Basics of Probability and Statistics Week 1 Challenge

1)To use the population variance you need all of the data available whereas to use the sample variance you only need a proportion of it. For example, if we take ten words at random from this page to calculate the variance of their length, a sample variance would be needed.

when we use N instead of N-1, we have an error called statistical bias, which means that the sample variance (the estimator) is systematically different from the true population parameter (in this case, the variance)

2)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'.

3) The possible numbers of sample of size n from a population of size N if sampling is done with replacement is Nn.

4)

The chances of both happening are

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

5)the probability that both the numbers on dice are same while rolling 2 dice is 1/6

6)The reason why standard deviation is so popular as a measure of dispersion is its relation with the normal distribution which describes many natural phenomena and whose mathematical properties are interesting in the case of large data sets