Basics of Probability and Statistics Week 1 Challenge
1. Why there is a difference in the formula of variance for population and sample
ans:
The formula for population variance is given as:
σ^2 = Σ(x-μ)^2/N
where σ^2 is the population variance, x is each data point in the population, μ is the population mean, and N is the total number of data points in the population.
the formula for sample variance is given as:
s^2 = Σ(x- x ̅)^2/(n-1)
where s^2 is the sample variance, x ̅ is the sample mean, and n is the sample size
The key difference between these two formulas is in the denominator. the difference in the formula for variance for population and sample is due to the need to adjust for the fact that a sample is only a subset of the population, and the sample mean may not be exactly equal to the population mean.
2. Difference between stratified and clustered sampling.
ans: 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.In Cluster Sampling, the aim is to reduce cost and increase the efficiency of sampling.
3. How many different samples can be created out of population of size n ?
ans: The number of different samples that can be created out of a population of size n depends on the sampling method and the size of the sample. different types of sampling are as:
Random sampling, stratified sampling, cluster sampling and systematic sampling
4. What is the probability of drawing 2 jacks from a pack of card ?
ans:
P(2 jacks without replacement) = (4/52) * (3/51) = 0.0045
P(2 jacks with replacement) = (4/52) * (4/52) = 0.0025
5. What is the probability that both the numbers on dice are same while rolling 2 dice ?
ans:
P(both dice show the same number) = number of favorable outcomes / total number of possible outcomes
P(both dice show the same number) = 6/36 = 1/6 = 0.1667
6. Why standard deviation when variance can measure the dispersion in data ?
ans: standard deviation is often preferred due to its ease of interpretation, intuitiveness, sensitivity to outliers, and widespread use.