01 Random Variables: Graphical Tools

Question 1

What do you need to do first when drawing a boxplot?

Answer 1

sort the data(vector)

Question 2

Which information do you need to draw a boxplot?

Answer 2

1) the qth quantiles (2,3,4)
2) the mean
3) the outside bars for outliers

Question 3

How do you calculate the qth quantile?

Answer 3

1) sorting the data

2) find X(qn) = datapoint x at the qth position of n (usually 0.25, 0.5, 0.75)

Question 4

How do you calculate the mean?

Answer 4

sum of all datapoints divided by the number of datapoints

Question 5

How do you calculate the outside bars?

Answer 5

x₍₀.₇₅₎ + 1.5 ( x₍₀.₇₅₎ - x₍₀.₂₅₎ )

x₍₀.₂₅₎ - 1.5 ( x₍₀.₇₅₎ - x₍₀.₂₅₎ )

Question 6

Which two indicators are essential to calculate & draw histograms?

Answer 6

origin x₀

binwidth h

Question 7

Which two indicators are essential to calculate & draw Kernel densities?

Answer 7

binwidth h

Kernel function K(•)

Question 8

Which Kernel functions are there?

Answer 8

Uniform
Triangle
Epanechnikov
Gaussian

Question 9

What scatterplots are there?

Answer 9

downward and upward sloping

Question 10

What are parallel coordinates plots?

Answer 10

you scale all p variables of interest into [ 0, 1 ]

Question 11

What are Chernoff-Flury faces?

Answer 11

high dimensional objects - each variable is assigned to a face element (eye, pupil, eyebrow…)

Question 12

What are Andrews’ Curves?

Answer 12

each row of a matrix gets transformed to a curve fuction -> can observe differences/tendencies

Question 13

What is important to check with the Andrews’ Curves?

Answer 13

Whether p (= number of variables) is odd or even

Question 14

What is p in a data matrix?

Answer 14

the number of columns = the number of variables

Question 15

What is n in a data matrix?

Answer 15

the number of rows = the number of observations

Question 16

What do you do when the quintiles do not match up with an exact number for the boxplot?

Answer 16

You round q * n !

i.e. if q = 0.25 and n = 10, n x q = 2.5 -> take the third observation

Question 17

How do you calculate the height within an interval in a histogram?

Answer 17

1/( total observations • binwidth) • [# observations within that interval]