Basics of Probability and Statistics Week 1 Challenge
1)Difference between the formula of variance of population and sample are as follows:
The main difference between population and sample variance relates to calculation of variance. First mean is calculated, then we calculate deviations from the mean, and thirdly the deviations are squared, fourthly the squared deviations are summed up and finally this sum is divided by number of items for which the variance is being calculated. Variance= Σ(xi-x)/n.when the variance is to be calculated from population data, n is equal to the number of items. Due to this, the value of variance calculated from data is higher than the value that could have been found out by using data.
2)Difference between stratified and clustered sampling
Stratified sampling is a type of probability sampling, in which first of all the population is separated into various mutually exclusive, homogeneous subgroups (strata), after that, a subject is selected randomly from each group (stratum), which are then combined to form a single sample. A stratum is nothing but a homogeneous subset of the population, and when all the stratum are taken together, it is known as strata.
The sub-types of stratified sampling are:
- Proportionate Stratified Sampling
- Disproportionate Stratified Sampling
Cluster sampling is defined as a sampling technique in which the population is divided into already existing groupings (clusters), and then a sample of the cluster is selected randomly from the population. The term cluster refers to a natural, but heterogeneous, intact grouping of the members of the population.
The types of cluster sampling are given below:
- Single-stage cluster sampling
- Two-stage cluster sampling
- Multistage cluster sampling
3)How many different samples can be created out of population of size n
4)The probability of drawing 2 jacks from a pack of card
5)The probability that both the numbers on dice are same while rolling 2 dice
When two dice rolled simultaneously Number of outcomes are 36 . If we are getting the same number on both sides is taken as the event then for the the first event the no.of outcomes are 6. Similarly, for the second event divide the no.of outcomes with the total no.of possible outcomes. i.e 6/ 6*6 = 1/6 .
6)Standard deviation when variance can measure the dispersion in data