Statistics Ch 3 - Measure Something

*Chapter 3:

Statistics - measure something.

Is a value, is a data

The process of measuring, is a method

Descriptive statistics: formula

Statistical inference: How good is going to be the forecasts or estimates with our limited data

Population: All the possible outcomes available. What is the parameter of the population

Sample: part of the population. Use the statistic

Ordinal scales: not organize or same difference values between the categories.

Interval scales: doesn't have a true zero. Because 0 degrees is a 0 but doesn’t mean that temperature doesn’t exist.

We are going to use the Ratio Scales.

Relative measure - Rate of Return

“Ex ante” before the fact”

With the ex post data we have to try to get the ex ante data.

Equal average formula in excel for Population arithmetic mean.

Difference between Population arithmetic mean and Sample arithmetic mean: is the same formula but in one use population (bigger) or sample (little)

Deviation or deviation from the mean: dispersion. Something relate with the risk.

Regular Mean: (1+2+3)/3. Add up all the observations.

Weighted arithmetic mean: Xw= (1/6)(1)+(1/2)(2)+(1/3)(3)=(2)(1/6).

Geometric mean: multiple all the observations and rain cuadrada. Noun of the Xi could be negative: Xi>=0

1+R=P1/P0 (Price relative)

1+R is a price relative

For historical data is better Geometric Mean

0        1        2

100        50        75

Mean= (50-100)/100=50% ; (75-50)/50=50% ; R=(-50%+50%)/2=0

GM= “raiz(1+R1)*(1+R2)” -1 ; ”raiz(0.5)*(1.5)” -1 = -13.39%

Page 14: Harmonic mean: 2/{(1/15)+(1/10)}=2/{(2+3)/30}=2/(5/30)=2*6=12

Range is a measure of risk.

Population: divided by N

Sample variance: divided by n-1

Degree of freedom: when Xbar is 10 we lose one degree of freedom.

Xbar=10        n=5

X1=3                Exi=5*10=50

X2=5

X3=15

X4=10

X5=50-(3+5+15+10)=17

Sample: s=“raiz cuadrada S al cuadrado”

Population: sigma=“raiz cuadrada SIGMA al cuadrado”

Example 14 page 124:

                        R        SD

Australia                5.0        13.6        CV=13.6/5=2.72

Hong Kong                9.4        22.4        CV=22.4/9.4=2.38

Singapore                9.3        19.2        CV=19.2/9.3=2.065