Week 1

Question 1

Descriptive statistics

Answer 1

summarize data using measures (e.g. of location and dispersion) that describe a distribution.

Question 2

Inferential statistics:

Answer 2

use probability theory to analyze phenomena subject to randomness (e.g. hypothesis testing).

Question 3

Parameter definition

Answer 3

A measurable characteristic of a population

Question 4

Statistic definition

Answer 4

A measurable characteristic of a sample

Question 5

Objective of Statistics

Answer 5

Estimate parameters using the data. Given a sample we want to infer the parameters that characterize the population, or the law of motion of a process (in general the DGP)

Question 6

Note about INPUT and OUTPUT

Answer 6

Bear always in mind that our INPUT is the observed data and the OUTPUT is estimates for the unknown parameters.

Question 7

Law of Large Numbers

Answer 7

A theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.

Question 8

Central Limit Theorem

Answer 8

establishes that, in most situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (a bell curve) even if the original variables themselves are not normally distributed.

Question 9

Absolute frequency

Answer 9

The absolute frequency is simply the total number of observations or trials within a given range.

Question 10

Relative frequency

Answer 10

How often something happens divided by all outcomes.

Question 11

Frequency distribution

Answer 11

The association of modalities and their frequencies. Frequency is how often something occurs.

Question 12

Histogram definition

Answer 12

A diagram consisting of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval.

Question 13

Calculating the density of the modality

Answer 13

Use relative frequencies and divide each modality by the width of the modality.

Question 14

Sample Statistics: Measures of Location

Answer 14

• Arithmetic mean
• Median
• Percentile
• Quartile

Question 15

Arithmetic mean

Answer 15

the average of a set of numerical values, as calculated by adding them together and dividing by the number of terms in the set.

Question 16

Median

Answer 16

The middle number (in a sorted list of numbers).

Question 17

Percentile

Answer 17

Values such that the distribution is divided in 100 equal parts. Computation:

1) Arrange the sample in ascending order
2) Observe the index i of the position of the pth percentile

Question 18

Sample Statistics: Measures of Variability

Answer 18

• Variance
• Standard deviation

Question 19

Variance

Answer 19

The average of the squared differences from the Mean.

1. First step is to find the Mean
2. Now we calculate each dog’s hight difference from the Mean
3. To calculate the Variance, take each difference, square it, and then average the result
   
   1. In Population divide by N
   2. In Sample divide by N-1

Question 20

Standard Deviation

Answer 20

And the Standard Deviation is just the square root of Variance

Question 21

Shape of distributions

Answer 21

1. Skewness: measure of asymmetry (third moment of the data)
2. Kurtosis: measure of “tailedness” (fourth moment of the data)

Question 22

Skewness

Answer 22

Data can be “skewed”, meaning it tends to have a long tail on one side or the other.

Question 23

Kurtosis

Answer 23