# Statistic

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```					Statistic
Date: 12/06/09 Notes: Why we study statistic? Answer:       For effective decision making For comparing two situation or things Use forecasting and predication purpose Measuring the risk that is associate with a specific variable To analyze the complex information into numerical data To estimate the situation Date: 14-jun-09

Time Series Analysis
To record variable data in different equal time period. (Or) To record any data by equal time intervals. The data/observation arrange regarding chronological order. Chronological: To arrange data or record data step by step.

Time series analysis: A set of observation/data which time series analyzed and it is used for certainty decision making. Example:
year 2000 2001 2002 production variable 120 Y1 100 Y2 140 Y3

Component time series: To record long term variation in specific data/information. The year shouldn’t be less than 15 years (Or) It measures the change in long term period of variation. Example:
year 2001 2002 2003 . . . continued Quarter-1 200 120 125 Quarter Quarter-2 Quarter-3 Quarter-4 195 205 110 115 120 125 130 100 115

Graphical Method: Used for predication/forecasting the line graph goes high means the company need to produce more products if the line graph goes down means the company need to find out the weakness or threat. Component of time series: Four basic of component of time series. 1) Secular Trend: is a long term of variation that continue or consist of many years and show the general direction of the change in observe value over a long period of time. It used to develop product, promote the sales and find out the problems.

2) Cyclical Trend: The up and down movement along the average trend is called cyclical trend. From one peak to another peak (means: from peak to trough and from trough to another peak) is one cycle and it is long term of variation.

Date: 15-jun-09

3) Seasonal Trend: The variation occur when the season change and it is a short term variation. Example: Ice cream and beverage is a seasonal product that the sales of these two product increase when summer.

4) Irregular Trend: Random variation in time series and the trend is not regular ( means it happen again and again Form Example: when the company burn or destory and everything asset and capital gets destory so the company will shutdown. And it is not possible to predict and forecasing the future. Note: Trend defination: means way direction Coded Time Variable It is used to simplifies the tend calculation .

Linear Trend Equation “Or” Equation Of Straight
Linear equation for odd number:

Date: 17-jun-09

Formula:

Example:

Linear equation for even number: Formula:

Date: 20-jun-09

Example:

Quadratic Trend Equation “Or” Equation of Parabola
Formula:

Date: 22-jun-09

Example:

Exponential Trend
Formula: Y = d(1+i)x
∑lny

Date: 27-Jul-09 lny

d = anti ln=

n lny lny ∑(xlny) ∑X2 lny lny

1+I = antiln

Example:

Moving Average Method

Date: 29-Jun-09

The average calculated by using “K” successive values of the observe series, then repeating operation by dropping one value at the beginning and including the first value after the preceding total, and so on is called moving average method.

Example:

Simple Regression Line
A regression which use 2 variables (X and Y). In business, increasing input or resource will increase the output production or profits. It shows relation between two variables. “Or” It investigates the dependence of one variable on another variable or it shows the relationship between dependent and independent variable. Dependent is Y = a+bx a = intersection b = slope The formula for solving regression line is: Independent

Y = a + bx Y = ∑y/n X = ∑x/n
n∑xy – (∑x)( ∑y)

b=

n∑x2 – (∑x)2

Suppose we hire a car on rent for one day and per day cost 25 \$ plus a charge of 0.30\$(30 percent for each mille the car is driven) Cost = 25\$ Cost of per mile = 0.30\$ Means: a = 25 and b = 0.30 And x is the number of miles Y is the cost of driven and x is the number of miles which is driven here we use linear equation: For 100 miles Y = a + bx

Y = 25 + (0.30)(100) Y = 55 For 400 miles Y = a + bx Y = 25 + (0.30)(400) Y = 145

Correlation
It measures the degree of two variables that vary or change together. “Or” The correlation of two variable that change in same direction. If both increase or decrease the correlation will be positive or if one increase another decrease the correlation will be negative. Example: The relationship of price, quantity and supply: When the price increases, the supply will increase too or if one decreases another also decrease so this correlation is positive. The relationship of price, quantity and demand:

When the price increase the demand will decrease so this correlation is negative.

Formula:

R=

∑(X – X)(Y – Y)

√∑(X – X) ∑(Y – Y)
2

2

Example:

Probability
Probability used for: Adnan notes:     Prediction Measure uncertainty about future event Predict favorable (successive of business) unfavorable (risk of business) Used to minimize the risk in business

m = total of outcome of possible favorable n = total number of possible outcome Alam Gir Notes: The concept of probability came from Grambling. Example: Tossing a coin: P(H) = ½ = 0.5 P(T) = ½ = 0.5

Notes: The total of probability is one “1”. Dice: Card: Total card = 52 Red = 26 Diamond = 13 Heart = 13 Black = 26 Spade = 13 Club = 13 For example if we look for king card so there are 4 king, so the probability is : 4/52 Foundation of probability:

Random Experiment: An experiment that produced different result is called random experiment. Example: Tossing the coin Coin has two faces = 2 The number of tossing = 2

2n
21 S = {H, T} H = Head T = Tail Experiment: A planned activity or a process which the results yield/give a set of data. Event: A possible outcome of an experiment. Means: Head and Tail are the event of experiment. Sample Space: A set which consisting all possible outcome that can result from a randome experiment and we denote by “S”. Sample space = S Example: in tossing a coin we will have two possible outcome S = {H, T}

Implementing on business:  To measure the risk in business for example if the international company want to operate in different country so probability will help to measure the risk of business where they want to operate in another country.

Definition of Probability (teacher):
The word probability has two basic meaning: 1. Quantitative(countable things) measure of uncertainty Example: today 70% is predicted to rain and 30% predicted not to be rain( the 70% and 30% is the quantitative) 2. A measure of degree of belief in a particular statement or problem.

Conceptual Approach:
There are 3 basic approaches or procedure to solve: 1: Classical Approach: An event which will occur.

Number of outcome where the event occur Total Number of possible outcome

Probability of an event = Example:
Tossing a coin: 1st to find out the Head/tail probability => P(H) = ½ = 0.5 P(T) = ½ = 0.5 2: Relative Frequency Approach: If a random experiment is repeated a large number of times. (A) => Event (m) => observed to be occurred (n) => total of any number of time. The event of (A) is: the limit of the relative frequency of m/n and n is the tends of infinity.

Formula:

Limit = m/n
n ∞
Example for dice: n = 10 m=8 P(H) = m/n P(4) = 8/10 = 0.8 >>>>> is the require probability.

Mutually Exclusive

Expected rate of return
Show the expectation that where a person find out a secure place to invest his money. If the probability goes high means that it is more secure to invest.

n

ŕ = ∑rp
i=1

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