Basics of Probability and Statistics Week 1 Challenge

1)

To put it simply (n−1) is a smaller number than (n). When you divide by a smaller number you get a larger number. Therefore when you divide by (n−1) the sample variance will work out to be a larger number.

Let’s think about what a larger vs. smaller sample variance means. If the sample variance is larger than there is a greater chance that it captures the true population variance. That is why when you divide by (n−1) we call that an unbiased sample estimate. Whereas dividing by (n) is called a biased sample estimate.

Because we are trying to reveal information about a population by calculating the variance from a sample set we probably do not want to underestimate the variance. Basically by just dividing by (n) we are underestimating the true population variance, that is why it is called a biased estimate.

Basically comes down to calculating a biased vs. unbiased sample variance estimate.

In one word it is bessel's correction to remove bias.

2)

In Cluster Sampling, the sampling is done on a population of clusters therefore, cluster/group is considered a sampling unit. In Stratified Sampling, elements within each stratum are sampled. In Cluster Sampling, only selected clusters are sampled. In Stratified Sampling, from each stratum, a random sample is selected.

3) nCs where n is population size and s is sample size.

4) 4C2/52C2

5) 1/6

6) Standard deviation measures how far apart numbers are in a data set. Variance, on the other hand, gives an actual value to how much the numbers in a data set vary from the mean. Apart from that Standard Deviation will maintain consistency with units unlike variance which is just a meadiatory measure.