Basics of Probability and Statistics Week 1 Challenge

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

For Both populations, we first need to find the difference of mean and Standard deviation then square all the deviations and sum all the squared deviation values

Here comes the point where for population variance we divide by the number of items in the population

Where in sample variance we divide by (number of item -1) because the sample is always a subset of the population to avoid unbiased output and making sample variance equal to population variance

2. Difference between stratified and clustered sampling

Stratified sampling: where the population is divided into Strata and simple random sampling is applied in each Strata, So each sampling data is from one Stratum not from the entire population. which help to reduce sampling error, avoid overlapping

Clustered sampling: the population is divided into similar groups/clusters where the selected cluster is sampled, So it reduce cost and increase efficiency

3. How many different samples can be created out of a population of size n

Depend on the confidence level, marginal error, and total population size, by using some sampling formula we can get sample size according to our need

and we can apply any of the convenient sampling techniques to get the required sample size from the population

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

Out of a total of 52 cards drawing 2 jacks is ( 2/52)

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

The total sample space is 36 and getting both the numbers same is 6 So P(Dice)=(6/36)

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

Because in Variance(σ²) we get final output unit as something like kg², So to get an actual unit of deviation (kg) we need standard deviation(σ)