Descriptive stats

Question 1

What’s the difference between descriptive and inferential statistics?

Answer 1

Descriptive –> describe sample data based on sample statistics
Inferential –> use sample statistics to learn on population parameters

Question 2

What is micro data?

Answer 2

Data collected on individuals

Question 3

What is macro data?

Answer 3

Data collected on a group of units

Question 4

What is a population?

Answer 4

The set of all statistical units object of interest

Question 5

What is the sample?

Answer 5

A subset drawn from the population

Question 6

What is non probability and probability sampling?

Answer 6

Non –> units are drawn from the population according to the judgement of the researcher
Probability –> units are drawn at random from the population, and every unit has the same probability to be drawn

Question 7

What is the inferential process?

Answer 7

It consists in drawing conclusions that concern the entire population from the information provided by a sample

Question 8

What are the two broad variable categories?

Answer 8

Numerical and categorical

Question 9

What are the subsets of numerical variables?

Answer 9

Discrete and continuous

Question 10

What are the subsets of categorical variables?

Answer 10

Ordinal and nominal

Question 11

What are the columns of a frequency distribution table?

Answer 11

Classes/groups; absolute frequencies and relative frequencies

Question 12

How is a histogram composed?

Answer 12

Horizontal axis –> intervals
Bars –> have an area equal to its relative frequency
Vertical axis –> interval density = relative frequency/interval width

Question 13

How can we calculate an interval density?

Answer 13

Relative frequency/interval width

Question 14

How does the number of intervals relate to the accuracy?

Answer 14

The higher the # of intervals, the higher the detail of the description.

Question 15

What are the three measures of central tendency?

Answer 15

Mode, median and mean

Question 16

What is the mode?

Answer 16

The level/value of a variable that is observed with the highest frequency

Question 17

What is the unique measure of central tendency for nominal variables?

Answer 17

Mode

Question 18

What is the median?

Answer 18

It is the central value. If odd–> (n+1)/2, if even it’s the median of the two central values

Question 19

What is the mean?

Answer 19

The arithmetic average of the values. (x1+x2+….+xn)/n

Question 20

What is the deviation?

Answer 20

It’s the difference of an observed value and the mean

Question 21

What are the properties of deviation?

Answer 21

• It’s positive when the value is higher than the mean and negative when not
• The sum of all deviations is equal to 0

Question 22

Do strange values have an impact on the median?

Answer 22

No, because it’s based on frequencies

Question 23

Do strange values have an impact on the mean?

Answer 23

Yes, because it’s computed using all values

Question 24

What are the measures of location? And to which type of data can they be computed for?

Answer 24

• Quartiles and percentiles;

- Ordinal categorical and numerical

Question 25

What are quartiles?

Answer 25

They divide the observation in four Q1- 25% of values are smaller than it Q2- it's the median Q3- 75% of the observations are smaller than it.

Question 26

What is the percentile?

Answer 26

The value that pth observations fall below it

Question 27

What are the 5 number summary? And how can it be represented?

Answer 27

Minimum, Q1,Q2,Q3 and maximum | By means of a boxplot

Question 28

How is the boxplot composed?

Answer 28

Height --> it's the IQR (Q3-Q1) Upper edge --> Q3 Lower edge --> Q1 Whiskers --> connect the outliers (1.5xIQR)

Question 29

What are the properties of a symmetrical/bell-shaped distribution?

Answer 29

Q1-min = Q3-max; Median-q1=Q3-median; | median-Q1

Question 30

What are the properties of a not bell-shaped distribution?

Answer 30

Q1-min = Q3-max; Median-q1=Q3-median; | median-Q1>Q1-min; Q3-median>Max-median

Question 31

What are the properties of a right-skewed distribution?

Answer 31

It's high on low values and low on high values Median - Q1 > Q3-median Mean > median

Question 32

What are the properties of a left-skewed distribution?

Answer 32

It's high on high values and low on low values The mean is not affected by low frequency values Median - Q1 < Q3-median

Question 33

What are the 4 measures of variability?

Answer 33

Range, IQR, variance and standard deviation

Question 34

What does thee IQR measure?

Answer 34

The spread of the central 50% of the observations

Question 35

What is the variance?

Answer 35

It's the average of the squared deviations. It measures the dispersion of a variable around its mean. It's always positive

Question 36

What is the coefficient of variation?

Answer 36

CV=s/mean, it expresses the standard deviation as percentage of the mean and allow for a comparison of the behavior of two variables when they have a different mean

Question 37

What does it mean to analyze the concentration of a variable?

Answer 37

It means to assess how far from the extremes the actual distribution is

Question 38

What does it mean a variable is very concentrated?

Answer 38

It's very far from being perfectly concentrated

Question 39

What does it mean a variable has a low concentration?

Answer 39

It's very close from being perfectly concentrated

Question 40

Can a concentration analysis be carried out for variables with negative values?

Answer 40

No

Question 41

What is the property needed for a variable so we can carry a concentration analysis?

Answer 41

It needs to be transferable

Question 42

How is qi distributed in a case of maximum concentration?

Answer 42

Q0-Qn-1=0 and Qn=1

Question 43

What is the coordinates of the maximum concentration?

Answer 43

{(n-1)/2n,0}

Question 44

How is qi distributed in a case of minimum concentration?

Answer 44

qi=fi for every i, that is, the concentration is always the same

Question 45

What are the properties of a concentration curve?

Answer 45

- Continuos - Convex - crosses (0,0) and (1,1)

Question 46

What is the gini index?

Answer 46

R= concentration area/maximum possible area (n-1)/2n

Question 47

When are the pietra and gini index equal to zero?

Answer 47

When fi=qi for all i, that is, when it has a minimum concentration

Question 48

If for two variables their high observations tend to occur with high values of the other too, what kind of linear association is there?

Answer 48

Positive

Question 49

If for two variables their high observations tend to occur with low values of the other too, what kind of linear association is there?

Answer 49

Negative

Question 50

What is the formula for the pearson's correlation in dex?

Answer 50

r = cov(X,Y)/ sx sy