Basics of Probability and Statistics Week 1 Challenge
Question1: Why there is a difference in the formula of variance for population and sample
Solution1: N-1 in denominator will give the sample variance which is equal to unknown population variance. Sample has to be 1 less than total population.
Question2: Difference between stratified and clustered sampling
Solution2: Stratified sampling means a sampling technique where population is divided into groups called as stratas.
- Groups are homogeneous in nature.
- Groups can be heterogeneous between each other
- Elements can be chosen from stratas
Cluster sampling means a sampling technique where population is divided into sub groups.
- Sub groups are heterogeneous in nature.
- Sub groups are homogeneous between each other
- Groups to be chosen for statistics
Question3: How many different samples can be created out of population of size n
Solution3: `2^n -1` are the total samples can be created out of population of size n
Question4: What is the probability of drawing 2 jacks from a pack of card
Solution4: Total probability is first jack probability * second jack probability
P(E) = (4/52) * (3/51)
P(E) = 12/2652 => 1/221 => 0.0045
Question5: What is the probability that both the numbers on dice are same while rolling 2 dice
Solution5: Total Outcomes T(O) = 36
Favorable Outcome F(O) = 6
P(E) = F(O)/ T(O) => 6/36 => 1/6
Question6: Why standard deviation when variance can measure the dispersion in data
Solution6: Standard deviation is the square root of variance and is used to identify the dispersion from mean whereas variance will give dispersion within data set.
- Variance is not coherent whereas standard deviation is coherent.
- Standard deviation shows how far normal distribution is from mean whereas variance measures outcomes varies from mean