Basics of Probability and Statistics Week 1 Challenge
1.Why there is a difference in the formula of variance for population and sample??
- Population variance refers to the value of variance that is calculated from population data, and sample variance is the variance calculated from sample data. Due to this value of the denominator in the formula for variance in case of sample data is ‘n-1’, and it is ‘n’ for population data.
- The logic of doing that is to compensate for our lack of information about the population data.In order to compensate this, the value of variance and standard deviation, which is squared root of variance are higher in case of sample data than variance from population data.
2.Difference between stratified and clustered sampling??
Startified sampling:
- Members of a sample in stratified sampling are chosen randomly from homogenous and non-overlapping strata.
- Each member of the sample must belong to one and only one strata so that the sample can represent the entire population.
- Stratified samples in the case of population density which varies majorly within a target region, can estimate with accuracy in different parts of the region.
- When strata during measurement have a lower standard deviation, stratification ensures a reduction in error in estimation.
Clustered sampling:
- Cluster sampling is cost-effective in contrast to other sampling techniques.
- Surveys on large populations are handled with help of cluster sampling.
- In a cluster sampling, the population should be heterogeneous but there must be homogeneity between clusters/groups
- The clusters must be representative of the total population.
3.How many different samples can be created out of population of size n?
n*2 samples
4.What is the probability of drawing 2 jacks from a pack of card?
2/52
5.What is the probability that both the numbers on dice are same while rolling 2 dice?
1/6*1/6=1/36
6.Why standard deviation when variance can measure the dispersion in data?
Standard deviation scales back the real units for the given data.