Basics of Probability and Statistics Week 1 Challenge

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

- Because we take a sample set from the population, the value of variation in the sample is not the true representation of the overall population.

- Since the sample is a subset of the population, the value of variance for the sample could be small when compared to the value of the variation of population, and to compensate this, we have (n-1) in the denominator to bring the value of the sample variance closer to that of the population variance.

2) Difference between stratified and clustered sampling

- In stratified sampling, we adequately represent different groups of a given population whereas, in clustered sampling, we divide the population into different groups and a random sample of those groups is taken into consideration.

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

- For a population of size 'n' there will be 'n' different samples.

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

- (4/52) x (3/51) = 12/2652 = 1/221

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

- 1/6

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

- The unit of variance is (unit)^2 and we need the value of the standard variation to be in (unit)^1.

- We also need an intermediate value for the calculation of the standard variation and hence we have variance to measure the dispersion of data