Basics of Probability and Statistics Week 1 Challenge

1. DIFFERENCE IN FORMULA OF VARIANCE AND SAMPLE    Main difference in the formula is N-1 and  N in the denominator                                                                                                                                         reason :  When you have an entire population and calculate population variance your results will be accurate because you have all the data about the population. But whenever you work with sample population the results aren't accurate littlebit Biased. Subracting 1 from the sample size corrects this bias (subracting 1 from sample size is known as Bessels correction ) 
2. DIFFERENCE BETWEEN STRAIFIED AND CLUSTERED SAMPLING                                                               STRATIFED SAMPLING                                                             CLUSTERED SAMPLING 

          1. Divide population from groups different from each other.       1. Divide population into comparable groups.

                  example: Gender, ages, races etc.                                               example: Schools, Cities etc

          2. Sample is taken randomly from each group .                        2. Sample is taken randomly from some                                                                                                                     groups. 

         3. More expensive to obtain stratification information                 3.  Reduces costs for sampling some areas                         before sampling.                                                                and organizations                                                                 

    3. HOW MANY DIFFERENT SAMPLES CAN BE CREATED OUT OF POPULATION OF SIZE n

           generally we have four sampling techniques to characterize samples using statics 

               so 4 number of samples can be created out of population of size n

    4.  WHAT IS THE PROBABILITY OF DRAWING 2 JACKS FROM A PACK OF CARDS 

             number of jacks in a pack of cards - 52 cards 

               Probability= Favorable events / Total possible events 

                total possible events= 52^1 =52 ;  Favorable events =    ⁴C₂          

                                Probability = 6/52 = 0.11

                     

    _{5.  WHAT IS THE PROBABILITY THAT BOTH THE NUMBERS ON THE DICE ARE SAME WHILE ROLLING} 

             _{six numbers on a dice} 

              _{PROBABILITY = 6/36 = 1/6 = 0.16}

    _{6.  WHY STANDARD DEVIATION WHEN VARIANCE CAN MEASURE THE DISPERSION IN DATA}

           _{Since variance is a squared quantity it cannot be directly compared to the data values of a data set  so standard deviation is a very common way of measuring disperstion.} 

_{for example if u are measuring data of speeds of vehicles  the units in variance is km^2/hr^2 after calculating standard deviation only we can compare to to the data set so standard deviation is used.}