scores could calculate the upper quartile (the 75th
percentile) and accept everyone whose score is equivalent to the 75th percentile or higher.
(Note that they would be calculating percentiles based on the scores of their applicants, not
of all students in the nation who took the SAT.)

Question 22

mean

Answer 22

A measure of central tendency that is obtained by adding up all the scores and dividing by the total
number of scores. It is the arithmetic average.

Question 23

formula

Answer 23

A formula is a shorthand way to explain what

operations we need to follow to obtain a certain result

Question 24

mean formula

Answer 24

y bar= (sigma y)/ N

Question 25

for the incarceration rate q on pg 142, wy select means?

Answer 25

Because the variable “incarceration rate” is an interval-ratio variable, we will select the
arithmetic mean as our measure of central tendency

Question 26

why is the mean the center of gravity of the distribution

Answer 26

Because the mean (unlike the mode and the median) incorporates all the scores in the
distribution, we can think of it as the center of gravity of the distribution. That is, the mean
is the point that perfectly balances all the scores in the distribution. If we subtract the mean
from each score and add up all the differences, the sum will always be zero!

Question 27

what is the difference between the mean versus the mode and median

Answer 27

unlike

with the mode or the median, every score enters into the calculation of the mean

Question 28

how are we investigating gender income inequality

Answer 28

gender income
equality has yet to be achieved. We continue our investigation of gender income inequality
by reviewing published income data.

Question 29

why may mean not be the best measure of central tendency for income? what is more commonly used?

Answer 29

, due to its sensitivity to extreme
values. median earnings. . We can use these medians to note the differences
between subgroups of the population or changes over time.

Question 30

what should you do when a researcher reports an avg score?

Answer 30

When mean income scores are reported, interpret with caution as extremely low or high
income values may skew the distribution. When a researcher reports an “average” score,
assess whether the calculation was based on a median or a mean.

Question 31

The distribution of interval-ratio variables can also be described by …

Answer 31

their general shape

Question 32

Using histograms, produced by SPSS, we will demonstrate how a distribution can be ….

Answer 32

either
symmetrical or skewed, depending on whether there are a few extreme values at one end of
the distribution

Question 33

symmetrical distribution

Answer 33

n The frequencies at the right and left tails of the distribution are identical; each
half of the distribution is the mirror image of the other.

Question 34

skewed distrib

Answer 34

n A distribution with a few extreme values on one side of the distribution.

Question 35

positvely skewed distrbution

Answer 35

A distribution with a few extremely high values. When the mean is higher than the median (or is positioned to the right of the
median), the distribution is positively skewed.

Question 36

negatively skewed distribution

Answer 36

A distribution with a few extremely low values. When the mean is lower than the median (or is positioned to the left of the median),
the distribution is negatively skewed.

Question 37

what is the main consideration in choosing a measure of central tendency

Answer 37

The variable’s level of measurement is the primary consideration in choosing a measure of
central tendency. The measure of central tendency should be appropriate to the level of
measurement. Thus, as shown in Figure 3.11, with nominal variables our choice is
restricted to the mode as a measure of central tendency.

Question 38

what measures of central tendency can we use with oridnal data

Answer 38

(1) the mode or (2) the median (or

sometimes both

Question 39

When the distribution is skewed, the mean may give 1 The 2 can be chosen as the preferred measure of central
tendency because neither is influenced by extreme scores.

Answer 39

1misleading information on the central
tendency because its value is affected by extreme scores in the distribution.

2median
or the mode

Question 40

what is the median calculated for

Answer 40

n. It is

often used to describe the most commonly occurring category of a nominal-level variable

Question 41

what happens with skewed distributions v symmetrical distributions

Answer 41

In a symmetrical distribution, the frequencies at the right and left tails of the distribution are
identical. In skewed distributions, there are either a few extremely high (positive skew) or a few
extremely low (negative skew) values