Describing data

Question 1

Micro data

Answer 1

collected on individuals

Question 2

Macro data

Answer 2

Collected on groups of units

Question 3

Population

Answer 3

The set of all statistical units of the interested object. Denoted by N

Question 4

Sample

Answer 4

Subset drawn from the population. Denoted by n

Question 5

Non-probability sampling

Answer 5

Units are drawn from the population according to the judgement of the researcher

Question 6

Probability sampling

Answer 6

Units are drawn from the population randomly. It ensures that the sample is representative of the population, by not favoring any part of N

Question 7

Inferential process

Answer 7

Drawing conclusions that concern the entire population from the information drawn from n.
Collection of techniques that make use of sample statistics to learn on N parameters

Question 8

Parameter

Answer 8

Numerical summary of a characteristic at N level

Question 9

Statistic

Answer 9

Numerical summary of a characteristic at n level

Question 10

Categorical values

Answer 10

Non numerical values, can be either nominal or ordinal

Question 11

Nominal categorical values

Answer 11

Non-numerical that cannot be ranked

Question 12

Ordinal categorical values

Answer 12

Non-numerical that can be ranked

Question 13

Numerical values

Answer 13

number values, can either be discrete or continuous

Question 14

Discrete Numerical value

Answer 14

takes on a finite number of values of infinite but COUNTABLE

Question 15

Numerical continuous values

Answer 15

Can take any value between two numbers (ex.: height and weight)

Question 16

How is a frequency distribution table composed (its columns)

Answer 16

RIGHT: observed distinct values (classes/groups)
MIDDLE: absolute frequency or absolute values of the observations
LEFT: relative frequency

Question 17

How can you represent a freq. table (not with intervals)?

Answer 17

Pie or bar chart

Question 18

How can you represent a freq. table (with intervals)?

Answer 18

Histogram

Question 19

How can you read a histogram?

Answer 19

HORIZONTAL AXIS: Intervals –> on each interval there is a bar having area equal to its relative frequency
VERTICAL AXIS: interval density

Question 20

How can you calculate an interval density?

Answer 20

relative frequency/ interval length

Question 21

The higher the number of intervals the ……….. is the degree of detail of the description

Answer 21

higher

Question 22

Mode

Answer 22

The level or value of a variable that is observed with the highest frequency = the most observed value

Question 23

What is the unique measure for nominal variables?

Answer 23

Mode

Question 24

Median

Answer 24

The central value of the distribution. It divides the sample in half

Question 25

How to calculate the median for odd and even numbers?

Answer 25

ODD: (n+1)/2 EVEN: any of the two middle observations, or the arithmetic avg of them

Question 26

How can we calculate the median from a frequency table?

Answer 26

It can either be the value in which the cumulative percentage is 50% or the first value that weights more than 50%

Question 27

Mean

Answer 27

Arithmetic average of all variable values. ONLY for numerical values

Question 28

Deviation

Answer 28

The difference between each observed value and the mean. Positive if higher than the mean and negative if lower

Question 29

How to calculate the mean from freq. distribution tables?

Answer 29

(Value*frequency) + (value2*freqeuency) +...... / n

Question 30

Do outliers affect the mean? Why?

Answer 30

Yes, because it is measured using ALL the values from the observation

Question 31

Do outliers affect the median? Why?

Answer 31

No, because it is measured only by using the frequencies

Question 32

What are the two measures of location and for what types of variables can they be used?

Answer 32

Quartiles and percentiles. | For ordinal categorical and numerical values

Question 33

What are the quartiles and what does each represent?

Answer 33

``` Q1 = approximately a quarter of the observations are smaller (25th %) Q2= Median Q3= approximately three quarters of the observations are smaller (75th %) ```

Question 34

What does the pth percentile represents?

Answer 34

It is the value such that approximately p% of the cases fall below

Question 35

What are the characteristics of a boxplot?

Answer 35

Lower edge = Q1 Upper edge = Q3 line = median Whiskers = values above/below 1.5x IQ range. Any value above/below are outliers

Question 36

How can we compute the IQ range?

Answer 36

IQ range = Q3-Q1

Question 37

What are the 5-number summary?

Answer 37

the most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median

Question 38

Bell-shaped distribution characteristics

Answer 38

Median-Q1=Q3-median Q1-Min = max - Q3 Median - Q1 < Q1-min Mean = median

Question 39

NOT Bell-shaped distribution characteristics

Answer 39

Median-Q1=Q3-median Q1-Min = max - Q3 Median - Q1 > Q1-min Mean = median

Question 40

Skewed-right distribution characteristics

Answer 40

Median-Q1>Q3-median Q1-Min > max - Q3 high on low values and low on high values

Question 41

Skewed-left distribution characteristics

Answer 41

Median-Q1

Question 42

What are the four measures of variability?

Answer 42

Range, IQ range, variance and standard variation

Question 43

What do the measures of variability show us?

Answer 43

How the frequencies are distributed across the values and if the units are spread uniformly across the variable

Question 44

Range

Answer 44

Max - Min value

Question 45

Why is the range affected by outliers?

Answer 45

Because it only uses extreme values

Question 46

What does the IQ measures?

Answer 46

The spread of the 50% central part of the distribution

Question 47

Variance

Answer 47

The average of the squared deviations

Question 48

What does the variance measures?

Answer 48

The dispersion or variability of a variable as the spread around its mean. It is ALWAYS positive If all values are equal then it's = 0

Question 49

Standard deviation

Answer 49

The square root of the variance

Question 50

Coefficient of variation

Answer 50

CV = sd/mean | NEEDED when comparing two variables, if they do not have the same mean

Question 51

What does a variable concentration analyzes?

Answer 51

It assesses how far from the extremes the actual distribution is

Question 52

What does a very concentrated variable means?

Answer 52

that the distribution is very different from the perfectly equal distribution

Question 53

What does a low concentrated variable means?

Answer 53

that the distribution is very close from the perfectly equal distribution

Question 54

For what type of variable is a concentration analysis carried out?

Answer 54

Only for POSITIVE numerical values that have the the property of TRANSFERABILITY

Question 55

Are bio metrical values, such as weight, transferable values?

Answer 55

No

Question 56

Are financial values transferable values?

Answer 56

Yes

Question 57

What is the name of the concentration curve?

Answer 57

The Lorenz curve

Question 58

What are the two variables needed for concentration and how to compute them?

Answer 58

Fi and Qi Fi = i/n Qi = value/n

Question 59

If Fi and Qi, for each i, are the same, what type of concentration do we have?

Answer 59

Minimun concentration

Question 60

If Qi=0 for each i except Qn, which is 1, what type of concentration do we have?

Answer 60

Maximum concentration

Question 61

In the Lorenz curve, the closer the curve is to the horizontal axis the ........... (greater/smaller) the concentration is

Answer 61

Greater

Question 62

In the Lorenz curve, the closer the curve is to the vertical axis the ........... (greater/smaller) the concentration is

Answer 62

Smaller

Question 63

What are the characteristics of the concentration/Lorenz curve?

Answer 63

Continuous, convex, it crosses the dots with the coordinates (0,0) and (1,1)

Question 64

Gini index

Answer 64

Denoted by R = concentration area/possible maximun area

Question 65

What is the maximun area formula?

Answer 65

(n-1)/2n

Question 66

When is the gini coefficient 1?

Answer 66

Max concentration

Question 67

When is the gini coefficient 0?

Answer 67

Min concentration

Question 68

What is a bivariate association? And how can it be done for numerical values?

Answer 68

The study of association between two values. It can be done with a cross tab/ contingency table

Question 69

What type of plot can be used to show conditional frequencies?

Answer 69

Stacked bar plot or Side bar plot

Question 70

When do we have a positive linear association between numerical values?

Answer 70

When high/low values of one variable tend to occur with high/low values of the other variable

Question 71

When do we have a negative linear association between numerical values?

Answer 71

When high/low values of one variable tend to occur with low/high values of the other variable

Question 72

With what measures can we assess linear association?

Answer 72

Covariance and Pearson index

Question 73

How is the pearson index calculated?

Answer 73

r= Cov (X,Y) /SxYx

Question 74

What does the Pearson index measures?

Answer 74

The direction and strength of the correlation between two numerical variables. It takes on values between -1 and 1

Question 75

What does the following pearson correlations indicate? | +1,-1,0

Answer 75

+1 - strong POSITIVE correlation -1 - strong NEGATIVE correlation 0 - no linear association

Question 76

If the median is closer to Q3 what is the distribution shape?

Answer 76

Left-skewed

Question 77

If the median is closer to Q1 what is the distribution shape?

Answer 77

Right skewed

Question 78

If the median is on the center what is the distribution shape?

Answer 78

Bell-shaped