Basics of Probability and Statistics Week 1 Challenge

Question1 .

The difference in the formula of variance for population and sample is due to the concept of degrees of freedom. The sample variance uses (n-1) in the denominator to provide an unbiased estimate of the population variance.

Answer 2.

Stratified sampling involves dividing the population into subgroups or strata and then randomly selecting samples from each stratum. Clustered sampling involves dividing the population into clusters and then randomly selecting entire clusters for sampling.

answer3

The number of different samples that can be created out of a population of size 'n' depends on the sampling method. For simple random sampling, there are n! (n factorial) possible samples.

Answrr 4

The probability of drawing 2 jacks from a standard deck of cards is calculated as the product of the probability of drawing the first jack (4/52) and the probability of drawing the second jack from the remaining cards (3/51).

Answer 5.

The probability that both numbers on two dice are the same is 1/6, as there are six possible outcomes for each die, and only one outcome results in both numbers being the same.

Answer 6

Standard deviation is preferred over variance for measuring dispersion because it is in the same unit as the original data, making it more interpretable. Standard deviation is the square root of variance, providing a measure of dispersion that is easier to relate to the data scale