Basics of Probability and Statistics Week 1 Challenge
1. Why is there a difference in the formula of variance for population and sample
Answer:
| BASIS FOR COMPARISON | STRATIFIED SAMPLING | CLUSTER SAMPLING |
|---|---|---|
| Meaning | Stratified sampling is one, in which the population is divided into homogeneous segments, and then the sample is randomly taken from the segments. | Cluster sampling refers to a sampling method wherein the members of the population are selected at random, from naturally occurring groups called 'cluster'. |
| Sample | Randomly selected individuals are taken from all the strata. | All the individuals are taken from randomly selected clusters. |
| Selection of population elements | Individually | Collectively |
| Homogeneity | Within group | Between groups |
| Heterogeneity | Between groups | Within group |
| Bifurcation | Imposed by the researcher | Naturally occurring groups |
| Objective | To increase precision and representation. | To reduce cost and improve efficiency. |
Since, the number of outcomes while rolling a dice = 6
Number of outcomes while rolling two dice = 62
= 36
The Sample Space for rolling a die is given as,
{(1,1) ,(1,2) , (1,3) , (1,4) , (1,5) , (1,6) ,
(2,1) ,(2,2) , (2,3) , (2,4) , (2,5) , (2,6) ,
(3,1) ,(3,2) , (3,3) , (3,4) , (3,5) , (3,6) ,
(4,1) ,(4,2) , (4,3) , (4,4) , (4,5) , (4,6) ,
(5,1) ,(5,2) , (5,3) , (5,4) , (5,5) , (5,6) ,
(6,1) ,(6,2) , (6,3) , (6,4) , (6,5) , (6,6)}
Sample points of getting same number on both dice- (1,1) ,(2,2) ,(3,3) ,(4,4) ,(5,5) & (6,6).
Thus, the number of favourable outcomes = 6
Total number of outcomes = 36
P (getting same number on both dice) = 6/36
= 1/6
Hence, the probability of getting same number on both the dice is 1/6.
- It is based on all values and thus, provides information about the complete series. Because of this, a change in even one value affects the standard deviation value.
- It is independent of origin but not of scale.
- It is helpful in advanced statistical calculations like the comparison of variability in two data sets.
- It can be used in the testing hypotheses.
- It is capable of further algebraic treatment.