Basics of Probability and Statistics Week 1 Challenge

1.Why there is a difference in the formula of variance for population and sample?

We are taking only a small set of data from population as a sample. In calculating a variance of sample to get a higher variance, we need to use (n-1) which is a lower number results in higher variance. The higher variance would be slightly near to variance of population.

2.Difference between stratified and clustered sampling.

Stratified sampling is a echnique in which data is splitted into strats or groups of certain characteristics and sample would be taken from each groups.

Eg:from a population ABCDEFG of ABC : DEF : GHI > BDI were taken as a sample using Startified sampling

Cluster Sampling is the technique in which the population are divided into clusters / differen groups and all elemnts in one paricular cluster were taken into an accoun as sample.

Eg:from a population ABCDEFG of ABC : DEF : GHI > ABC were taken as a sample using Cluster sampling.

3.How many different samples can be created out of population of size n

if population (n) , (r) number of samples we can create n!/r!(n-r)!.

4.What is the probability of drawing 2 jacks from a pack of card is:

4c2/52c2->1/221

5.What is the probability that both the numbers on dice are same while rolling 2 dice

6/36->1/6

6.Why standard deviation when variance can measure the dispersion in data?

Variance would allow us to calculathe dispersion of data. the dispersion value can be any negative or positive values, so inorder to convert the negative value into positive , we square the dispersion values. in this case the units will also get squared. Inorder make the consistency of units in dispersion values we calculate standard deviation which is nothing but a square root of variance.