section 2.2: considering categorical data

Question 1

what is a contingency table?

Answer 1

a table that summarizes data for two categorical variables

Question 2

what is a bar plot?

Answer 2

common way to display a single categorical variable

Question 3

what is a relative-frequency bar plot?

Answer 3

a bar plot where proportions instead of frequencies are shown

Question 4

how are bar plots different than histograms?

Answer 4

Bar plots are used for displaying distributions of categorical variables, while
histograms are used for numerical variables. The x-axis in a histogram is a
number line, hence the order of the bars cannot be changed, while in a bar plot
the categories can be listed in any order

Question 5

what is variance?

Answer 5

the standard deviation squared

Question 6

what is the equation for variance?

Answer 6

s^2 = (sum of(x - x̄)^2)/(n-1)

Question 7

what points make a larger difference in variance?

Answer 7

points that are far away from the mean

Question 8

Why do we use the squared deviation in the calculation of variance?

Answer 8

To get rid of negatives so that observations equally distant from the mean are weighed equally.
To weigh larger deviations more heavily.

Question 9

what is standard deviation?

Answer 9

the square root of the variance, and has the
same units as the data

Question 10

what is the median?

Answer 10

the value that splits the data in half when ordered in ascending order

Question 11

what is the 50th percentile?

Answer 11

the median

Question 12

what is the 25th percentile?

Answer 12

the first quartile, Q1

Question 13

what is the 75th percentile?

Answer 13

the third quartile, Q3

Question 14

what is interquartile range (IQR)?

Answer 14

where the middle 50% of the data is

Question 15

what is the equation for IQR?

Answer 15

IQR = Q3 - Q1

Question 16

what does the box in a box plot represent?

Answer 16

represents the middle 50% of the data, and
the thick line in the box is the median

Question 17

what is the max upper whisker reach of a box plot?

Answer 17

Q3 + 1.5 x IQR

Question 18

what is the max lower whisker reach of a box plot?

Answer 18

Q1 - 1.5 x IQR

Question 19

what is an outlier?

Answer 19

observation beyond the maximum reach of the whiskers

Question 20

why is it important to look for outliers?

Answer 20

Identify extreme skew in the distribution.

Identify data collection and entry errors.

Provide insight into interesting features of the data.

Question 21

what are the robust statistics?

Answer 21

median and IQR

Question 22

what are the non-robust statistics?

Answer 22

mean, variance (standard deviation)

Question 23

for skewed distributions it is often more helpful to use ___________ to describe the center and spread

Answer 23

median and IQR

Question 24

for symmetric distributions it is often more helpful to use __________ to describe the center and spread

Answer 24

the mean and SD

Question 25

if a distribution is symmetric, the center is defined as _______

Answer 25

the mean mean ~ median

Question 26

if a distribution is skewed or has extreme outliers, the center is defined as _______

Answer 26

the median

Question 27

if a distribution is right-skewed, the mean is

Answer 27

greater than the median

Question 28

if a distribution is left-skewed, the mean is

Answer 28

less than the median

Question 29

what is a side by side bar plot?

Answer 29

Displays the same information by placing bars next to, instead of on top of, each other

Question 30

what is a standardized stacked bar plot?

Answer 30

a stacked bar plot where the variables are measured as a proportion compared to the whole

Question 31

what is a mosaic plot?

Answer 31

visualization technique suitable for contingency tables that resembles a standardized stacked bar plot with the benefit that we still see the relative group sizes of the primary variable as well.

Question 32

what are the ways to measure center?

Answer 32

histograms, mean (average), median

Question 33

what are the ways to measure shape?

Answer 33

modality, skewness

Question 34

what are the ways to measure spread?

Answer 34

variance (standard deviation), IQR

Question 35

If you would like to estimate the typical household income for a student, would you be more interested in the mean or median income?

Answer 35

the median, because the distribution is skewed