M2 - Tutorial Descriptive Statistics

Question 1

Arithmetic mean

Answer 1

durschschnitt aller werte

Question 2

Median

• uneven n
• even n

Answer 2

• for uneven n the xmed is the value sin the middle of a sorted list
• for even n the xmed is the arithmetic mean of the two values in the middle

Question 3

Mode

Answer 3

most frequent parameter value

Question 4

p-quantil

e.g.

Answer 4

values which divide the n values into two parts, of which at least a fraction p of the data is less/equal to xp, and at least a fraction 1-p is greater/equal xp

10% quantil: mind 10% der daten sind kleiner/gleich x10% und 90% der daten sind größer/gleich x10%

Question 5

variance s²

Answer 5

measures the spread of data around the mean

Question 6

standard deviation

• if small
• if large
• advantage over variance

Answer 6

used to quantify the amount of variation of a set of data values

• if small, the data points are close to the mean
• if high, the data points are spread out over a wider range
• it is expressed in the same unit as the data (unlike variance)

Question 7

advantage coefficient of variance

Answer 7

it is irrespective of scale –> appropriate for comparing different spreads

Question 8

skewness & coeff. of skewness

• left
• right
• symmetric

Answer 8

• left-skewed: the bigger part of the distribution is concentrated on the right gm < 0
• right-skewed: the bigger part of the distribution is concentrated on the left gm > 0
• symmetric: right and left half are almost mirror-image
  gm = 0

Question 9

Kurtosis / Peakedness

• peaked
• flattened
• normal

Answer 9

• how sharp?
• peaked: leptokurtic distribution y > 0
• flattened: platykurtic y < 0
• normal: mesokurtic y = 0

Question 10

Digression: Data types

Answer 10

• nominal: a few possible values
• ordinal: few ranked values
• interval: any value within a certain interval; no meaningful zero
• ratio: numbers, with meaningful zero denoting that there is no variable

Question 11

creation of dummy variables

• why
• how

Answer 11

• why? if there is a binary variable (=1/0; yes/no), which is indicator for a continuous variable
• create dummy for every state (=1, set all others = 0)