Basics of Probability and Statistics Week 1 Challenge

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

ans : It is because the variance calculated for the whole population and variance calculated for just the sample are diffferent. it is to get a better and unbiased estimate considering the size of the popultion to the sample taken.

2) Difference between stratified and clustered sampling?

ans : In stratified sampling population is divided into sub-populations. ex: the stats for attackers and defenders in a football game can be be divided to subpopulations as both these roles vary differently. In clustered sampling popultion is grouped to mutiple sample groups and then samples are chosen by simple random sampling. ex: If restaurant chain needs to find the performance of it restaurants at the certain cities, samples from those cities can be clutered together.

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

ans: depends of a few factors like how times the sample is taken, with or without replacement. but in general srs from a smaple size of N from a population of N its n*N.

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

ans: probability of drawing one jack is = 4/52.

probability of drawing two jacks is = 4C2/52C2 = 0.004524 or 0.45 %

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

ans: probability of getting a particular number on two dice = 1/6 x 1/6 = 1/36

probability of getting the same number = 6 x 1/36 = 1/6 = 0.1667 or 16.67%

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

ans: since standard deviatio is the square root of variance it presents the same units of the oringinals values which can be easier for analysis. ex: while calculating a data set with a unit km/hr, the variance's unit will be km^2/hr^2. standard deviation brings down the units to the original value.