Analysis of a Single Variable

Question 1

The distribution of a variable tells us

Answer 1

The distribution of a variable tells us what
values it takes and how often it takes those
values.

Question 2

Two methods of visualizing categorical
distributions:

Answer 2

– Pie chart
– Bar graph

Question 2

Categorical Variables

Answer 2

Variables that put the individual into
one of several groups or categories

Question 3

Pie Chart

Answer 3

A pie chart shows how a
whole group (the sample)
is subdivided into smaller
groups (the categories).
* The size of a slice is
proportional to the
fraction of the sample in
that category.
– The sum of the
percentages shown by
each slice must add to
100%

Question 4

Bar Graph

Answer 4

A bar graph
represents each
category as a
vertical bar.
* The height of the
bar shows the
category count or
percentage.
Bar Graph
* While every single
category must be
represented in a pie
chart (percentages
sum to 100%), we
can choose to omit
categories in a bar
graph depending on
our desired
comparisons.

Question 5

Quantitative Variables

Answer 5

Variables that take values for which
arithmetic operations make sense

Question 6

The distribution of a quantitative
variable tells us

Answer 6

The distribution of a quantitative
variable tells us what values the variable takes
and how often it takes these values

Question 7

Methods of visualizing quantitative
distributions:

Answer 7

– Histogram
– Stemplot (Stem-and-leaf plot)
– Boxplot

Question 8

A histogram

Answer 8

A histogram is graph of the distribution of a
quantitative variable whose values are grouped
together
* To make a histogram:
1. Divide the data range into classes of equal width,
such that each individual only falls into one class
2. Count the individuals in each class
3. Draw the histogram
* Classes on horizontal axis; count on vertical axis

Question 9

– Stem:

Answer 9

consists of all but the
final digit

Question 10

Leaf:

Answer 10

the final digit

Question 11

stemplot advanatge

Answer 11

good for small dataset

Question 12

histograms vs stemplot

Answer 12

– Unlike histograms, stemplots show the actual
values of the data
* Histograms are generally more flexible than
stemplots, because you can choose the width
of the classes.

Question 13

Symmetric distribution

Answer 13

The right and left sides of
the histogram are approximately mirror images of
each other

Question 14

Skewed to the right

Answer 14

The right side of the
histogram extends much further out than the left

Question 15

Skewed to the left:

Answer 15

The left side of the histogram
extends much further out than the right

Question 16

– Unimodal

Answer 16

one peak

Question 17

bimodal

Answer 17

two peaks

Question 18

multimodal

Answer 18

multiple peaks

Question 19

ordered observation is the median

Answer 19

Sort n observations from smallest to largest. The
(n+1)/2 ordered observation is the median.

Question 20

The variance

Answer 20

The variance measures the dispersion (spread
about the mean) of all the observations

Question 21

The standard deviation

Answer 21

The standard deviation is the square root of
the variance: